Related papers: Typicality for Generalized Microcanonical Ensemble…
We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the…
The evolution of a quasi-isolated finite quantum system from a nonequilibrium initial state is considered. The condition of quasi-isolation allows for the description of the system dynamics on the general basis, without specifying the…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator $\rho$ of low purity, $\tr\rho^2\ll 1$, and yielding the ensemble averaged expectation value $\tr(\rho A)$ for any…
The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase…
The emergence of statistical mechanics from quantum dynamics is a central problem in quantum many-body physics. Deriving observables aligned with the prediction of the canonical ensemble for a quantum system relies on the presence of a bath…
It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e.,…
An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
Quantum systems are invariably open, evolving under surrounding influences rather than in isolation. Standard open quantum system methods eliminate all information on the environmental state to yield a tractable description of the system…
With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
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…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
Microcanonical description is characterized by the presence of an internal symmetry closely related with the dynamical origin of this ensemble: the reparametrization invariance. Such symmetry possibilities the development of a non…
We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its…
Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…