Related papers: Grand-Canonical Typicality
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course,…
We describe a Monte Carlo scheme for simulating polydisperse fluids within the grand canonical ensemble. Given some polydisperse attribute $\sigma$, the state of the system is described by a density distribution $\rho(\sigma)$ whose form is…
We study a classically chaotic system which is described by a Hamiltonian $H(Q,P;x)$ where $(Q,P)$ are the canonical coordinates of a particle in a 2D well, and $x$ is a parameter. By changing $x$ we can deform the `shape' of the well. The…
When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total…
On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines---within fluctuations and behaviour very near the origin---smooth canonical matrices whose forms depend on the rank of…
We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…
We derive the equation of the critical curve and calculate the renormalized masses of the $SO(N)$-symmetric $\lambda\phi^{4}$ model in the presence of a homogeneous external source. We do this using the Gaussian-Perturbative approximation…
A theoretical scheme for the treatment of an open molecular system with electrons and nuclei is proposed. The idea is based on the Grand Canonical description of a quantum region embedded in a classical reservoir of molecules. Electronic…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
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 Random Transverse Field Ising Chain is the simplest disordered model presenting a quantum phase transition at T=0. We compare analytically its finite-size scaling properties in two different ensembles for the disorder (i) the canonical…
The CSL dynamical collapse structure, adapted to the relativistically invariant model where the collapse-generating operator is a one-dimensional scalar field $\hat\phi(x,t)$ (mass $m$) is discussed. A complete solution for the density…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
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…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the R\'{e}nyi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single…
Motivated by the qualitative picture of Canonical Typicality, we propose a refined formulation of the Eigenstate Thermalization Hypothesis (ETH) for chaotic quantum systems. The new formulation, which we refer to as subsystem ETH, is in…
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By…