Search Results (10)

In the present paper, a modification of the standard mean-field model is considered, allowing for the description of the formation of a dynamic equilibrium between infected and recovered persons in a population of constant size. The key point of this model is that it highlights two-infection transfer mechanisms depending on the physical nature of the contact between people. We separate the transfer mechanism related directly to the movement of people (the so-called transport processes) from the one occurring at zero relative speed of persons (the so-called social contacts). Under the framework of a physical chemical analogy, the dependencies for the infection transfer rate constants are proposed for both purely transport and social mechanisms of spread. These dependencies are used in discussing the formation of quasi-stationary states in the model, which can be interpreted as endemic equilibrium states. The stability of such endemic equilibria is studied by the method of Lyapunov function. Full article

The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers. Full article

This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described. A generating functional method to constructing irreducible current algebra representations is reviewed, and the ergodicity of the corresponding representation Hilbert space measure is mentioned. The algebraic properties of the so called coherent states are also reviewed, generated by cyclic representations of the Heisenberg algebra on Hilbert spaces. Unbelievable and impressive applications of coherent states to the theory of nonlinear dynamical systems on Hilbert spaces are described, along with their linearization and integrability. Moreover, we present a further development of these results within the modern Lie-algebraic approach to nonlinear dynamical systems on Poissonian functional manifolds, which proved to be both unexpected and important for the classification of integrable Hamiltonian flows on Hilbert spaces. The quantum current Lie algebra symmetry properties and their functional representations, interpreted as a universal algebraic structure of symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics on functional manifolds, are analyzed in detail. Based on the current algebra symmetry structure and their functional representations, an effective integrability criterion is formulated for a wide class of completely integrable Hamiltonian systems on functional manifolds. The related algebraic structure of the Poissonian operators and an effective algorithm of their analytical construction are described. The current algebra representations in separable Hilbert spaces and the factorized structure of quantum integrable many-particle Hamiltonian systems are reviewed. The related current algebra-based Hamiltonian reconstruction of the many-particle oscillatory and Calogero–Moser–Sutherland quantum models are reviewed and discussed in detail. The related quasi-classical quantum current algebra density representations and the collective variable approach in equilibrium statistical physics are reviewed. In addition, the classical Wigner type current algebra representation and its application to non-equilibrium classical statistical mechanics are described, and the construction of the Lie–Poisson structure on the phase space of the infinite hierarchy of distribution functions is presented. The related Boltzmann–Bogolubov type kinetic equation for the generating functional of many-particle distribution functions is constructed, and the invariant reduction scheme, compatible with imposed correlation functions constraints, is suggested and analyzed in detail. We also review current algebra functional representations and their geometric structure subject to the analytical description of quasi-stationary hydrodynamic flows and their magneto-hydrodynamic generalizations. A unified geometric description of the ideal idiabatic liquid dynamics is presented, and its Hamiltonian structure is analyzed. A special chapter of the review is devoted to recent results on the description of modified current Lie algebra symmetries on torus and their Lie-algebraic structures, related to integrable so-called heavenly type spatially many-dimensional dynamical systems on functional manifolds. Full article

Resonant tunneling devices are still under study today due to their multiple applications in optoelectronics or logic circuits. In this work, we review an out-of-equilibrium GaAs/AlGaAs double-barrier resonant tunneling diode system, including the effect of donor density and external potentials in a self-consistent way. The calculation method uses the finite-element approach and the Landauer formalism. Quasi-stationary states, transmission probability, current density, cut-off frequency, and conductance are discussed considering variations in the donor density and the width of the central well. For all arrangements, the appearance of negative differential resistance (NDR) is evident, which is a fundamental characteristic of practical applications in devices. Finally, a comparison of the simulation with an experimental double-barrier system based on InGaAs with AlAs barriers reported in the literature has been obtained, evidencing the position and magnitude of the resonance peak in the current correctly. Full article

