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We analyze Feynman's work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946-47 during his course on Mathematical Methods. The motivation for such a work was Feynman's involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers or several other circuits, with the risk of introducing distortion at each step. In order to deal with such a problem, Feynman designed a theoretical "reference amplifier", thus enabling a characterization of the distortion by means of a benchmark relationship between phase and amplification for each frequency, and providing a standard tool for comparing the operation of real devices. A general theory was elaborated, from which he was able to deduce the basic features of an amplifier just from its response to a pulse or to a sine wave of definite frequency. Moreover, in order to apply such a theory to practical problems, a couple of remarkable examples were worked out, both for high-frequency cutoff amplifiers and for low-frequency ones. A special consideration deserves a mysteriously exceptional amplifier with best stability behavior introduced by Feynman, for which different physical interpretations are here envisaged. Feynman's earlier work then later flowed in the Hughes lectures on Mathematical Methods in Physics and Engineering of 1970-71, where he also remarked on causality properties of an amplifier, that is on certain relations between frequency and phase shift that a real amplifier has to satisfy in order not to allow output signals to appear before input ones. Quite interestingly, dispersion relations to be satisfied by the response function were introduced., 19 pages, 6 figures

Richard P. Feynman's work on gravitation, as can be inferred from several published and unpublished sources, is reviewed. Feynman was involved with this subject at least from late 1954 to the late 1960s, giving several pivotal contributions to it. Even though he published only three papers, much more material is available, beginning with the records of his many interventions at the Chapel Hill conference in 1957, which are here analyzed in detail, and show that he had already considerably developed his ideas on gravity. In addition he expressed deep thoughts about fundamental issues in quantum mechanics which were suggested by the problem of quantum gravity, such as superpositions of the wave functions of macroscopic objects and the role of the observer. Feynman also lectured on gravity several times. Besides the famous lectures given at Caltech in 1962-63, he extensively discussed this subject in a series of lectures delivered at the Hughes Aircraft Company in 1966-67, whose focus was on astronomy and astrophysics. All this material allows to reconstruct a detailed picture of Feynman's ideas on gravity and of their evolution until the late sixties. According to him, gravity, like electromagnetism, has quantum foundations, therefore general relativity has to be regarded as the classical limit of an underlying quantum theory; this quantum theory should be investigated by computing physical processes, as if they were experimentally accessible. The same attitude is shown with respect to gravitational waves, as is evident also from an unpublished letter addressed to Victor F. Weisskopf. In addition, an original approach to gravity, which closely mimics (and probably was inspired by) the derivation of the Maxwell equations given by Feynman in that period, is sketched in the unpublished Hughes lectures., Comment: 47 pages, no figures, final version. Dedicated to the Memory of Erasmo Recami

Introducing some fundamental concepts of quantum physics to high school students, and to their teachers, is a timely challenge. In this paper we describe ongoing research, in which a teaching–learning sequence for teaching quantum physics, whose inspiration comes from some of the fundamental papers about the quantum theory of radiation by Albert Einstein, is being developed. The reason for this choice goes back essentially to the fact that the roots of many subtle physical concepts, namely quanta, wave–particle duality and probability, were introduced for the first time in one of these papers, hence their study may represent a useful intermediate step towards tackling the final incarnation of these concepts in the full theory of quantum mechanics. An extended discussion of some elementary tools of statistical physics, mainly Boltzmann’s formula for entropy and statistical distributions, which are necessary but may be unfamiliar to the students, is included. This discussion can also be used independently to introduce some rudiments of statistical physics. In this case, part of the inspiration came from some of Einstein’s papers. We present preliminary, qualitative results obtained with both teachers and selected pupils from various high schools in southern Italy, in the course of several outreach activities. Although the proposal was only tested in this limited context for now, the preliminary results are very promising and they indicate that this proposal can be fruitfully employed for the task.

