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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

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.

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 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.

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

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.

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.

A modified version of the Ishimori model endowed with SU(1,1) symmetry is proposed. Some classes of both rational and biperiodic exact singular solutions are obtained. These solutions are characterized by a topological charge.

A Comment on the Letter by Di Xiao, Junren Shi, and Qian Niu, Phys. Rev. Lett. 95, 137204 (2005). The authors of the Letter offer a Reply.

Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels or to accelerate some quantum processes as, for example, the factorization in Shor's Algorithm. Moreover, entanglement is a physical observable directly measured by the von Neumann entropy of the system. We have used this concept in order to give a physical meaning to the electron correlation energy in systems of interacting electrons. The electronic correlation is not directly observable, since it is defined as the difference between the exact ground state energy of the many--electrons Schroedinger equation and the Hartree--Fock energy. We have calculated the correlation energy and compared with the entanglement, as functions of the nucleus--nucleus separation using, for the hydrogen molecule, the Configuration Interaction method. Then, in the same spirit, we have analyzed a dimer of ethylene, which represents the simplest organic conjugate system, changing the relative orientation and distance of the molecules, in order to obtain the configuration corresponding to maximum entanglement., Comment: 15 pages, 7 figures, standard latex

Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic'' central extension is introduced. It is used to describe non-relativistic anyons coupled to an electromagnetic field. Our theory exhibits an anomalous velocity relation of the type used to explain the Anomalous Hall Effect. The Hall motions, characterized by a Casimir of the enlarged algebra, become mandatory for some critical value(s) of the magnetic field. The extension of our scheme yields the semiclassical effective model of the Bloch electron., Comment: LaTeX, 7 pages. No figures. One more reference added

We generated electron beams by a Nb polycrystalline photocathode illuminated by different wavelength excimer lasers; an XeCl and a KrCl. The cathode surface roughness was 0.09. At low accelerating voltage, the electron beams were governed by the space-charge effect and their intensity never resulted clipped as previous by the Child-Langmuir law. Instead, the output current waveform was similar to the laser one under saturation regime. The quantum efficiencies were 3.2 x 10-5 and 6.7 x 10-7 for the KrCl and XeCl irradiation, respectively.

We report the experimental characteristics of electron beam propagation under space-charge regime. The electron beams were generated by a Nb polycrystalline photocathode illuminated by two different excimer lasers, a XeCl ~308 nm! and a KrCl ~222 nm!. The laser photon energies were very close to the Nd work function. The cathode surface was mechanically worked in order to study the photoemission from a smooth and a rough surface. At low accelerating voltage the electron beam was dominated by the space-charge effect and its resulting pulse never clipped as predicted by the Child–Langmuir law. Instead, it presented as fast a rise time as the laser one, an intermediate zone, and a tail longer than the laser pulse one. On the other hand, under saturation regime the output current wave form was similar to the laser one. The quantum efficiency was higher for the rough cathode. It corresponded to 3.231025 and 6.731027 for the KrCl and XeCl irradiation, respectively. The maximum current value was an electron bunch containing 980 mA ~8.9 nC!, by means of 1.7 mJ KrCl laser energy and 10 kV of accelerating voltage.

Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF.

We construct the hierarchy of nonlinear difference-difference equations associated with the discrete Schrodinger spectral problem. As examples of equations contained in this hierarchy we obtain the discrete-time Toda and Volterra lattice equations. In the case of the time-discrete Toda lattice, we construct its Lie point and generalized symmetries. Finally, we present its Backlund transformations and relate it to the already constructed symmetries.

A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show that the methods developed in studying classical non-Abelian pure Chern-Simons actions, can be naturally implemented by means of a geometrical interpretation of such systems. The Chern-Simons equation of motion turns out to be related to time evolving 2-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss-Mainardi-Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed., Comment: 24 pages, 1 figure, submitted to J. Math. Phys

Inspired by the geometrical methods allowing the introduction of mechanical systems confined in the plane and endowed with exotic galilean symmetry, we resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide class of 3D systems, involving not commuting and/or not canonical variables, but possessing geometric as well gauge symmetries in position and momenta space too. As a paradigmatic example, a charged particle simultaneously interacting with a magnetic monopole and a dual monopole in momenta space is considered. The main features of the motions, conservation laws and the analogies with the planar case are discussed. Possible physical realizations of the model are proposed.

A classical magnetic model with compact su(2) and non-compact su(1,1) spin phase space admitting the Hirota bilinear form is presented in an arbitrary number of space dimensions. The essential point of the construction is the presence of a velocity field with non-trivial vorticity tensor related to a topological current density. The model modifies in particular a variety of familiar topological equations, such as the Heisenberg ferromagnets and the (2+1)-dimensional O(3) sigma -model. Using the bilinear representation, several special cases and exact solutions of physical interest (spin waves, domain walls and vortices) are considered.

A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed whithin the anyon theory. Thus, we show that static magnetic vortices correspond to the self-dual Chern - Simons solitons and are described by the Liouville equation. The related magnetic topological charge is associated with the electric charge of anyons. Furthermore, vortex - antivortex configurations are described by the sinh-Gordon equation and its conformally invariant extension. Physical consequences of these results are discussed., Comment: 15 pages, Plain TeX, Lecce, June 1993

Recently it has been shown that in two spatial and one temporal dimensions (2+1) there exist localized solitons [1–4]. These coherent structures display a richer phenomenology than the one dimensional solitons. Different effects have been reported successively in a series of papers [5–8]. Some of them are due to the fact that the soliton solution is structurally unstable with respect to special choices of the parameters [6]. Also some quantum-like effects as the non conservation of the number of solitons have been discovered by using direct methods [9–10]. This report is dedicated to the study of the origin and generality of these new effects in the context of the Spectral Transform (ST) theory developed in [11–12].