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron. Full article

We investigate the overdamped Langevin motion for particles in a potential well that is asymptotically flat. When the potential well is deep as compared to the temperature, physical observables, like the mean square displacement, are essentially time-independent over a long time interval, the stagnation epoch. However, the standard Boltzmann–Gibbs (BG) distribution is non-normalizable, given that the usual partition function is divergent. For this regime, we have previously shown that a regularization of BG statistics allows for the prediction of the values of dynamical and thermodynamical observables in the non-normalizable quasi-equilibrium state. In this work, based on the eigenfunction expansion of the time-dependent solution of the associated Fokker–Planck equation with free boundary conditions, we obtain an approximate time-independent solution of the BG form, being valid for times that are long, but still short as compared to the exponentially large escape time. The escaped particles follow a general free-particle statistics, where the solution is an error function, which is shifted due to the initial struggle to overcome the potential well. With the eigenfunction solution of the Fokker–Planck equation in hand, we show the validity of the regularized BG statistics and how it perfectly describes the time-independent regime though the quasi-stationary state is non-normalizable. Full article

In the paper, several theoretical approaches to the determination of the reduced absorption and emission coefficients under local thermodynamic equilibrium conditions were exposed and discussed. The full quantum-mechanical procedure based on the Fourier grid Hamiltonian method was numerically robust but time consuming. In that method, all transitions between the bound, free, and quasi-bound states were treated as bound–bound transitions. The semi-classical method assumed continuous energies of ro-vibrational states, so it did not give the ro-vibrational structure of the molecular bands. That approach neglected the effects of turning points but agreed with the averaged-out quantum-mechanical spectra and it was computer time efficient. In the semi-quantum approximation, summing over the rotational quantum number J was done analytically using the classical Franck–Condon principle and the stationary–phase approximation and its consumption of computer time was lower by a few orders of magnitude than the case of the full quantum-mechanical approach. The approximation described well the vibrational but not the rotational structure of the molecular bands. All the above methods were compared and discussed in the case of a visible and near infrared spectrum of LiHe, Li₂, and Cs₂ molecules in the high temperature range. Full article

While it is known that strongly correlated transition metal oxides described by a multi-band Hubbard model show microscopic multiscale phase separation, little is known about the possibility to manipulate them with vacuum ultraviolet (VUV), 27 eV lighting. We have investigated the photo-induced effects of VUV light illumination of a super-oxygenated La₂NiO_4+y single crystal by means of scanning photoelectron microscopy. VUV light exposure induces the increase of the density of states (DOS) in the binding energy range around E_b = 1.4 eV below E_F. The photo-induced states in this energy region have been predicted due to clustering of oxygen interstitials by band structure calculations for large supercell of La₂CuO_4.125. We finally show that it is possible to generate and manipulate oxygen rich domains by VUV illumination as it was reported for X-ray illumination of La₂CuO_4+y. This phenomenology is assigned to oxygen-interstitials ordering and clustering by photo-illumination forming segregated domains in the La₂NiO_4+y surface. Full article

We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb) with negligible dissipation. For the classical equilibrium Boltzmann distribution, W_c,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc_,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using W_c,eq), the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases) are assumed to be quasi-definite functionals regarding their dependences on momentum (q). That yields orthogonal polynomials, H_Q,n(q), for Weq (and for stationary W_st), non-equilibrium moments, W_n, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary W_st is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq) for the W_n’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant W_eq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not far from Gaussian, and thermalization could possibly be justified. Full article

In plasmas, Debye screening structures the possible correlations between particles. We identify a phase space minimum h_* in non-equilibrium space plasmas that connects the energy of particles in a Debye sphere to an equivalent wave frequency. In particular, while there is no a priori reason to expect a single value of h_* across plasmas, we find a very similar value of h_* ? (7.5 ± 2.4)×10^?22 J·s using four independent methods: (1) Ulysses solar wind measurements, (2) space plasmas that typically reside in stationary states out of thermal equilibrium and spanning a broad range of physical properties, (3) an entropic limit emerging from statistical mechanics, (4) waiting-time distributions of explosive events in space plasmas. Finding a quasi-constant value for the phase space minimum in a variety of different plasmas, similar to the classical Planck constant but 12 orders of magnitude larger may be revealing a new type of quantization in many plasmas and correlated systems more generally. Full article