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We consider the asymptotically flat standing wave solutions to the Poisson-Schrodinger system of equations. These equations are also known as the Schrodinger-Newton equations and are the Newtonian limit of the Einstein-Klein-Gordon equations. The asymptotically flat standing wave solutions to the Poisson-Schrodinger equations are known as static states. These solutions can be parametrized using a variety of choices of two continuous parameters and one discrete parameter, each having a useful physical-geometrical interpretation. The values of the discrete variable determines the number of nodes (zeros) in the solution. We use numerical inversion techniques to analyze transformations between various informative choices of parametrization by relating each of them to a standard set of three parameters. Based on our computations, we propose explicit formulas for these relationships. Our computations also show that for the standard choice of continuous variables, the zero-node ground state yields a minimum value of a geometrically natural discrete variable. We give an explicit formula for this minimum value. We use these results to confirm two related observations from previous work by the author and others, and suggest additional applications and approaches to understand these phenomena analytically. Key words: Poisson-Schrodinger, Schrodinger-Newton, Einstein-Klein-Gordon, scalar field dark matter, boson stars. Nous considerons les solutions en ondes stationnaires asymptotiquement plates du systeme d'equations de Poisson-Schrodinger. Ces equations sont aussi connues comme les equations de Schrodinger-Newton et sont la limite newtonienne des equations de Einstein-Klein-Gordon. Les solutions en ondes stationnaires asymptotiquement plates des equations de Poisson-Schrodinger sont connues comme les etats statiques. Ces solutions peuvent etre parametrees en utilisant une variete de choix de deux parametres continus et d'un parametre discret, chacun ayant une interpretation physico-geometrique utile. La valeur de la variable discrete determine le nombre de nreuds (zero) dans la solution. Nous utilisons des techniques d'inversion numerique pour analyser la transformation entre les differents choix de parametrage en reliant chacun d'entre eux a un ensemble standard de trois parametres. Sur la base de nos calculs, nous proposons des formules explicites pour ces relations. Nos calculs montrent aussi que, pour le choix standard de de variables continues, l'etat fondamental sans nreud conduit a une valeur minimale de la variable discrete naturellement geometrique. Nous fournissons une formule explicite pour cette valeur minimale. Nous utilisons ces resultats pour confirmer deux relations reliees obtenues dans des travaux anterieurs du present auteur et d'autres et suggerons des applications additionnelles et des approches pour comprendre analytiquement ces phenomenes. [Traduit par la Redaction] Mots-cles: Poisson-Schrodinger, Schrodinger-Newton, Einstein-Klein-Gordon, champ scalaire de matiere noire, etoiles a bosons., 1. Introduction The Poisson-Schrodinger system of partial differential equations couples the Schrodinger equation, which is often used to model the behavior of quantum particles, with the Poisson equation, which models [...]

The degeneracy associated with dynamical symmetry of a potential can be identified in quantum mechanics, by solving the Schrodinger equation analytically, using the method of separation of variables in at least two different coordinate systems, and in classical mechanics by solving the Hamilton-Jacobi equation. In the present pedagogical review, the notion of separability and superintegrability of a potential, with profound implications, is discussed. In an earlier tutorial paper, we addressed the [n.sup.2]-fold degeneracy of the hydrogen atom using the Casimir operators corresponding to the SO(4) symmetry of the 1/r potential. The present paper is a sequel to that work, in which we solve the Schrodinger equation for the hydrogen atom using separation of variables in the parabolic coordinate systems. In doing so, we take the opportunity to revisit some excellent works on symmetry and degeneracy in classical and quantum physics, if only to draw attention to these insightful studies, which unfortunately miss even a mention in most undergraduate and even graduate level courses in quantum mechanics and atomic physics. Key words: parabolic coordinates, accidental degeneracy, hydrogen atom symmetry, separability, integral of motion. La degenerescence associee a la symetrie dynamique du potentiel peut etre identifiee, en mecanique quantique par la solution de l'equation de Schrodinger analytiquement dans au moins deux systemes de coordonnees via la methode de separation des variables et en mecanique classique en solutionnant l'equation de Hamilton-Jacobi. Dans le present texte pedagogique, nous discutons les profondes implications de la separabilite et de la superintegrabilite d'un potentiel. Dans un tutoriel precedent, nous avons examine la degenerescence [n.sup.2] fois de l'atome d'hydrogene, en utilisant l'operateur de Casimir correspondant a la symetrie SO(4) du potentiel en 1/r. Le present article en est la suite, oU nous solutionnons l'equation de Schrodinger pour l'atome d'hydrogene dans le systeme des coordonnees paraboliques. Ce faisant, nous avons l'opportunite de revisiter certains excellents travaux sur la symetrie et la degenerescence en physique classique et quantique, ne serait-ce que pour attirer l'attention sur ces etudes eclairantes qui, malheureusement, ne sont meme pas mentionnees dans la plupart des cours de mecanique quantique et de physique atomique, tant au premier cycle qu'aux cycles avances. Mots-cles : coordonnees paraboliques, degenerescence accidentelle, symetrie de l'atone d'hydrogene, separabilite, integrale (premiere) de mouvement, constante du mouvement., 1. Introduction This paper is written as a sequel to an earlier tutorial article published by our group, 'The 'accidental' degeneracy of the hydrogen atom is no accident!' [1]. In [...]

