相关论文: Derivation and Improvements of the Quantum Canonic…
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the…
We propose a tensor network algorithm for the efficient sampling of quantum pure states belonging to a generalized microcanonical ensemble. The algorithm consists in an adaptation of the power method to a recently introduced ensemble of…
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…
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and…
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…
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…
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 has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a…
Usual approach to the foundations of quantum statistical physics is based on conventional micro-canonical ensemble as a starting point for deriving Boltzmann-Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical…
We propose a Gaussian ensemble as a description of the long-time dynamics of isolated quantum integrable systems. Our approach extends the Generalized Gibbs Ensemble (GGE) by incorporating fluctuations of integrals of motion. It is…
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…
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…
Shortened abstract: Microcanonical equilibrium macrostates are characterized as the solutions of a constrained minimization problem, while canonical equilibrium macrostates are characterized as the solutions of a related, unconstrained…
Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here we propose a theory of…
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…
Starting from the quantum mechanics for $N$ particles, we show that we can directly derive the microcanonical ensemble average of the physical quantity $A$ by using only the long time average and the equal probability assumption for the…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
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…
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical…