Related papers: Statistical mechanics of a nonlinear discrete syst…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
This work investigates a quantum system described by a Hamiltonian operator in a two dimensional noncommutative space. The system consists of an electron subjected to a perpendicular magnetic field $\mathbf{B}$, coupled to a harmonic…
Stochastic extensions of the Schrodinger equation have attracted attention recently as plausible models for state reduction in quantum mechanics. Here we formulate a general approach to stochastic Schrodinger dynamics in the case of a…
We study the classical non-equilibrium statistical mechanics of scalar field theory on the lattice. Steady states are analyzed near and far from equilibrium. The bulk thermal conductivity is computed, including its temperature dependence.…
This work presents a unified perspective on thermal equilibrium and quantum dynamics by examining the simplest quantum system, a qubit, as a minimal model. We show that both the thermal partition function and the Loschmidt amplitude can be…
Equilibrium statistical mechanics provides a robust framework for characterizing phase transitions in systems whose microsopic dynamics are time-reversible. Efforts to develop and validate theoretical frameworks for time-irreversible,…
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
The statistical mechanics of 1D and 2D Ginzburg-Landau systems is evaluated analytically, via the transfer matrix method, using an expression of the ground state energy of the quartic anharmonic oscillator in an external field. In the 2D…
We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
The localization of energy in the discrete nonlinear Schroedinger equation is explained with statistical methods. The partition function and the entropy of the system are computed for low-amplitude initial conditions. Detailed predictions…
We introduce a mass conserving stochastic perturbation of the discrete nonlinear Schr\"odinger equation that models the action of a heat bath at a given temperature. We prove that the corresponding canonical Gibbs distribution is the unique…
We revisit here the problem of the collective non-equilibrium dynamics of a classical statistical system at a critical point and in the presence of surfaces. The effects of breaking separately space- and time-translational invariance are…
We consider the Schr\"odinger equation with a Hamiltonian given by a second order difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the construction and…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…