Based on the integral representation of the three-dimensional Coulomb transition matrix elaborated by us formerly with the use of specific symmetry of the interaction in the four-dimensional Euclidean space introduced by Fock, the possibility of analytical solution of the integral equation for the partial wave transition matrices at the excited bound state energy has been studied. New analytical expressions for the partial s-, p-, and d-wave Coulomb t-matrices for like-charged particles and the expression for the partial d-wave t-matrix for unlike-charged particles at the energy of the first excited bound state have been derived. Key words: Coulomb transition matrix, partial wave expansion, Lippmann-Schwinger equation, Fock method, analytical solution. Sur la base de la representation integrale de la matrice de transition de Coulomb en 3D, elaboree par nous anterieurement en utilisant la symetrie specifique de l'interaction dans l'espace euclidien introduit par Fock, nous etudions la possibilite d'une solution analytique de l'equation integrale des matrices de transition en ondes partielles a l'energie d'etats lies excites. Nous derivons de nouvelles expressions analytiques des matrices t de Coulomb pour les ondes partielles s, p et d pour des particules chargees de meme signe et l'expression de la matrice t pour onde d pour des particules chargees de signes differents a l'energie du premier etat excite. [Traduit par la Redaction] Mots-cles : matrice de transition de Coulomb, expansion en ondes partielles, equation de Lippmann-Schwinger, methode de Fock, solution analytique., 1. Introduction The Coulomb transition matrix, which in the momentum space is a function of the initial and final relative momenta and the energy, provides all information about the system [...]

In this study, we consider a phantom cosmology in which a scalar field is minimally coupled to gravity. For anisotropic locally rotational symmetric (LRS) Bianchi type I space-time, we use the Noether symmetry approach to determine the potential of such a theory. It is shown that the potential must be in the trigonometric form as a function of the scalar field. We solved the field equations of the theory using the result obtained from the Noether symmetry. Our solution shows that the universe has an accelerating expanding phase. Key words: LRS Bianchi type I space-time, phantom cosmology, Noether symmetry approach, dark energy, conserved quantity. Nous considerons ici une cosmologie fantome dans laquelle le champ scalaire est couple minimalement a la gravite. Pour un espace-temps de type I de Bianchi localement symetrique sous rotation et anisotrope, nous utilisons l'approche geometrique de Noether pour determiner le potentiel d'une telle theorie. Nous montrons que le potentiel doit etre dans une forme trigonometrique comme fonction du champ scalaire. Nous solutionnons les equations de champ de la theorie en utilisant le potentiel obtenu de l'approche geometrique de Noether. Nos resultats montrent que l'univers a une phase d'expansion acceleree. [Traduit par la Redaction] Mots-cles: espace-temps de type I de Bianchi localement symetrique sous rotation, cosmologie fantome, approche symetrique de Noether, energie sombre, quantite conservee., 1. Introduction Since the end of the last century, the analysis of the observational studies, such as type Ia supernovae [1], cosmic microwave background [2], etc., show that our universe [...]

In this paper, spatially homogeneous anisotropic axially symmetric holographic dark energy cosmological model with generalized Chaplygin gas is obtained in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124, 925 (1961)). To obtain a determinate solution of the field equations we have used a power law between the metric potentials. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of the Universe. All the models obtained and presented here are expanding, non-rotating, and accelerating. Also some important features of the models including look-back time, distance modulus, and luminosity distance versus redshift, and their significances are discussed. Key words: axially symmetric metric, holographic dark energy, Chaplygin gas, Brans-Dicke theory. Nous investigons ici un modele cosmologique de l'energie sombre holographique axialement symetrique, spatialement homogene et anisotrope, avec un gaz de Chaplygin generalise, dans la theorie scalaire-tenseur de Brans-Dicke (Brans et Dicke. Phys. Rev. 124, 925 (1961)). Afin d'obtenir une solution determinee des equations de champ, nous utilisons une loi de puissance entre les potentiels metriques. Nous trouvons que la distribution anisotrope de l'energie sombre mene a la presente expansion acceleree de l'univers. Tous les modeles presentes ici sont en expansion, sans rotation et en acceleration. Nous discutons egalement quelques caracteristiques importantes des modeles, incluant le temps de regard vers le passe, le module de distance et la distance de luminosite, versus le decalage vers le rouge, avec leurs significations. [Traduit par la Redaction] Mots-cles: metrique axialement symetrique, energie sombre holographique, gaz de Chaplygin, theorie de Brans-Dicke., 1. Introduction The holographic principle emerged in the context of black holes, where it was noted that a local quantum field theory cannot fully describe black holes [1]. Some long-standing [...]

By exploring diverse simple cases, we show that the virial theorem (VT) of Clausius rests on limits of integration in temporal averages being specified by spatial symmetry, rather than on long durations as heretofore claimed. We show the VT results from linear momentum cancelling in all directions over the restricted space that defines any given bound state, via a balance that involves canonical conjugate pairs of position and momentum; this constraint differs from conservation of energy or momentum. The importance of space is underscored by considering behavior of the ideal gas, which is time- independent. Because each distinct force induces a specific type of motion, which in turn has a characteristic length scale, separate VTs are required for each process, which we confirm by example. Combining unrelated potentials in the VT or in its underlying mathematical identity is invalid because this procedure, used in astrophysics, permits energy exchanges that violate selection rules, symmetry constraints, or thermodynamic law. Our analysis unearths an erroneous numerical factor concerning rotation, helps explain the origin of axial spin in our Solar System, and casts doubt on the historical link of gravitation with temperature. Key words: virial theorem, Lagrange-Jacobi identity, ideal gas, canonical conjugates. En examinant plusieurs cas simples, nous montrons que le theoreme du viriel (VT) de Clausius repose sur des limites finies d'integration de moyennes dans le temps basees sur des symetries spatiales, plutot que sur de longues durees comme generalement presente. Nous montrons que le moment lineaire s'annule dans toutes les directions sur un espace borne qui definit tout etat lie, en utilisant un equilibre qui implique la paire canonique conjuguee d'impulsion-position; cette contrainte est differente de celles basees sur la conservation de l'energie ou de l'impulsion. L'importance de l'aspect spatial est soulignee en considerant le comportement du gaz parfait, qui est independant du temps. Parce que chaque force distincte induit un mouvement different, qui a sa propre echelle de longueur caracteristique, differents VT sont requis pour chaque processus, ce que nous confirmons par un exemple. La combinaison de potentiels non relies dans le meme VT ou dans sa formulation mathematique est invalide, parce que cette procedure, utilisee en astrophysique, permet des echanges d'energie qui violent les regles de selection, les contraintes de symetrie ou les lois de la thermodynamique. Notre analyse fait ressortir des facteurs numeriques errones concernant la rotation, aide a expliquer l'origine du spin axial dans notre systeme solaire et jette un doute sur le lien historiquement fait entre la gravite et la temperature. [Traduit par la Redaction] Mots-cles: theoreme du viriel, formulation Lagrange-Jacobi, gaz parfait, canonique conjuguee. PACS Nos.: 11.27.+d, 05.70.-a., 1. Introduction The virial theorem (VT) of Clausius [1] describes diverse phenomena in bound, conservative systems whose scales range from quantum to astronomical [2-4]. Because Clausius was concerned with temperature [...]

