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The capture of scintillation light emitted by liquid Argon and Xenon under molecular excitations by charged particles is still a challenging task. Here we present a first attempt to design a device able to have a sufficiently high photon detection efficiency, in order to reconstruct the path of ionizing particles. The study is based on the use of masks to encode the light signal combined with single-photon detectors, showing the capability to detect tracks over focal distances of about tens of centimeters. From numerical simulations it emerges that it is possible to successfully decode and recognize signals, even of rather complex topology, with a relatively limited number of acquisition channels. Thus, the main aim is to elucidate a proof of principle of a technology developed in very different contexts, but which has potential applications in liquid argon detectors that require a fast reading. The findings support us to think that such innovative technique could be very fruitful in a new generation of detectors devoted to neutrino physics. The capture of scintillation light emitted by liquid Argon and Xenon under molecular excitations by charged particles is still a challenging task. Here we present a first attempt to design a device able to grab sufficiently high luminosity in order to reconstruct the path of ionizing particles. This preliminary study is based on the use of masks to encode the light signal combined with single-photon detectors. In this respect, the proposed system is able to detect tracks over focal distances of about tens of centimeters. From numerical simulations it emerges that it is possible to successfully decode and recognize signals, even complex, with a relatively limited number of acquisition channels. Such innovative technique can be very fruitful in a new generation of detectors devoted to neutrino physics and dark matter search. Indeed the introduction of coded masks combined with SiPM detectors is proposed for a liquid-Argon target in the Near Detector of the DUNE experiment.

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce the critical properties implied in terms of the the dynamics of coexistence curves in the space of thermodynamic variables., Comment: 10 pages, 6 plots

We analyse a recent generalised free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform heliconical structures, and we find new liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. These new configurations are characterised by a localised pattern given by the variation of the conical angle. We study the equilibrium differential equations and find numerical solutions and analytical approximations., Published Version

Recently the hybridization of microwave-frequency cavity modes with collective spin excitations has attracted large interest for the implementation of quantum computation protocols, which exploit the transfer of information among these two physical systems. Here we investigate the interaction among the magnetization precession modes of a small yttrium iron garnet sphere and the microwave electromagnetic modes, resonating in a tridimensional aluminum cavity. In the strong coupling regime, anticrossing features were observed corresponding to various magnetostatic modes, which were excited in a magnetically saturated sample. Time-resolved studies show evidence of Rabi oscillations, demonstrating coherent exchange of energy among photonic and magnon modes. To facilitate the analysis of the standing spin-wave patterns, we propose here a procedure, based on the introduction of a scaling variable. The resulting easier identification of magnetostatic modes can be exploited to investigate, control, and compare many-level hybrid systems in cavity- and opto-magnonics research.

Because of their peculiar nonlinear electro-optic properties, liquid crystals are excellent materials for the production of low-cost photonic components, like for example optical filters and switches and integrated devices for optical waveguides. In this work, we show analitically how fingers in frustrated chiral nematic liquid crystals can be exploited in waveguiding, since they are able to select specific polarization components. Moreover, we show how an external uniform electric field can be used to switch between different textures affecting the propagation through the waveguide. As usual, for rectangular waveguides, the thickness of the layer in which the liquid crystal is confined is used to tune the number of modes propagating inside of it.

Cholesteric Liquid Crystals (CLCs), subject to externally applied magnetic fields and confined between two parallel planar surfaces with strong homeotropic anchoring conditions, are found to undergo transitions to different types of helicoidal configurations with disclinations. Analytical and numerical studies are performed in order to characterise their properties. In particular, we produce a phase diagram for the transitions from the nematic state to the helicoidal phases in terms of the molecular chirality and the strength of the applied magnetic field., Comment: Published version

Lo scambio di idee tra colleghi dello stesso dipartimento influenza in modo significativo gli interessi scientifici reciproci, anche se non direttamente. Sebbene si possa essere in campi di ricerca distanti, ma si è disponibili all’incontro intellettuale, le diverse prospettive assumono delle connotazioni differenti, gusti ed esperienze che altrimenti non avrebbero potuto essere realizzate altrove. Questo è certamente quello che è successo tra la prospettiva dello storico della scienza e la linea di ricerca, alla quale l’autore si è dedicato nei primi anni della sua attività, orientata all’esplorazione in un contesto geometrico di una classe rilevante di sistemi dinamici.

