Large deviations for ideal quantum systems

Abstract

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.

28 pages, LaTeX 2e

References in corpus (1)

• Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

Cited by in corpus (20)

• The large deviation approach to statistical mechanics
• Non-equilibrium equalities with unital quantum channels
• Spatial random permutations and infinite cycles
• Large deviations in quantum lattice systems: one-phase region
• Large deviations for quantum spin systems
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Large deviations in rarefied quantum gases
• Typical support and Sanov large deviations of correlated states
• Feynman cycles in the Bose gas
• Bose--Einstein Condensation in the Large Deviations Regime with Applications to Information System Models
• Derivation of the Euler Equations from Quantum Dynamics
• Large Deviations, Central Limit and dynamical phase transitions in the atom maser
• Large Deviations in the Superstable Weakly Imperfect Bose Gas
• Large deviation generating function for energy transport in the Pauli-Fierz model
• Large Deviation Principle for Non-Interacting Boson Random Point Processes
• Large Deviations in Weakly Interacting Fermions -- Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
• On the Fluctuations of Macroscopic Observables in Quantum Nonequilibrium Steady States
• Large deviations in the quantum quasi-1D jellium
• Ruelle-Lanford functions for quantum spin systems