相关论文: Canonical Typicality For Other Ensembles Than Micr…
We study how the grand-canonical density matrix arises in macroscopic quantum systems. ``Canonical typicality'' is the known statement that for a typical wave function $\Psi$ from a micro-canonical energy shell of a quantum system $S$…
GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix $\rho$ there is a unique measure…
For a quantum system, a density matrix rho that is not pure can arise, via averaging, from a distribution mu of its wave function, a normalized vector belonging to its Hilbert space H. While rho itself does not determine a unique mu,…
We consider an isolated macroscopic quantum system in a pure state $\psi_t$ evolving unitarily in a separable Hilbert space $\mathcal{H}$ and take for granted that different macro states $\nu$ correspond to mutually orthogonal subspaces…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…
We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures,…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
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…
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…
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The thermal equilibrium distribution over quantum-mechanical wave functions is a so-called Gaussian adjusted projected (GAP) measure, $GAP(\rho_\beta)$, for a thermal density operator $\rho_\beta$ at inverse temperature $\beta$. More…
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…
We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently…
Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we…
A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal…
Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics…
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…