We formulate a didactic proposal for introducing some fundamental concepts of quantum physics to advanced high school students, and to their teachers. The inspiration comes from some of the fundamental papers about the subject by Albert Einstein, in which many of these concepts, for example light quanta, wave-particle duality, and probability, were introduced for the first time, in a characteristically illuminating way. The proposal can be supplemented by a discussion of elementary tools of statistical physics, which are needed at some point. Preliminary results, both with students and teachers, are very promising.

An important issue within the present economic crisis is understanding the dynamics of the public debt of a given country, and how the behavior of average consumers and tax payers in that country affects it. Starting from a model of the average consumer behavior introduced earlier by the authors, we propose a simple model to quantitatively address this issue. The model is then studied and analytically solved under some reasonable simplifying assumptions. In this way we obtain a condition under which the public debt steadily decreases., Comment: 4 pages, 1 figures, submitted for publication to Physica A

We retrace an ab initio relativistic derivation of Maxwell's equations that was developed by Feynman in unpublished notes, clarifying the analogies and the differences with analogous treatments present in the literature. Unlike the latter, Feynman's approach stands out because it considers electromagnetic potentials as primary, reflecting his ideas about the quantum foundations of electromagnetism. Some considerations about the foundations of special relativity, which are naturally suggested by this approach, are given in appendix., 17 pages, no figures, submitted for publication

We study the analog of Snell's law for particles moving across the interface of two regions with two different potential energies, from two different points of view. First, a simple demonstration involving marbles and a potential step is shown. Then, from a theoretical point of view, this law describing mechanical refraction is derived from the Maupertuis and Jacobi variational principles, in close analogy with the well known derivation of Snell's law for refraction from Fermat's least time principle. Finally, the relativistic version of mechanical refraction is obtained by the Maupertuis principle, by trading the Newtonian dispersion relation with the relativistic one. The pedagogical significance of this treatment is discussed.

The coefficient of restitution of the bounces of a marble on a table is here studied and measured in terms of the total bouncing time. Interesting links arise with mathematics (geometric series) as well as philosophy (Zeno’s paradox), which make our proposal appealing for an interdisciplinary teaching-learning sequence. The relevance of this work for high school and undergraduate students is discussed with emphasis on students’ misconceptions when dealing with infinite processes.

We discuss a previously unpublished description of electromagnetism outlined by Richard P. Feynman in the 1960s in five handwritten pages, recently uncovered among his papers, and partly developed in later lectures. Though similar to the existing approaches deriving electromagnetism from special relativity, the present one extends a long way towards the derivation of Maxwell's equations with minimal physical assumptions. In particular, without postulating Coulomb's law, homogeneous Maxwell's equations are written down by following a route different from the standard one, i.e. first introducing electromagnetic potentials in order to write down a relativistic invariant action, which is just the inverse approach to the usual one. Also, Feynman's derivation of the Lorentz force exclusively follows from its linearity in the charge velocity and from relativistic invariance. Going further, i.e. adding the inhomogeneous Maxwell's equations, requires some more physical input, and can be done by just following conventional lines, hence this task was not pursued here. Despite its incompleteness, this way of proceeding is of great historical and epistemological significance. We also comment about its possible relevance to didactics, as an interesting supplement to usual treatments., Comment: 17 pages, no figures

The quest for a microscopic foundation of Thermodynamics is addressed within the Nonunitary Newtonian Gravity model through the study of a specific closed system, namely a three-dimensional harmonic nanocrystal. A numerical calculation of the nanocrystal von Neumann entropy as a function of time is performed, showing a sharp monotonic increase, followed by a stabilization at late times. This behavior is consistent with the emergence of a micro-canonical ensemble within the initial energy levels, signaling, in this way, the establishment of a non-unitary gravity-induced thermal equilibrium., Comment: 2 figures, 8 pages. arXiv admin note: text overlap with arXiv:1801.02500

It is explicitly shown that a one-family parameter model reproducing the nonlinear Newton-Schr\"odinger equation as the parameter goes to infinity is free from any causality violation problem for any finite value of it. This circumstance arises from the intrinsic mechanism of spontaneous state reduction of the model, absent in the Newton-Schr\"odinger limit. A specific ideal EPR experiment involving a superposition of two distinct CM's position states of a massive lump is analyzed, showing recovered compatibility with QM. Besides, the new framework suggests a soft version of the Many Worlds Interpretation, in which the typical indiscriminate proliferation of Everett branches, together with the bizarre inter-branches communications made possible by nonlinearity, are strongly suppressed in the macroscopic world by the same mechanism of state reduction., Comment: 11 pages, 2 figures

Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic black body radiation. We show that all nonlocal effects are transient and most relevant in the first period of acceleration.

We discuss a less known aspect of Feynman's multifaceted scientific work, centered about his interest in molecular biology, which came out around 1959 and lasted for several years. After a quick historical reconstruction about the birth of molecular biology, we focus on Feynman's work on genetics with Robert S. Edgar in the laboratory of Max Delbruck, which was later quoted by Francis Crick and others in relevant papers, as well as in Feynman's lectures given at the Hughes Aircraft Company on biology, organic chemistry and microbiology, whose notes taken by the attendee John Neer are available. An intriguing perspective comes out about one of the most interesting scientists of the XX century., On the centenary of the birth of Richard P. Feynman (May 11, 1918 - February 15, 1988)

The result of a numerical simulation of two interacting particles in the framework of Nonunitary Newtonian Gravity is presented here. Particles are held close together by a 3-d harmonic trap and interact with each other via an `electrical' delta-like potential and via the ordinary Newtonian term, together with a fluctuational nonunitary counterpart of the latter. Fundamental nonunitarity can be seen as arising from the interaction of the physical degrees of freedom with (gravitational) hidden copies of them. Starting from an energy eigenstate within the ordinary setting, it is shown that, while energy expectation remains constant, a slow net variation of the von Neumann entropy for the system as a whole takes place, with a small modulation induced on the relative entanglement entropy of the two particles. Besides, the simulation shows explicitly how fundamental gravity-induced entropy can be clearly distinguished from the subjective notion of coarse-grained entropy, i.e. from the entropy of one particle with respect to the `environment' of the other., Comment: 10 pages, 3 figures

The goal of international trade theories is to explain the exchange of goods and services between different countries, aiming to benefit from it. Albeit the idea is very simple and known since ancient history, smart policy and business strategies need to be implemented by each subject, resulting in a complex as well as not obvious interplay. In order to understand such a complexity, different theories have been developed since the sixteenth century and today new ideas still continue to enter the game. Among them, the so called classical theories are country-based and range from Absolute and Comparative Advantage theories by A. Smith and D. Ricardo to Factor Proportions theory by E. Heckscher and B. Ohlin. In this work we build a simple hydrodynamic model, able to reproduce the main conclusions of Comparative Advantage theory in its simplest setup, i.e. a two-country world with country A and country B exchanging two goods within a genuine exchange-based economy and a trade flow ruled only by market forces. The model is further generalized by introducing money in order to discuss its role in shaping trade patterns. Advantages and drawbacks of the model are also discussed together with perspectives for its improvement., Comment: 8 pages, 2 figures

Understanding consumption dynamics and its impact on the whole economy and welfare within the present economic crisis is not an easy task. Indeed the level of consumer demand for different goods varies with the prices, consumer incomes and demographic factors. Furthermore crisis may trigger different behaviors which result in distortions and amplification effects. In the present work we propose a simple model to quantitatively describe the time evolution over a brief period of the amount of money an average consumer decides to spend, depending on his/her available budget. A simple hydrodynamical analog of the model is discussed. Finally, perspectives of this work are briefly outlined., Comment: 5 pages, 7 figures