In this work, we analyze the scattering of light by the so-called spherulites or skyrmions in cholesteric liquid crystals. These are quasi-planar localized excitations of the director configuration. We compute the cross section of the polarization conversion for polarized incident light in the Born approximation, considering the anisotropic optical properties of the liquid crystal and the shape of the spherulite. We compare the results obtained by the analytical and the numerical skyrmion solutions found for several values of the model parameters. Finally, possible practical employments and theoretical extensions in the study of the phenomenon are foreseen.

We study the light scattering by localized quasi planar excitations of a Cholesteric Liquid Crystal known as spherulites. Due to the anisotropic optical properties of the medium and the peculiar shape of the excitations, we quantitatively evaluate the cross section of the axis-rotation of polarized light. Because of the complexity of the system under consideration, first we give a simplified, but analytical, description of the spherulite and we compare the Born approximation results in this setting with those obtained by resorting to a numerical exact solution. The effects of changing values of the driving external static electric (or magnetic) field is considered. Possible applications of the phenomenon are envisaged., 18 pages, 14 figures

In this work, we study surface modifications of AISI 420 stainless steel specimens in order to improve their surface properties. Oxidation resistance and surface micro-hardness were analyzed. Using an ion beam delivered by a Laser Ion Source (LIS) coupled to an electrostatic accelerator, we performed implantation of low energy yttrium ions on the samples. The ions experienced an acceleration passing through a gap whose ends had a potential difference of 60 kV. The gap was placed immediately before the samples surface. The LIS produced high ions fluxes per laser pulse, up to 3x1011 ions/cm2, resulting in a total implanted flux of 7x1015 ions/cm2. The samples were characterized before and after ion implantation using two analytical techniques. They were also thermally treated to investigate the oxide scale. The crystal phases were identified by an X-ray diffractometer, while the micro-hardness was assayed using the scratch test and a profilometer. The first analysis was applied to blank, implanted and thermally treated sample surface, while the latter was applied only to blank and implanted sample surfaces. We found a slight increase in the hardness values and an increase to oxygen resistance. The implantation technique we used has the advantages, with respect to conventional methods, to modify the samples at low temperature avoiding stray diffusion of ions inside the substrate bulk.

Within the framework of Oseen-Frank theory, we analyse the static configurations for chiral liquid crystals. In particular, we find numerical solutions for localised axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known as either \textit{spherulites} or \textit{cholesteric bubbles}, which have been observed experimentally in these systems. Relations with nonlinear integrable equations have been outlined and are used to study asymptotic behaviors of the solutions. By using analytical methods, we build approximated solutions of the equilibrium equations and we analyse the generation and stabilization of these states in relation to the material parameters, the external fields and the anchoring boundary conditions., 13 pages, 13 figures, Conference: PMNP 2017: 50 years of IST, Gallipoli (LE)- Italy June 17-24, 2017

The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra $o(3,1)$ as its maximal finite-dimensional subalgebra. The entire algebra generates the conformal group of the Euclidean plane $E_2$. This infinite-dimensional algebra distinguishes the elliptic Liouville equation from the hyperbolic one with its symmetry algebra that is the direct sum of two Virasoro algebras. Following a discretisation procedure developed earlier, we present a difference scheme that is invariant under the group $O(3,1)$ and has the elliptic Liouville equation in polar coordinates as its continuous limit. The lattice is a solution of an equation invariant under $O(3,1)$ and is itself invariant under a subgroup of $O(3,1)$, namely the $O(2)$ rotations of the Euclidean plane.

We consider the Ω-deformed $$ \mathcal{N}=2 $$ SU(2) gauge theory in four dimensions with N f = 4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters e 1 , e 2, the scalar field expectation value a, and the hypermultiplet masses m = (m 1 , m 2 , m 3 , m 4). Motivated by recent findings in the $$ \mathcal{N}={2}^{*} $$ theory, we explore the theories that are characterized by special fixed ratios e 2 /e 1 and m /e 1 and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π N of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the $$ \mathcal{N}={2}^{*} $$ gauge theory, the full prepotential of the Π N theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov’s recursion for the Π N conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π1 and Π2 conformal blocks.

We consider an electrically charged particle simultaneously interacting with a magnetic monopole and a dual monopole in the momentum space. It is a prototype of a three-dimensional system involving noncommuting and/or noncanonical variables but having geometric and also gauge symmetries in both the position and momentum spaces. We discuss the main features of the motions and conservation laws and the analogies to the case of planar motion.