Author(s): Alexandru Florin Dobrin (corresponding author) [1] Our understanding of the world around us is summarized in the standard model of particle physics. This model describes the building blocks of [...]

Author(s): Bertram Blank Author Affiliations: Mirror symmetry broken for nuclear ground states Nature likes symmetry. Examples range across size scales from macroscopic objects, such as spiderwebs or honeycombs, to the [...], The principle of mirror symmetry, which states that nuclear structure remains the same when protons are swapped for neutrons and vice versa, has been found to be broken in the lowest-energy forms of a mirror pair of nuclei. Bromine-73 and strontium-73 have different ground-state configurations.

Icosahedral symmetry is ubiquitous in nature, and understanding possible deformations of structures exhibiting it can be critical in determining fundamental properties. In this work we present a framework for generating and representing deformations of such structures while the icosahedral symmetry is preserved. This is done by viewing the points of an orbit of the icosahedral group as vertices of an icosahedral polytope. Contraction of the orbit is defined as a continuous variation of the coordinates of the dominant point--which specifies the orbit in an appropriate basis--toward smaller positive values. Exact icosahedral symmetry is maintained at any stage of the contraction. All icosahedral orbits or polytopes can be built by successive contractions. This definition of contraction is general and can be applied to orbits of any finite reflection group. PACS Nos.: 61.05.-a, 61.18.-j, 61.48.-c. La symetrie icosaedrique est omnipresente dans la nature et la comprehension des deformations possibles des structures est critique pour determiner les proprietes fondamentales. Nous presentons ici un cadre de travail pour generer et representer les deformations de ce type de structures, tout en preservant la symetrie icosaedrique. Ceci est fait en prenant des points d'une orbite du groupe icosaedre comme des sommets d'un polytope icosaedrique. La contraction de l'orbite est definie par des variations continues des coordonnees du point dominant--ceci positionne l'orbite dans une base appropriee--vers de plus petites valeurs positives. Nous maintenons la symetrie icosaedrique a toutes les etapes de la contraction. Toutes les orbites/polytopes icosaedriques peuvent etre construites par contractions successives. Cette definition de la contraction est generale et peut etre appliquee aux orbites de n'importe quel groupe de reflexion fini. [Traduit par la Redaction], 1. Introduction In the optimization of self-assembled structures in nature, the formation of regular polyhedrals is a ubiquitously encountered strategy. Examples of this include the formation of hollow-cage fullerenes [1], [...]

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local bosonic and fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new fermionic gauge transformation of the 'position' and 'spin' variables in the action decouples from that of the 'einbein' and 'gravitino'. It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases. PACS Nos.: 04.20.Fy, 11.10.Ef. Nous reconsiderons les symetries de jauge d'une particule avec spin par un examen direct du Lagrangien en utilisant une procedure systematique basee sur les identites de Noether. Il s'avere possible de trouver un ensemble de transformations de jauge bosoniques et fermioniques locales qui ont une structure de groupe de jauge simple, ce qui est une vraie algebre de Lie, a la fois pour les cas avec et sans masse. Cette nouvelle transformation de jauge fermionique des variables de << position >> et de <>dans l'action decouple de celle de l'<< einbein>>et du<>. Il est aussi possible de redefinir ces champs de telle sorte que cette algebre simple de commutateurs des transformations de jauge peut etre obtenue directement en partant du Lagrangien ecrit a l'aide de ces nouvelles variables. Nous discutons une extension possible de notre analyse de ce modele simple vers des cas plus compliques. [Traduit par la Redaction], 1. Introduction For four decades, supersymmetry has been studied intensively. The local version of this symmetry, supergravity, is most easily realized by the spinning particle [1-3]; this is supergravity theory [...]

An approach to constructing quantum systems with dynamical symmetry is proposed. As examples, we construct generalized systems of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position- dependent mass. They have symmetries that are similar to the corresponding ones, and can be solved by using the algebraic method. We also exhibit an example of the method applied to the noncentral field. PACS Nos.: 03.65.-w, 03.65.Fd, 03.65.Ge. Nous proposons une approche pour construire des systemes quantiques avec des symetries dynamiques. Comme exemples, nous construisons des systemes generalises de l'atome d'hydrogene et de l'oscillateur harmonique, qui peuvent etre vus comme des systemes dont la masse depend de la position. Ils ont les symetries des systemes originaux et peuvent etre solutionnes en utilisant la methode algebrique. Nous donnons egalement un exemple de la methode appliquee a un champ non central. [Traduit par la Redaction], 1. Introduction It is known that solvable models provide essential insights into the understanding of physical theory. Much effort has been made to find solvable models [1-5], meanwhile, various methods [...]

The first class constraints in N = 1 supergravity in 2 + 1 dimensions are used to construct a generator of three gauge symmetries (including a local supersymmetry) that leave the action invariant. The algebra of these symmetries closes. This generator is used to quantize the model; a ghost involving both bosonic and fermionic components arises. PACS No.: 11.10Ef. Nous utilisons des contraintes de premiere classe N = 1 en 2 + 1 dimensions pour construire un generateur de trois symetries de jauge (incluant une supersymetrie locale) qui laissent Taction invariante. L'algebre des trois symetries est fermee. Ce generateur est utilise pour quantifier le modele; un fantome emerge impliquant les composantes bosonique et fermionique. [Traduit par la Redaction], 1. Introduction Gravity in 2 + 1 dimensions has been extensively treated [1-3] and its supersymmetric extension considered [4]. In these discussions, the local symmetries of the theory have been [...]