We study the unconventional transmission properties of a wave-packet through a PT-symmetric potential region, as describing actual electromagnetic wave propagation along a waveguide filled with gain and loss media. The non-trivial behavior of the transmission probability manifests in the giant amplification of the incident electromagnetic signal of given wavelengths for well-defined configurations, depending on the gain/loss contrast. Maximum transmission peaks are related to spectral singularities and a strict correlation exists between the "resonant" wavelengths and the gain/loss contrast. The transit times are as well calculated, showing their surprising vanishing in the opaque barrier limit, independently of the gain/loss contrast, which is reminiscent of some sort of Hartman effect. Also, non-local effects manifest in the presence of negative delay times for given configurations, while a correlation is apparent between maximum delay times and transmission probability peaks, though appreciably depending on the gain/loss contrast., Latex, 8 pages, 5 figures

We explore the low-temperature thermodynamic properties and crossovers of ad-dimensional classical planar Heisenberg ferromagnet in a longitudinal magnetic field close to its field-induced zero-temperature critical point by employing the two-time Green’s function formalism in classical statistical mechanics. By means of a classical Callen-like method for the magnetization and the Tyablikov-like decoupling procedure, we obtain, for anyd, a low-temperature critical scenario which is quite similar to the one found for the quantum counterpart. Remarkably, ford>2the discrimination between the two cases is found to be related to the different values of the shift exponent which governs the behavior of the critical line in the vicinity of the zero-temperature critical point. The observation of different values of the shift-exponent and of the related critical exponents along thermodynamic paths within the typical V-shaped region in the phase diagram may be interpreted as a signature of emerging quantum critical fluctuations.

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter theta (in appropriate units), a one-to-one correspondence between an abelian noncommutative field theory (NCFT) and a non-abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings nu =m/pm+2, recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in a previous work (V. Marotta, A. Naddeo, Nucl. Phys. B 810(2009) 575) for the Jain series nu =m/2pm+1. The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids., Comment: 20 pages, 1 figure; Nuclear Physics B (2010), in print

Recently a one-dimensional closed ladder of Josephson junctions has been studied (G. Cristofano et al., Phys. Lett. A 372 (2008) 2464) within a twisted conformal field theory (CFT) approach (G. Cristofano et al., Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B 641 (2002) 547) and shown to develop the phenomenon of flux fractionalization (G. Cristofano et al., Eur. Phys. J. B 49 (2006) 83). That led us to predict the emergence of a topological order in such a system (G. Cristofano et al., JSTAT (2005) P03006). In this letter we analyze the ground states and the topological properties of fully frustrated Josephson junction arrays (JJA) arranged in a Corbino disk geometry for a variety of boundary conditions. In particular minimal configurations of fully frustrated JJA are considered and shown to exhibit the properties needed in order to build up a solid state qubit, protected from decoherence. The stability and transformation properties of the ground states of the JJA under adiabatic magnetic flux changes are analyzed in detail in order to provide a tool for the manipulation of the proposed qubit., Comment: 24 pages, 4 figures

We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By focusing on the case of negative V, i.e., attractive intersite interaction, we study the phase diagram at finite temperature and find, for various values of the filling and of the on-site coupling U, a phase transition towards a state with phase separation. We determine the critical temperature as a function of the relevant parameters, U/|V|, n and z and we find a reentrant behavior in the plane (U/|V|,T). Finally, several thermodynamic properties are investigated near criticality., 7 pages, 7 figures. EPJB Topical Issue on Novel Quantum Phases and Mesoscopic Physics in Quantum Gases

Relevant contributions by Majorana regarding Compton scattering off free or bound electrons are considered in detail, where a (full quantum) generalization of the Kramers-Heisenberg dispersion formula is derived. The role of intermediate electronic states is appropriately pointed out in recovering the standard Klein-Nishina formula (for free electron scattering) by making recourse to a limpid physical scheme alternative to the (then unknown) Feynman diagram approach. For bound electron scattering, a quantitative description of the broadening of the Compton line was obtained for the first time by introducing a finite mean life for the excited state of the electron system. Finally, a generalization aimed to describe Compton scattering assisted by a non-vanishing applied magnetic field is as well considered, revealing its relevance for present day research., Comment: latex, amsart, 10 pages, 1 figure