We consider a chain of SU(2)4 anyons with transitions to a topologically ordered phase state. For half-integer and integer indices of the type of strongly correlated excitations, we find an effective low-energy Hamiltonian that is an analogue of the standard Heisenberg Hamiltonian for quantum magnets. We describe the properties of the Hilbert spaces of the system eigenstates. For the Drinfeld quantum SU(2)k×\(\overline {SU(2)_k } \) doubles, we use numerical computations to show that the largest eigenvalues of the adjacency matrix for graphs that are extended Dynkin diagrams coincide with the total quantum dimensions for the levels k = 2, 3, 4, 5. We also formulate a hypothesis about the reason for the universal behavior of the system in the long-wave limit.

In this work, the photoemission performance of rough and smooth cathodes is presented. The cathodes were made up of pure yttrium metal bulk. For evaluation of the photocathodes, a KrF excimer laser, operating at 248 nm wavelength, 5 eV photon energy and 23 ns full width at half maximum (FWHM) was used. The targets were tested in a vacuum photodiode cell at 10^(-7) mbar; they were irradiated at normal incidence and the anode-cathode distance was set to 5 mm. The measurements were performed after a series of electric breakdowns between anode and cathode, induced under high laser energy and high accelerating voltage. This operation was performed in order to restore/increase the surface roughness. For the rough cathode, the maximum output current was 10.5 A, reached at 25 kV and 12 mJ laser energy; the maximum quantum efficiency (QE) value was 1.3 x 10^(-4), whereas for the smooth cathode, the maximum output current was 8.4 A and the maximum QE value was 7.0 x 10^(-5), calculated in the same experimental conditions. The temporal behavior of photoemission from these cathodes was studied. Plasma production and Schottky effect played a fundamental role in this process.

In this work, wave formation in laser-produced plasma is investigated by an analysis of time-of-flight signal of the electron pulse. Electrons are extracted from a non-equilibrium plasma, generated by pulsed laser ablation on a solid Ge target. The process is represented by ion-acoustic waves, which are generated from an external perturbation, given by the positive bias voltage of a Faraday cup. The characteristics of the waves depend substantially on the geometry of the plasma expansion chamber and on laser fluence, but are independent on bias potential. A KrF excimer UV laser was employed for plasma generation. Measurements were performed at two different laser fluences, 4 and 7 J/cm2. The plasma created propagates with a mean velocity of about 1.1 × 104 m/s. A movable Faraday cup was employed in order to collect electrons at different bias voltage values.

The main purpose of this article is to show how symmetry structures in par- tial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are com- pared with exact solutions satisfying the same boundary conditions. All three discretizations are on four point lattices. One preserves linearizability of the equation, another the infinite- dimensional symmetry group as higher symmetries, the third one preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point in- variant scheme that gives a better approximation of the equation, but significantly worse numerical results for solutions is presented and discussed.

The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries. We do however construct a difference system approximating the Liouville equation that is invariant under the maximal finite subgroup ##IMG## [http://ej.iop.org/images/1751-8121/48/2/025204/jpa504755ieqn1.gif] {$S{{L}_{x}}(2,mathbb{R})otimes S{{L}_{y}}(2,mathbb{R})$} . The invariant scheme is an explicit one and provides a much better approximation of exact solutions than a comparable standard (noninvariant) scheme and also than a scheme invariant under an infinite dimensional group of generalized symmetries.

The main physical result of this paper are exact analytical solutions of the heavenly equation, of importance in the general theory of relativity. These solutions are not invariant under any subgroup of the symmetry group of the equation. The main mathematical result is a new method of obtaining noninvariant solutions of partial differential equations with infinite dimensional symmetry groups. The method involves the compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup, the latter acting transitively on the submanifold of the common solutions. By studying the integrability of the resulting conditions, one can provide an explicit foliation of the entire solution manifold of the considered equations., 32 pages, Latex, corrected typos, submitted to J. Phys. A: Math. Gen. on April 13, 2001

The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand, to periodic systems on the other. Boundary conditions are introduced to reduce theories on an infinite lattice to those on semi-infinite, or finite ones.

