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Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to…
We consider a system of particles confined in a box $\La\subset\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low…
We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested…
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields.…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble, whereas canonical ones fail in the most interesting, mostly inhomogeneous, situations like phase separations or away from the thermodynamic…
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive…
We consider a stochastic $N$-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…