In a tunneling experiment across a quantum dot it is possible to change the coupling between the dot and the contacts at will, by properly tuning the trasparency of the barriers and the temperature. Gate voltages allow for changes of the relative position of the dot addition energies and the Fermi level of the leads. Here we discuss the two limiting cases: weak and strong coupling in the tunneling Hamiltonian. In the latter case Kondo resonant conductance can emerge at low temperature in a Coulomb blockade valley. We give a pedagogical approach to the single-channel Kondo physics at equilibrium and review the Nozieres scattering picture of the correlated fixed point. We emphasize the effect of an applied magnetic field and show how an orbital Kondo effect can take place in vertical quantum dots tuned both to an even and to an odd number of electrons at a level crossing. We extend the approach to the two-channel overscreened Kondo case and discuss recent proposals for detecting the non-Fermi liquid fixed point which could be reached at strong coupling., Comment: 31 pages, invited review article

We show how the recently proposed CFT for a bilayer Quantum Hall system at filling nu=m/pm+2, the Twisted Model (TM), is equivalent to the system of two massless scalar bosons with a magnetic boundary interaction as introduced in Nucl. Phys. B443 (1995) 444, at the so called magic points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Such an analogy is further developed in terms of the TM boundary states, by describing the interaction between an impurity with a Hall system., Comment: 13 pages, no figures, Latex

We identify the impurity interactions of the recently proposed CFT description of a bilayer quantum Hall system at filling ν= m pm+2 [Mod. Phys. Lett. A 15 (2000) 1679]. Such a CFT is obtained by m -reduction on the one layer system, with a resulting pairing symmetry and presence of quasi-holes. For the m =2 case boundary terms are shown to describe an impurity interaction which allows for a localized tunnel of the Kondo problem type. The presence of an anomalous fixed point is evidenced at finite coupling which is unstable with respect to unbalance and flows to a vacuum state with no quasi-holes.

We study the quantum dynamics of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) in a double-well potential inspired by the experimental protocol recently developed by NIST group. We focus on the regime where the number of atoms is very large and perform a two-mode approximation. An analytical solution of the two-site Bose-Hubbard-like Hamiltonian is found for several limiting cases, which range from a strong Raman coupling to a strong Josephson coupling, ending with the complete model in the presence of weak nonlinear interactions. Depending on the particular limit, different approaches are chosen: a mapping onto an SU(2) spin problem together with a Holstein-Primakoff transformation in the first two cases and a rotating wave approximation (RWA) when dealing with the complete model. The quantum evolution of the number difference of bosons with equal or different spin between the two wells is investigated in a wide range of parameters; finally the corresponding total atomic current and the spin current are computed. We show a spin Josephson effect which could be detected in experiments and employed to build up realistic devices., Comment: 18 pages

The temperature dependence of magnetization in ferromagnetic nanostructures (e.g., nanoparticles or nanoclusters) is usually analyzed by means of an empirical extension of the Bloch law sufficiently flexible for a good fitting to the observed data and indicates a strong softening of magnetic coupling compared to the bulk material. We analytically derive a microscopic generalization of the Bloch law for the Heisenberg spin model which takes into account the effects of size, shape and various surface boundary conditions. The result establishes explicit connection to the microscopic parameters and differs significantly from the existing description. In particular, we show with a specific example that the latter may be misleading and grossly overestimates magnetic softening in nanoparticles. It becomes clear why the usual $T^{3/2}$ dependence appears to be valid in some nanostructures, while large deviations are a general rule. We demonstrate that combination of geometrical characteristics and coupling to environment can be used to efficiently control magnetization and, in particular, to reach a magnetization higher than in the bulk material., 7 pages, 4 figures

We show how the low-energy properties of the 2-leg XXZ spin-1/2 ladders with general anisotropy parameter $\Delta $ on closed geometries can be accounted for in the framework of the m-reduction procedure developed in [1]. In the limit of quasi-decoupled chains, a conformal field theory (CFT) with central charge c=2 is derived and its ability to describe the model with different boundary conditions is shown. Special emphasis is given to the Mobius boundary conditions which generate a topological defect corresponding to non trivial single-spinon excitations. Then, in the case of the 2-leg XXX ladders we discuss in detail the role of various perturbations in determining the renormalization group flow starting from the ultraviolet (UV) critical point with c=2., Comment: 23 pages, 5 figures; J. Stat. Mech.: Theory Exp. (2008), in print