In this work the experimental results of an electron beam generated from a Cu photocathode are reported. Anexcimer laser of 222 nm wavelength illuminated the cathode. The electron beam generated got a maximum outputcurrent of 410 mA at 50 kV accelerating voltage. To assess the geometrical beam qualities an emittance meter wasdeveloped. This instrumentation allowed to determine the electron beam characteristics measuring the current directionby small Faraday cups. The emittance values were calculated analysing the beamlet spatial distribution and calculatingthe distribution function containing the 80%, 50% and 10% of total points in the phase space. The correspondingnormalised emittances were 10, 9 and 0.6p mm mrad. The emittance in the zero charge limit was also calculated whichcan be ascribed to the thermal emittance, the plasma e•ect and the surface imperfections. Analysing even 2 ns theFaraday cup pulses, we also measured the time evolution of the emittance on x-axis and y-axis. The values foundincreased as the current intensity increased, while they decreased at the tail of the current demonstrating a residualemittance. Considering a cathode plane surface, we developed a mathematics package for calculating the theoreticalvalue of the emittance. O 2000 Elsevier Science B.V. All rights reserved.PACS: 29.25; 42.55; 41.80Keywords: Electron beam; Emittance; Photocathode

The integrability of a system which describes constant mean curvature surfaces by means of the adapted Weierstrass–Enneper inducing formula is studied. This is carried out by using a specific transformation which reduces the initial system to the completely integrable two-dimensional Euclidean nonlinear sigma model. Through the use of the apparatus of differential forms and Cartan theory of systems in involution, it is demonstrated that the general analytic solutions of both systems possess the same degree of freedom. Furthermore, a new linear spectral problem equivalent to the initial Weierstrass–Enneper system is derived via the method of differential constraints. A new procedure for constructing solutions to this system is proposed and illustrated by several elementary examples, including a multi-soliton solution.

The Skyrme-Faddeev model admits exact analytical non localized solutions, which describe magnetic domain wall solutions when multivalued singularities appear or, differently, always regular periodic nonlinear waves, which may degenerate into linear spin waves or solitonic structures. Here both classes of solutions are derived and discussed and a general discusssion about the existence of integrable subsectors of the model is addressed.

We show that the classical non-Abelian pure Chern–Simons action is related to nonrelativistic models in (2+1) dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern–Simons fields, associated with the isotropy subgroup of the considered symmetric space. Thus a relation between the Chern–Simons theory and the Davey–Stewartson hierarchy is established in a natural way. The Backlund transformations are interpreted in terms of Chern–Simons constraints. Moreover, certain nonintegrable Heisenberg models can be embedded into the pure Chern–Simons theory. The main classical and quantum properties of these systems are discussed.

We show that the classical non-abelian pure Chern-Simons action is related in a natural way to completely integrable systems of the Davey-Stewartson hyerarchy, via reductions of the gauge connection in Hermitian spaces and by performing certain gauge choices. The B\"acklund Transformations are interpreted in terms of Chern-Simons equations of motion or, on the other hand, as a consistency condition on the gauge. A mapping with a nonlinear $\sigma$-model is discussed., Comment: 11 pages, Latex

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation of periodic wave states, leading to a quasi-linear system. The reduction to general hydrodynamic systems have been considered and it is compared with other integrable reductions of the system., Comment: 16 pages, 5 figures

A system of partial differential equations, describing one-dimensional nematic liquid crystals is studied by Lie group analysis. These equations are the Euler–Lagrange equations associated with a free energy functional that depends on the mass density and the gradient of the mass density. The group analysis is an algorithmic approach that allows us to show all the point symmetries of the system, to determine all possible symmetry reductions and, finally, to obtain invariant solutions in the form of travelling waves. The Hamiltonian formulation of the dynamical equations is also considered and the conservation laws found by exploiting the local symmetries.

Resorting to the Lagrange–Souriau 2-form formalism, a wide class of systems are derived in non-commuting and/or non-canonical variables, nor the Darboux theorem can be helpful, because of the gauge character of all phase-space variables. As a paradigmatic example, the motion of a charged particle in a magnetic monopole field in the presence of a momentum space monopole is considered.

In the present article we perform the symmetry analysis of the Skyrme-Faddeev system at the level of point symmetries. We provide a new simple approximate expression for the axisymmetric solutions, with an accuracy of 10−4 in the static energy value. Furthermore, we proceed to a reduction with respect to all discrete Platonic rotation subgroups, providing the equation for the radial profile function.

We formulate the two-dimensional planar classical continuous Heisenberg spin model as a constrained Chern-Simons gauged nonlinear Schrödinger system. Several physical consequences in the framework of the anyon field theory are discussed. We study the Hamiltonian structure of the model, which is quantized using the gauge invariant approach. A preliminary study of the quantum states is presented.