In the integer quantum Hall effect, the topology of the bulk Landaulevel energy bands requires the existence of gapless edge states at any interface with the vacuum. The metrological precision [...], Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires and graphene. Recently, a new method has emerged with the recognition that symmetry-protected topological (SPT) phases (1,2), which occur in systems with an energy gap to quasiparticle excitations (such as insulators or superconductors), can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties. For example, time reversal symmetry endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, fixing the orientation of their spin relative to their momentum (3,4). Weakly breaking this symmetry generates a gap on the surface (5), resulting in charge carriers with finite effective mass and exotic spin textures (6). Analogous manipulations have yet to be demonstrated in two-dimensional topological insulators, where the primary example of a SPT phase is the quantum spin Hall state (7,8). Here we demonstrate experimentally that charge-neutral monolayer graphene has a quantum spin Hall state (9,10) when it is subjected to a very large magnetic field angled with respect to the graphene plane. In contrast to time-reversal-symmetric systems (7), this state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the large magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferro-magnetic instability (11-13), which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with a tunable bandgap and an associated spin texture (14).

Recently, via adiabatic invariance, Majhi and Vagenas quantized the horizon area of the general class of a static spherically symmetric space-time. Very recently, applying the period of the gravity system with respect to the Euclidean time, Zeng and Liu derived area spectra of a Schwarzschild black hole and a Kerr black hole. It is noteworthy that the preceding methods are not useful for the quasi-normal modes. In this paper, based on those works, and as a further study, adopting near horizon approximation, applying the laws of black hole thermodynamics, we would like to investigate the black hole spectroscopy from a class of Plebanski and Demianski space-times by using two different methods. The result shows that the area spectrum of the black hole is [DELTA]A = 8[pi][l.sup.2.sub.p], which confirms the initial proposal of Bekenstein, and the result is consistent with that already obtained by Maggiore with quasi-normal modes. PACS Nos.: 04.70.-s, 04.70.Dy, 97.60.Lf. Recemment, Majhi et Vagenas ont utilise l'invariance adiabatique pour quantifier la surface d'horizon d'une classe generale d'espace-temps statiques et spheriquement symetriques. Tres recemment, Zeng et Liu ont utilise la periodicite du systeme gravitationnel par rapport au temps Euclidien pour deriver les spectres de surface des trous noirs de Schwarzschild et de Kerr. Il vaut la peine de noter que cette methode ne fonctionne pas pour les modes quasi-normaux. Ici, nous avancons ce travail, adoptons une approximation pour l'horizon proche et appliquons les lois de la thermodynamique des trous noirs afin d'etudier la spectroscopie du trou noir pour une classe d'espace-temps de Plebanski et Demianski a l'aide de deux methodes differentes. Le resultat montre que le spectre du trou noir est [DELTA]A = 8[pi][l.sup.2.sub.p], ce qui confirme la proposition initiale de Bekenstein et est coherent avec le resultat de Maggiore avec les modes quasi-normaux. [Traduit par la Redaction], 1. Introduction It is widely believed that the horizon area of a black hole in equilibrium has a discrete and equally spaced spectroscopy, that is, [A.sub.n] = [gamma][l.sup.2.sub.p]n, where n [...]

In the presence of spin and pseudo-spin symmetries, we obtain approximate analytical bound state solutions to the Dirac equation with scalar-vector inverse quadratic Yukawa potential including a Yukawa tensor interaction for any arbitrary spin-orbit quantum number, κ. The energy eigenvalues and their corresponding two-component spinor wave functions are obtained in closed form using the parametric Nikiforov-Uvarov method. It is noticed that the tensor interaction removes the degeneracy in the spin and p-spin doublets. Some numerical results are obtained for the lowest energy states within spin and pseudo-spin symmetries. PACS Nos.: 03.65.Ge, 03.65.Fd, 03.65.Pm, 02.30.Gp. En presence de symetries de spin et de pseudo-spin, nous obtenons une solution analytique approximative pour les etats lies d'une equation de Dirac avec un potentiel de Yukawa quadratique inverse scalaire-vecteur, incluant une interaction tenseur de Yukawa pour toute valeur du nombre quantique de spin-orbite κ. La methode de Nikiforov-Uvarov nous permet d'obtenir les valeurs propres d'energie et, sous forme analytique, leurs spineurs a deux composantes correspondants. On note que l'interaction tensorielle leve la degenerescence dans les doublets spin et p-spin. Nous completons avec quelques resultats numeriques pour les plus bas etats d'energie a symetries de spin et de pseudo-spin. [Traduit par la Redaction], 1. Introduction Recently, tensor potentials were introduced into the Dirac equation with the substitution p → p - imωβU(r)[??] and a spin-orbit coupling is added to the Dirac Hamiltonian [1, [...]

Superspace techniques are used to formulate a supersymmetric model on an AdS3 surface embedded in four dimensions. In this model, the supersymmetry transformation is the "square root" of the transformation generated by the isometry generators of Ad[S.sub.3]. Because momentum is not an isometry generator, supersymmetry does not result in equal masses for a bosonic field and its fermionic partner. We express this model in terms of coordinates that characterize the Ad[S.sub.3] space. In one coordinate system, it is possible to define a subspace with a Minkowski metric. It becomes possible to infer a model in Ad[S.sub.4] space in which there is a symmetry transformation that relates bosonic and fermionic fields. This model is not a consequence of being formulated in a superspace and the fermionic symmetry transformation is not the "square root" of an isometry of Ad[S.sub.4]. PACS No.: 11.30.Pb. Nous utilisons des techniques de superespace pour elaborer un modele supersymetrique sur une surface AdS3 plongee dans un espace a quatre dimensions. Dans ce modele, la transformation supersymetrique est la racine carree de la transformation generee par les generateurs d'isometrie de Ad[S.sub.3]. Puisque le momentum n'est pas un generateur d'isometrie, la supersymetrie ne donne pas des masses egales pour un champ bosonique et son partenaire fermionique. Nous presentons ce modele a l'aide de coordonnees qui caracterisent l'espace Ad[S.sub.3]. Ilyaun systeme de coordonnees qui permet de definir un sous-espace avec une metrique de Minkowski. Il devient alors possible d'inferer un modele dans un espace Ad[S.sub.4] dans lequel il y a une transformation de symetrie qui relie champs bosoniques et fermioniques. Ce resultat n'est pas la consequence d'une formulation dans un superespace et la transformation fermionique de supersymetry impliquee n'est pas la racine carree de l'isometrie de Ad[S.sub.4]. [Traduit par la Redaction], 1. Introduction Much work has been done on formulating field theory on spaces of constant curvature (see, for example, refs. 1-13). This topic has become more prominent with the introduction [...]