A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable, contributions to the ground state energy of an atom with given Z coming also from any other Z. Instead, contributions relevant mainly for pedagogical reasons count simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as a simple alternative to Hylleraas' method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas., Comment: amsart, 20 pages, no figures

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3, Comment: 9 pages, 2 figures; to be published on EPJB

Aim of this work is to calculate explicitly the result of the experiment of superposition of a mirror in the Michelson photon cavities interferometric device proposed by Marshall, Simon, Penrose and Bownmeester, as expected within a recently proposed model of non-unitary self-gravity inducing localization. As for other proposals of modifications of Quantum Mechanics in a non-unitary sense, aimed to account for both unitary evolution and irreversible collapse, like in the famous Ghirardi-Rimini-Weber and Pearle's models, it turns out that, for the experimental parameters proposed, no effect is detectable at all. It is pointed out that the enhancing properties of matter granularity does not substantially change this conclusion. Parameters have also been exploratively varied in a certain range beyond the proposed values. It is shown that within `sensible' parameters, that are not yet attainable within current technology, the model exhibits a peculiar signature with respect to other collapse models as far as parameters space is explored. Besides, the calculation offers a way to see non-unitary gravity at work in a quasi-realistic setting., Comment: 16 pages, 3 figures

We study the quantum dynamics of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto a SU(2) spin problem together with a Holstein-Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase-separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunneling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms., 12 pages, 7 figures, accepted for publication in J. Phys. B

In a recent paper, by exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter $\theta $ (in appropriate units), a general one-to-one correspondence between the $m$-reduced conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings $\nu =% \frac{m}{pm+2}$ and an Abelian noncommutative field theory (NCFT) has been established . That allowed us to add new evidence to the relationship between noncommutativity and quantum Hall fluids\cite% {ncmanybody}. On the other hand, the $m$-reduced CFT is equivalent to a system of two massless scalar bosons with a magnetic boundary interaction as introduced by Callan et al., at the so called ``magic''\ points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Here we develop such a point of view by focusing on the case $m=2$ which corresponds to a quantum Hall bilayer. The key role of a localized impurity which couples the two layers is emphasized and the effect of noncommutativity in terms of generalized magnetic translations (GMT) is fully exploited. As a result, general GMT operators are introduced, in the form of a tensor product, which act on the QHF and defect space respectively, and a comprehensive study of their rich structure is performed., Comment: 18 pages, 1 figure, accepted for publication in International Journal of Modern Physics A

A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function's framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good agreement with the exact numerical transfer-matrix data for the one-dimensional case and with the exact high-temperature-series results for the three-dimensional one. In particular, for the ferromagnetic chain, the zero-field susceptibility results are found to be consistent with the exact analytical ones obtained by M.E. Fisher. However, the formula derived in the present paper provides more accurate predictions in a wide range of temperatures of experimental and numerical interest., Comment: 19 pages, 3 figures

The new formal analogy between superfluid systems and cosmology, which emerges by taking into account the back-reaction of the vacuum to the quanta of sound waves \cite{noi}, enables us to put forward some common features between these two different areas of physics. We find the condition that allows us to justify a General Relativity (GR) derivation of the hydrodynamical equation for the superfluid in a four-dimensional space whose metric is the Unruh one \cite{Unruh}. Furthermore we show how, in the particular case taken into account, our hydrodynamical equation can be deduced within a four-dimensional space from the wave equation of a massless scalar field., Accepted for publication in Modern Physics Letters A

A new analogy between superfluid systems and cosmology is here presented, which relies strongly on the following ingredient: the back-reaction of the vacuum to the quanta of sound waves. We show how the presence of thermal phonons, the excitations above the quantum vacuum for $T> 0$, enable us to deduce an hydrodynamical equation formally similar to the one obtained for a perfect fluid in a Universe obeying the Friedmann-Robertson-Walker metric., Accepted for publication in Modern Physics Letters B

The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter theta (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a non-abelian theory of twisted fields on ordinary space. We focus on a particular conformal field theory (CFT), the one obtained by means of the m-reduction procedure (V. Marotta, J. Phys. A 26 (1993) 3481; V. Marotta, Mod. Phys. Lett. A 13} (1998) 853; V. Marotta, Nucl. Phys. B 527 (1998) 717; V. Marotta, A. Sciarrino, Mod. Phys. Lett. A 13 (1998) 2863), and show that it is the Morita equivalent of a NCFT. Finally, the whole m-reduction procedure is shown to be the image in the ordinary space of the Morita duality. An application to the physics of a quantum Hall fluid at Jain fillings nu =m/2pm+1 is explicitly discussed in order to further elucidate such a correspondence and to clarify its role in the physics of strongly correlated systems. A new picture emerges, which is very different from the existing relationships between noncommutativity and many body systems (A. P. Polychronakos, arXiv:0706.1095v2)., Comment: 16 pages, 2 figures

We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $\theta $ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and a nonabelian theory of twisted fields on ordinary space. We concentrate on a particular conformal field theory (CFT), the one obtained by means of the m-reduction procedure (V. Marotta, J. Phys. A 26 (1993) 3481; Mod. Phys. Lett. A 13 (1998) 853; Nucl. Phys. B 527 (1998) 717), and show that the Morita equivalence also holds at this level. An application to the physics of a quantum Hall fluid at Jain fillings \nu =m/2pm+1 is explicitly considered in order to further elucidate such a correspondence., Comment: 12 pages, 1 figure

We show that a system of spinless Fermi particles, localized on the sites of the Bethe lattice with coordination number z and interacting through a repulsive nearest-neighbor interaction, exhibits a phase transition to a charge-ordered state. The phase diagram in the n-T plane is derived. Relevant thermodynamic quantities, such as the free energy, the specific heat, the entropy and the compressibility are analyzed in detail., 7 pages, 9 figures

A fermionic model, built up of q species of localized Fermi particles, interacting by charge correlations, is isomorphic to a spin-q/2 Ising model. However, the equivalence is only formal and the two systems exhibit a different physical behavior. By considering a Bethe lattice with q=1, we have exactly solved the models. There exists a critical temperature below which there is a spontaneous breakdown of the particle-hole symmetry for the first model, and of the spin symmetry for the second. While the spin system is always stable and exhibits a homogeneous ferromagnetic phase below T_{c}, the fermionic system for T, Comment: 2 pages, 4 figures

We exactly solve the ferromagnetic spin- 1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coordination number z. Nonlocal correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities.

Following a suggestion given in Nucl. Phys. B 300 (1988)611,we show how the U(1)*Z_{2} symmetry of the fully frustrated XY (FFXY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at "paired states" fillings nu =1 (cfr. Cristofano et al.,Mod. Phys. Lett. A 15 (2000)1679;Nucl. Phys. B 641 (2002)547). The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the physical properties of the FFXY model. In particular the whole phase diagram is recovered by analyzing the flow from the Z_{2} degenerate vacuum of the c=2 CFT to the infrared fixed point unique vacuum of the c=3/2 CFT. The last theory is known to successfully describe the critical behavior of the system at the overlap temperature for the Ising and vortex-unbinding transitions., Comment: 18 pages, 1 figure, to appear in JSTAT

Following a suggestion given in Phys. Lett. B 571(2003) 621, we show how a bilayer Quantum Hall system at fillings nu =1/p+1 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (Phys. Rev. B 72 (2005) 041305) which evidence the presence of a topological defect in the transport properties of the bilayer system., Comment: 10 pages, 4 figures; talk given by A. Naddeo at "X Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors, Vietri sul Mare (SA),Italy, 3-14 October 2005