A multidimensional model for a ferromagnetic continuum with hydrodynamical properties, which can be regarded as a modified Landau-Lifshitz equation, is presented. The treatment of some physical examples suggests that the fluid vorticity has to be proportional to the magnetic topological current. The model can be written in the Hirota bilinear form. In two spatial dimensions, the existence of a positive definite ‘energy’ functional is shown. The Bogomol'nyi inequality leads to the self-dual equations of the model, which can be expressed by the Liouville equation. By using time-dependent gauge transformations, a wide class of solutions can be generated. These are, in general, associated with the linear problem of the modified Kadomtsev-Petviashvili equation. In some particular cases, the isolated vortices can move along arbitrary trajectories on the plane. The quantization problem of the time-dependent vortex configurations is briefly discussed, in relation to the possible evaluation of their energy spectrum.

A spin-field model in two space and one time dimensions is proposed and investigated using a bilinearization technique. This model, which can be considered as a modified version of the Ishimori system, allows a Hamiltonian formulation, a symmetry algebra of Kac-Moody type with a loop-algebra structure, and the conformal invariance property. Many nonlinear excitations are found, which turn out to be of the helical and roton type, meronlike configurations endowed with a fractional topological charge, radially symmetric solutions, and domain walls. Our results are compared with those of the study of the O(3) nonlinear \ensuremath{\sigma} model and the Ishimori system. Finally, the physical role of both our model and the Ishimori system is discussed in the light of certain reduced equations which find applications in the theory of vortex filaments in liquid $^{4}\mathrm{He}$ and in dealing with the two spin-correlation functions of the two-dimensional Ising model in the scaling limit.

A self-dual Chern-Simons system and its Lax pair are derived from the tangent space representation of a two-dimensional nonlinear σ-model, endowed with a gauge field. The related “matter” field density obeys the Liouville equation, whose N-soliton solutions correspond to the magnetic vortices in the static self-dual planar Heisenberg model. It is shown that the topological charge and the total vorticity correspond to the electric charge and the magnetic flux for the Chern-Simons system, respectively. General holomorphic solutions of the system studied generate a large class of static solutions to the Davey-Stewartson and Ishimori equations.

Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects., Comment: Review paper. Published version

Partially invariant solutions of a general class of nonlinear Schrodinger equations, involving four arbitrary functions of the modulus rho of the solution and its derivative rho x, are obtained. The modulus rho ( xi ) is assumed to depend on a symmetry variable xi , whereas the phase omega (x,t) depends on both independent variables. Both rho and omega are obtained explicitly, as are the conditions on the coefficients in the equation, necessary for such solutions to exist.

The concept of partially invariant solutions is discussed in the framework of the group analysis of systems of partial differential equations. Using a general and systematic approach based on subgroup classification methods, nontrivial partially invariant solutions for specific equations are explicitly obtained, belonging to the NLKGE and NLLE classes in two dimensions. It is proven that the obtained partially invariant solutions are distinct from the invariant ones and from solutions obtained by other methods of reducing PDEs to ODEs.

The gauge equivalence between a noncompact version of the Ishimori spin model and the Davey–Stewartson equation is established. Explicit relationships connecting the corresponding two sets of fields involved in these systems are obtained via any pair of complex functions satisfying an equation of the Schrodinger type for a free particle. Using these formulas, two examples of classes of nontrivial exact singular solutions to the Davey–Stewartson equation are given. One of them is of the closed stringlike type, while the other is doubly periodic and is expressed in terms of Riemann theta functions. The role played by the symmetry group associated with the gauge equivalent equations under consideration is also clarified.

We consider a universal representation for the Hamiltonian of systems in topologically ordered phase states. We show that for strongly correlated electronic systems, the Hamiltonian expressed in terms of projectors of the Temperley-Lieb algebra on the spin singlet state has the form of a two-dimensional Bloch matrix in the case of doubly linked excitation world lines; in this case, different topological orderings are separated by a quantum critical point where the matrix elements of the Hamiltonian vanish.

Weakly nonlinear dispersive longitudinal waves in an infinite homogeneous collisionless plasma in the presence of an external constant and uniform magnetic field are considered. Under specific physical assumptions and for an arbitrary three-dimensional envelope modulation of a plane wave, a purely differential system is derived. Taking into account the effect of wave-wave and wave-particle interaction, the evolution of the modulation is described by a modified nonlinear Schrödinger equation, coupled to the space perturbation charge densities. The generation of a static mode is described. As a particular case the electron waves are discussed and some special solutions, resorting to the theory of the perturbed solitions.