It is desirable to understand the movement of both matter and energy in the universe based upon fundamental principles of space and time. Time dilation and length contraction are features of Special Relativity derived from the observed constancy of the speed of light. Quantum Mechanics asserts that motion in the universe is probabilistic and not deterministic. While the practicality of these dissimilar theories is well established through widespread application inconsistencies in their marriage persist, marring their utility, and preventing their full expression. After identifying an error in perspective the current theories are tested by modifying logical assumptions to eliminate paradoxical contradictions. Analysis of simultaneous frames of reference leads to a new formulation of space and time that predicts the motion of both kinds of particles. Proper Space is a real, three-dimensional space clocked by proper time that is undergoing a densification at the rate of c. Coordinate transformations to a familiar object space and a mathematical stationary space clarify the counterintuitive aspects of Special Relativity. These symmetries demonstrate that within the local universe stationary observers are a forbidden frame of reference; all is in motion. In lieu of Quantum Mechanics and Uncertainty the use of the imaginary number i is restricted for application to the labeling of mass as either material or immaterial. This material phase difference accounts for both the perceived constant velocity of light and its apparent statistical nature. The application of Proper Space Kinematics will advance more accurate representations of microscopic, macroscopic, and cosmological processes and serve as a foundation for further study and reflection thereafter leading to greater insight., 1 Introduction The planets dancing in the heavens, an apple falling to earth each kindle curiosity about the dynamical universe. The mysteries of the unseen world and its apparent influences [...]

In this paper, we investigate exact solutions of the field equations for charged, anisotropic, static, cylindrically symmetric space-time. We use a barotropic equation of state linearly relating the radial pressure and energy density. The analysis of the matter variables indicates a physically reasonable matter distribution. In the most general case, the central densities correspond to realistic stellar objects in the presence of anisotropy and charge. Finally, we conclude that matter sources are less affected by the electromagnetic field. PACS Nos.: 04.40.Nr, 04.40.Dg, 04.20.Jb. Nous etudions ici des solutions exactes des equations de champ pour l'espace-temps a symetrie cylindrique, statique, anisotrope et charge. Nous utilisons l'equation d'etat barotrope qui relie lineairement la pression radiale et la densite d'energie. L'analyse des variables de matiere indique une distribution de matiere physiquement raisonnable. Dans le cas le plus general, les densites centrales correspondent a des objets stellaires realistes en presence d'anisotropie et de charge. Finalement, nous concluons que les sources de matiere sont moins affectees par le champ electromagnetique. [Traduit par la Redaction], 1. Introduction Since the pioneering work of anisotropic relativistic models [1], the study of models to explore the interior of a star has been an interesting problem. They discussed the [...]

Author(s): Premala Chandra [sup.1] , Piers Coleman [sup.1] [sup.2] , Rebecca Flint [sup.3] Author Affiliations: (1) Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, 136 Frelinghuysen Road, [...], The development of collective long-range order by means of phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry, whereas superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5 kelvin in the heavy-fermion compound URu.sub.2Si.sub.2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu.sub.2Si.sub.2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such &apos;hastatic&apos; order hybridizes uranium-atom conduction electrons with Ising 5f.sup.2 states to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction-electron &apos;sea&apos;, a colossal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant, energy-dependent nematicity in the tunnelling density of states. The formation of Ising quasiparticles in URu.sub.2Si.sub.2 results from &apos;hastatic&apos; order, which breaks double time-reversal symmetry, mixing states of integer and half-integer spin, and accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Novel &apos;hastatic&apos; order in condensed matter At temperatures below 17.5 K, the heavy-fermion uranium compound URu.sub.2Si.sub.2 exists in a mysterious &apos;hidden-order&apos; phase that has eluded characterization for 25 years. In this study the authors have used various pieces of experimental evidence to establish the nature of the spontaneous phase transition that takes place at 17.5 K, and conclude that both single and double time-reversal symmetry occur, resulting in mixing of itinerant conduction electrons and localized &apos;Ising&apos; states in the 5f.sup.2 orbital of uranium atoms. This is a fundamentally new type of order, which the authors dub hastatic (from the Latin hasta, a spear), and which they say could be a phenomenon that applies to other systems in which mixing with f-orbital states takes place.

A non-abelian gauge field with a topological action is coupled to a spin-3/2 Majorana spinor. The symmetries of this model are analyzed using the Dirac constraint formalism. These symmetries include a fermionic symmetry and the algebra of these symmetries closes; it is not the algebra of supergravity. The action is invariant without the need to introduce auxiliary fields. PACS No.: 11.30.Pb. Resume : Un champ de jauge non abelien avec action topologique est couple a un spineur de Majorana. Nous analysons les symetries de ce modele a l'aide du formalisme de contraintes de Dirac. Ces symetries incluent une symetrie fermionique et leur algebre est fermee, mais n'est pas l'algebre de la supergravite. L'action est invariante, sans avoir besoin d'introduire des champs auxiliaires. [Traduit par la Redaction], 1. Introduction The idea of extending the Poincare group through use of anti-commuting (fermionic) generators led to both globally supersymmetric and locally supersymmetric (supergravity) theories [1]. These models were devised [...]

