An inverse problem in quantum statistical physics
type: Item
instance of: scholarly article
title: An inverse problem in quantum statistical physics
zbMATH Open document ID: 1201.82025
author: Florian Méhats
author: Olivier Pinaud
published in: Journal of Statistical Physics
publication date: 2010-09-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1002.1453
review text: The authors address the problem to establish existence and uniqueness of a statistical operator minimizing the quantum free energy given by the sum of von Neumann entropy and kinetic energy, with the constraint of a given local density \(n(x)\). They provide a rigorous positive answer to the question in dimension one, in a finite box with periodic boundary conditions. The thus obtained statistical operator indeed has a Gibbs form with a suitable chemical potential. The motivation for this work is to obtain a rigorous definition of the notion of local quantum equilibrium state, which is at the basis of recently derived quantum hydrodynamic models.
reviewed by: Bassano Vacchini
Mathematics Subject Classification ID: 82C10
Mathematics Subject Classification ID: 76Y05
zbMATH DE Number: 5786221
zbMATH Keywords: quantum hydrodynamic models
zbMATH Keywords: inverse problem
zbMATH Keywords: density matrix
zbMATH Keywords: entropy minimization under constraint
zbMATH Keywords: quantum statistical physics
zbMATH Keywords: moment realizability
zbMATH Keywords: local equilibrium state
zbMATH Keywords: chemical potential
MaRDI profile type: Publication
OpenAlex ID: W2020284323
arXiv ID: 1002.1453
cites work: Self-consistent relaxation-time models in quantum mechanics
cites work: Central Limits and Homogenization in Random Media
cites work: Quantum drift-diffusion modeling of spin transport in nanostructures
cites work: On quantum extensions to classical spherical harmonics expansion/Fokker-Planck models
cites work: Derivation of viscous correction terms for the isothermal quantum Euler model
cites work: Quantum moment hydrodynamics and the entropy principle
cites work: Quantum energy-transport and drift-diffusion models
cites work: Q5465392
cites work: An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
cites work: Isothermal Quantum Hydrodynamics: Derivation, Asymptotic Analysis, and Simulation
cites work: On quantum hydrodynamic and quantum energy transport models
cites work: Q3530645
cites work: Lieb--Thirring type inequalities and Gagliardo--Nirenberg inequalities for systems
cites work: Compactness properties for trace-class operators and applications to quantum mechanics
cites work: Entropic Discretization of a Quantum Drift-Diffusion Model
cites work: Q3370606
cites work: Q3379025
cites work: On the inverse problem in statistical mechanics
cites work: Global Weak Solutions to Compressible Navier–Stokes Equations for Quantum Fluids
cites work: A derivation of the isothermal quantum hydrodynamic equations using entropy minimization
cites work: Derivation of New Quantum Hydrodynamic Equations Using Entropy Minimization
cites work: Domain of definition of Levermore's five-moment system
cites work: Q3874765
cites work: Moment closure hierarchies for kinetic theories.
cites work: Analysis.
cites work: Hydrodynamical limit for a Hamiltonian system with weak noise
cites work: Q3909512
cites work: Q5694963
DOI: 10.1007/S10955-010-0003-Z
description: scientific article; zbMATH DE number 5786221