Related papers: Typicality for Generalized Microcanonical Ensemble…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what…
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…
A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…
For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems.…
We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum…
Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles…
Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble…
It is shown, that the only reason for possibility of using microcanonical ensemble is that there are probabilistic processes in microworld, that are not described by quantum mechanic. On a simple example it is demonstrated, that canonical…
We review here the microcanonical and canonical ensembles constructed on an underlying generalized quantum dynamics and the algebraic properties of the conserved quantities. We discuss the structure imposed on the microcanonical entropy by…
Expectation value of dynamical variables in thermodynamically equilibrium state can be typically provided through well-known canonical average. The average includes tremendous number of possible states considered far beyond practically…
We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The…
We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
We discuss a property of our recently introduced generalized canonical ensemble (J. Stat. Phys. 119 (2005) 1283). We show that this ensemble can be used to transform metastable or unstable (nonequilibrium) states of the standard canonical…