We recall the solvable PT-symmetric quantum square well on an interval of x ∈ (-L, L):= [G.sup.(2)] (with an α-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval [G.sup.(2)] (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a q-pointed equilateral star graph [G.sup.(q)] endowed with the simplest complex-rotation-symmetric external α-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3,..., there exists the same q-independent and infinite subfamily of the real energies, and (ii)at any special q = 2, 6, 10,..., there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finally proposed. PACS Nos: 03.65.Ca, 03.65.Db, 03.65.Ta, 03.70.+k Nous prenons un potentiel quantique carre a symetrie PT sur un intervalle x [elemento de] (-L, L):= [G.sup.(2)] (non hermitique et dependant de [alfa] a cause des conditions aux limites de Robin) et nous le generalisons. Globalement, nous remplacons simplement l'intervalle de support support [G.sup.(2)] (reinterprete comme un graphe etoile a deux branches avec couplage de Kirchoff au vertex x = 0), par un graphe etoile equilateral a q branches [G.sup.(q)], dote des conditions aux limites externes de Robin dependantes de [alfa] a symetrie de rotation complexe la plus simple. Nous en obtenons la forme remarquablement compacte du determinant seculaire. Son analyse revele que : (i) pour tout entier q = 2,3,..., il existe la meme sous-famille infinie d'energies propres reelles independantes de q et (ii)qu'a toute valeur entiere particuliere, q = 2, 6, 10,..., il existe une sousfamille infinie additionnelle d' energies propres reelles qui dependent de q. Dans l'optique de propositions recentes pour construire dynamiquement l' espace de Hilbert d' un systeme quantique, nous avancons une interpretation en termes d' etats lies physiques pour ces energies propres. [Traduit par la Redaction], 1. Introduction The heuristic use of the concept of PT symmetry, that is, of the parity-times-time-reversal symmetry of quantum Hamiltonians H and (or) of the toy-model wave functions ψ(x) (with, [...]

We consider a static, cylindrically symmetric, charged, gravitating object as a perfect fluid and investigate the gravitational binding energy. It is found that only the localized part of the mass function provides the gravitational binding energy, whereas the nonlocalized part generated by the electric coupling does not contribute to it. PACS Nos: 04.40.Nr, 41.20.-q, 04.20.Cv Nous etudions un objet charge a symetrie cylindrique en interaction avec un fluide parfait et nous analysons l'energie de liaison gravitationnelle. Nous trouvons que seule la partie localisee de la fonction de masse contribue a l'energie de liaison gravitationnelle, alors que la partie non localisee generee par le couplage electrique n'y contribue pas. [Traduit par la Redaction], 1. Introduction In relativistic astrophysics, the energy required to break up a body in space is the gravitational binding energy, which is found to be equal to the negative of [...]

This paper investigates cylindrically symmetric distribution of an anisotropic fluid under the expansion-free condition, which requires the existence of a vacuum cavity within the fluid distribution. We have discussed two families of solutions that further provide two exact models in each family. Some of these solutions satisfy the Darmois junction condition while some show the presence of a thin shell on both boundary surfaces. We also formulate a relation between the Weyl tensor and energy density. PACS Nos: 04.20.-q, 04.40.-b, 04.40.Dg, 04.40.Nr Nous etudions ici la distribution a symetrie cylindrique d'un fluide anisotrope en expansion libre, qui exige l'existence d'une cavite vide a l'interieur de la distribution. Nous analysons deux familles de solution, chacune fournissant a son tour deux modeles exacts. Certaines de ces solutions satisfont la condition de jonction de Darnois, alors que d'autres presentent de minces couches sur les deux surfaces limites. Nous formulons aussi une relation entre le tenseur de Weyl et la densite d'energie. [Traduit par la Redaction], 1. Introduction In general relativity, the expansion scalar measures the change of small volumes of the fluid with respect to time. An explosion in the center leads to an overall [...]

In designing an optical system, nature demands that only a few basic 'ingredients' be used: refractive index, gain and loss. There is no doubt as to how useful index contrast [...], The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of 'parity-time symmetry' in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity-time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity-time symmetry to a new generation of multifunctional optical devices and networks.

In this paper, we complement the analysis involving the 'fundamental' solutions of the Klein-Gordon equation in de Sitter space-times given by Yagdjian and A. Galstian (Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Using the symmetry generators, we classify and reduce the underlying equations and show how this process may lead to exact solutions by quadratures. PACS Nos: 04.25.-g, 02.30.Hq, 02.30.Jr, 02.40.-k Nous completons ici l'analyse impliquant les solutions fondamentales de l'equation de Klein-Gordon dans un espace-temps de de Sitter, rapportees par Yagdjian et Galstian (Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Utilisant les generateurs de symetrie, nous classifions et reduisons les equations sous-jacentes et montrons comment ce processus peut mener aux solutions exactes par quadratures. [Traduit par la Redaction], 1. Introduction The Einstein theory of general relativity is a field theory of gravitation [1]. The equations that represent the theory are known as Einstein field equations [R.sub.[mu]v] - 1/2 [...]

