Related papers: Statistical Mechanics of Lam\'e Solitons
We analyze the low temperature asymptotics of the quasi-stationary distribution associated with the overdamped Langevin dynamics (a.k.a. the Einstein-Smoluchowski diffusion equation) in a bounded domain. This analysis is useful to…
In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into Landau-Lifshitz (LL) equation, which describes the…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
Effects of Lie type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the…
We investigate the statistical mechanics of the photonic Ablowitz-Ladik lattice, the integrable version of the discrete nonlinear Schr\"odinger equation. In this regard, we demonstrate that in the presence of perturbations the complex…
Here we comment on the thermodynamic inconsistency problem and the reformulation of statistical mechanics of widely studied quasiparticle models of quark-gluon plasma. Their starting relation, the expression for pressure itself is a wrong…
Local integrals of motion (LIOMs) play a key role in understanding the long-time properties of closed macroscopic systems. They were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of…
We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the…
We revisit the exact thermodynamic description of the classical sine-Gordon field theory, a notorious integrable model. We found that existing results in the literature based on the soliton-gas picture did not correctly take into account…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic Lattice Dynamics provides a powerful…
We investigate the low-temperature electrical and thermal transport properties in atomically precise metallic heterostructures involving strongly-correlated electron systems. The model of the Mott-insulator/ band-insulator superlattice was…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use…
Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven, damped nonlinear Schr\"odinger equation. We find that the ordinary differential equations, which…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…