Related papers: A generalized quantum microcanonical ensemble
It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…
We consider conditions under which an isolated quantum system approaches a microcanonical equilibrium state. A key component is the eigenstate thermalisation hypothesis, which proposes that all energy eigenstates appear thermal. We…
The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the macrostate levels of definition of nonequivalent ensembles are introduced. The many…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying…
The Blume-Capel model with infinite-range interactions presents analytical solutions in both canonical and microcanonical ensembles and therefore, its phase diagram is known in both ensembles. This model exhibits nonequivalent solutions and…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
Few parameters dependent generalised entropy includes Tsallis entropy, R{\'e}nyi entropy, Sharma-Mittal entropy, Barrow entropy, Kaniadakis entropy, etc as particular representatives. Its relation to physical systems is not always clear. In…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the…
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum…
The approach to equilibrium for systems interacting with their environment by being regularly exposed to low energy, low intensity pulses of some type of quanta is studied. Assuming a randomness condition on the interaction of these quanta…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
The main purpose of this tutorial is to elucidate in details what should be meant by ensemble of states in quantum mechanics, and to properly address the problem of discriminating, exactly or approximately, two different ensembles. To this…
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 generalize L\'evy's lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a much more general class of measures, so-called GAP measures. For any given density matrix $\rho$ on a…