The approach of Noether symmetries with gauge term in the Gauss-Bonnet dilatonic theory of gravity is used for different values of the state parameter, [omega], of the background matter. It is found that for [omega] = -1 (dark energy Universe), [omega] = 0 (matter-dominated Universe), and [omega] = 1 (the case of stiff matter), for the existence of Noether gauge symmetries, the potential V([phi]) and the coupling of the Gauss-Bonnet term with gravity [LAMBDA]([phi]) are obtained as exponential functions of the scalar field f. For the case of arbitrary [omega] the coupling parameter [LAMBDA]([phi]) is found as a linear function of the scalar field f and the potential is a constant, for the existence of Noether gauge symmetries. Here it is observed that both the potential and coupling parameter depend on the evolutionary history of the Universe. PACS Nos: 11.30.-j, 40.50.-h, 98.80.-k Nous utilisons l'approche de Noether pour les symetries avec terme de jauge, dans une theorie de Gauss-Bonnet de la gravite avec dilaton, pour differentes valeurs du parametre d'etat [omega] de la matiere constituant le fond. Nous trouvons, dans les cas [omega] = -1 (univers domine par l' energie sombre), [omega] = 0 (univers domine par la matiere) et [omega] = 1 (matiere rigide), qu'afin de garantir les symetries de jauge de Noether, le potentiel [LAMBDA]([phi]) et le couplage du terme de Gauss- Bonnet avec la gravite [LAMBDA]([phi]) apparaissent comme des fonctions exponentielles du champ scalaire [phi]. Pour des valeurs autres arbitraires de [omega], le parametre de couplage [LAMBDA]([phi]) est obtenu comme une fonction lineaire du champ scalaire [phi] et le potentiel est constant, ce qui assure une symetrie de jauge de Noether. Nous observons [phi] que le potentiel et la constante de couplage dependent de l'evolution historique de l' univers. [Traduit par la Redaction], 1. Introduction Theories of modified gravity have received much attention in recent years in attempts to explain accelerated expansion of the Universe, which has been proved observationally [1]. Among these [...]

This paper explores Ampere's circuital law (ACL) from an educational perspective. The interchangeability of the amperian loop with the current loop, an intrinsic symmetry of ACL that is seldom addressed in the literature or textbooks, is illustrated here. It is verified that the symmetry axis of a circular current is an amperian loop. The attempt to apply ACL to a finite wire, a common source of student misunderstanding, is used to highlight the limitations of ACL. The generalisation of ACL is illustrated using an instructive example where the displacement current is unconfined and not spatially uniform. This work is primarily intended for teachers and more advanced undergraduate students, who may benefit from the ideas that are presented here. PACS Nos: 03.50.De, 41.20.-q, 01.50.-i, 01.40.-d, 01.40.Fk Nous reetudions ici le theoreme d'Ampere, dans une perspective pedagogique. Nous illustrons l'interchangeabilite de la boucle d'Ampere et la boucle de courant, une symetrie intrinseque du theoreme qui est rarement discutee dans la litterature ou les manuels. Nous verifions que l'axe de symetrie d'un courant circulaire est une boucle d'Ampere. Afin d'illustrer les limitations du theoreme, nous utilisons l' application du theoreme a un fil de longueur finie, une source frequente de malentendus chez les etudiants. Nous illustrons la generalisation du theoreme d'Ampere a l'aide d'un exemple pedagogique ou le courant de deplacement n' est pas confine ni spatialement uniforme. Ce travail vise surtout les enseignants et les etudiants des 2e et 3e cycles qui peuvent profiter des idees presentees ici. [Traduit par la Redaction], 1. Introduction Ampere's circuital law (ACL) is an important topic in electromagnetism (e.g., see refs. 1-4) partly because of its use in situations, such as the infinite current wire and [...]

Cooling antihydrogen atoms is important for future experiments both to test the fundamental CPT symmetry by high resolution laser spectroscopy and also to measure the gravitational acceleration of antimatter. Laser cooling of antihydrogen can be done on the strong 1S-2P transition at the wavelength of Lyman-alpha (121.6 nm). A continuous wave laser at the Lyman-alpha wavelength based on solid-state fundamental lasers is described. By using a two-photon and a near one-photon resonance a scan across the whole phase matching curve of the four-wave mixing process is possible. Furthermore the influence of the beam profile of one fundamental beam on the four-wave mixing process is studied. PACS Nos: 36.20.-k, 37.10.De, 42.65.Ky Le refroidissement des atomes d'anti-hydrogene est important dans les experiences a venir pour verifier la symetrie fondamentale CPT par spectroscopie laser a haute resolution et pour mesurer l'acceleeration gravitationnelle de l'antimatiere. Le refroidissement laser de l'anti-hydrogene peut se faire sur la transition intense 1S-2P a la longueur d'onde Lyman alpha (121.6 nm). Nous deecrivons un laser continu a la longueur d'onde Lyman alpha, dont les elements sont des lasers a solide. En utilisant des resonances a deux photons et a pres d'un photon, un balayage sur toute la courbe d'adaptation de phase du melange a quatre ondes devient possible. Nous etudions aussi l'influence du profil d'un faisceau eelesmentaire sur le meecanisme de melange a quatre ondes. [Traduit par la Redaction], 1. Introduction Future high resolution laser spectroscopy of antihydrogen in a magnetic trap can provide very stringent tests of the fundamental symmetry between matter and antimatter (CPT symmetry) [1]. The [...]

This paper examines the energy problem in General Relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged black hole solutions. We conclude that energy must be re-scaled by some factor in the second-order approximation. PACS No: 2000MSC Nous etudions ici le probleme de l'energie en relativite generale en utilisant la meethode des symetries approximatives de Lie pour les equations differentielles. Nous evaluons au deuxieme ordre d'approximation les symetries des equations geodeesiques pour la solution trou noir charge; de la theeorie des cordes. Nous concluons que nous devons apporter une correction d'echelle a l'energie dans l'approximation au deuxieme ordre. [Traduit par la Redaction], 1. Introduction One of the most important issues of General Relativity (GR) is the localization of energy-momentum. It is a conserved quantity in classical mechanics. In GR, energy conservation is [...]

A question of mirror symmetry of the universe is considered in terms of the relationship between observer and the observed system. By including observer into the system, the handedness becomes a purely relative property; thereby the system represents both left and right spatial orders. Topologically interpreted, this logical conclusion suggests that universe represents a multiply connected space of the properties related to Mobius strip. Keywords: universe, Alice matter, handedness, Mobius strip, Poincare sphere, One of the most intriguing cases of human experience is connected with looking at the mirror. This, otherwise trivial activity, gives us a possibility of reflection that goes far beyond [...]

We report the design and experimental testing of a high-spatial-resolution nulling microellipsometer. This microellipsometer design is based on the previously reported principle of rotational polarization symmetry to improve the signal-to-noise ratio of spatially resolved ellipsometric measurements. Through the use of an electro-optic polarization rotator, a null detection scheme is made possible and implemented. Surface profiling of a lithographically patterned microstructure is demonstrated with the nulling microellipsometer. A lateral spatial resolution of 0.48 [micro]m is calculated with a numerical aperture of 0.9 and an illumination wavelength of 632.8 nm. [c] 2010 Optical Society of America OCIS codes: 070.6110, 120.2130, 260.1440, 260.5430.

Nature has mastered the art of creating complex structures through self-assembly of simpler building blocks. Adapting such a bottom-up view provides a potential route to the fabrication of novel materials. However, this approach suffers from the lack of a sufficiently detailed understanding of the noncovalent forces that hold the self-assembled structures together. Here we demonstrate that nature can indeed guide us, as we explore routes to helicity with achiral building blocks driven by the interplay between two competing length scales for the interactions, as in DNA. By characterizing global minima for clusters, we illustrate several realizations of helical architecture, the simplest one involving ellipsoids of revolution as building blocks. In particular, we show that axially symmetric soft discoids can self-assemble into helical columnar arrangements. Understanding the molecular origin of such spatial organisation has important implications for the rational design of materials with Useful optoelectronic applications. anisotropic interactions | columnar arrangements | helix | self-assembly www.pnas.org./cgi/doi/10.1073/pnas.0906676106

We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn--Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.

Numerical investigations show that the spontaneous break of symmetry in annular incompressible jets occurs in the laminar flow regime and is controlled by both the Reynolds number and the blockage ratio. In the blockage ratio range between 0.50 and 0.89 the transition critical Reynolds number decreases with increasing blockage ratio, according to a defined formula. Transition to asymmetry happens in the steady regime, before the transition to the unsteady flow. Asymmetry is characterized by a preferential flow direction from one side of the jet boundary layer to the diametrically opposite side. The plane of preferential direction passes through the geometry centerline and represents the single plane of flow symmetry. Experiments reported in literature have confirmed the existence of flow asymmetry in an annular jet flow. [DOI: 10.1115/1.3176960] Keywords: annular jets, break of symmetry, laminar flow, CFD

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states. coherent X-ray diffraction | higher-order correlations | structure

Colloidal particle dispersions feature a wide variety of attractive and repulsive interactions and mechanical packing constraints that have been exploited to assemble a diverse set of structures, including Pickering emulsions [...], The assembly of complex structures out of simple colloidal building blocks is of practical interest for building materials with unique optical properties (for example photonic crystals (1) and DNA biosensors (2)) and is of fundamental importance in improving our understanding of self-assembly processes occurring on molecular to macroscopic length scales (3-5). Here we demonstrate a self-assembly principle that is capable of organizing a diverse set of colloidal particles into highly reproducible, rotationally symmetric arrangements. The structures are assembled using the magnetostatic interaction between effectively diamagnetic and paramagnetic particles within a magnetized ferrofluid. The resulting multipolar geometries resemble electrostatic charge configurations such as axial quadrupoles ('Saturn rings'), axial octupoles ('flowers'), linear quadrupoles (poles) and mixed multipole arrangements ('two tone'), which represent just a few examples of the type of structure that can be built using this technique.

The number of known elementary particles is now very large, and to reduce their diverse properties to order it is useful to look for symmetries between them. Symmetry properties of various kinds, and the conservation laws associated with them, are discussed here. After giving a brief survey of the general types of particle encountered in nature, we discuss first the symmetries related to space and time, and associated with the conservation laws of momentum, energy, angular momentum, and parity. Later we discuss the so-called internal symmetries, in which different particles are regarded as different states of a single basic entity. Theories of this type--particularly the 'eightfold way'--have had considerable success in systematizing the properties of the known particles.

Professor Herbert Dingle was a long-time critic of the special theory of relativity, who believed for many years that the theory was self-contradictory. Although he was unsuccessful in persuading the [...]

Author(s): F. Ronning [1]; T. Helm [2]; K. R. Shirer [2]; M. D. Bachmann [2]; L. Balicas [3]; M. K. Chan [4]; B. J. Ramshaw [4, 5]; R. D. McDonald [...]

Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of [pi]/(3[square root of 2]) ~ 0.7405. Much more recently, an unusually high-density packing of [approximately equal to] 0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high-density packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of [pi]/4. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at [c.sup.*] = [square root of 2] - 1. biaxial order | packing | truncated cones

We present a mathematically simple procedure to explain spontaneous symmetry breaking in quantum systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a symmetry broken state in crystals, antiferromagnets, and even superconductors. It has the advantage that it automatically brings to the fore the main players in spontaneous symmetry breaking: the symmetry-breaking field, the thermodynamic limit, and the global excitations of a 'thin' spectrum. [DOI: 10.1119/1.2730839]

Abstract: The concepts of frame indifference and relative frame indifference are discussed critically in the context of materials with memory. It is shown that frame indifference implies relative frame indifference [...]

The studies of symmetry-breaking were reported for self consistent field wave functions applied to three homonuclear diatomics: F(sub 2)(super +), O(sub 2)(super +), and Cr(sub 2). The report stated that simplest way to understand symmetry breaking was a consequence of the incorrect asymptotic behavior of limited wave functions at long interatomic distances.

An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in quantum mechanics--the two-dimensional delta function interaction and the 1/[r.sup.2] potential. The former has been treated in this journal; in this article we discuss the physics of the latter together with experimental consequences. [DOI: 10.1119/1.1456071] (Received 28 September 2001; accepted 8 January 2002)

Quantum phase interference molecular magnets with tetragonal symmetry are considered. Spin-coherence-state path integral method is used to demonstrate this concept.

The authors review the publications on the superconductors with the order parameter of unconventional symmetry. The topics of interest include superconducting states, superconducting phase diagram and the properties of these states.

Chemical research is presented describing the asymmetric structural determination study of epoxidated enones employing the complex oxide and BINOL triphenylarsine compound.