In a free fermion chain, the coarse-grained density distribution becomes almost uniform at sufficiently large typical times for any initial state with fixed macroscopic particle number, proving macroscopic irreversibility from unitary evolution.
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.
verdicts
UNVERDICTED 3representative citing papers
Rigorous proof that random half-chain initial states in a low-density free-fermion model thermalize, with local particle counts matching equilibrium at long times with high probability.
The paper establishes that typical states in a grand-canonical micro-canonical Hilbert subspace produce the grand-canonical density matrix and a GAP/Scrooge wave-function distribution for the subsystem.
citing papers explorer
-
Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain
In a free fermion chain, the coarse-grained density distribution becomes almost uniform at sufficiently large typical times for any initial state with fixed macroscopic particle number, proving macroscopic irreversibility from unitary evolution.
-
Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system
Rigorous proof that random half-chain initial states in a low-density free-fermion model thermalize, with local particle counts matching equilibrium at long times with high probability.
-
Grand-Canonical Typicality
The paper establishes that typical states in a grand-canonical micro-canonical Hilbert subspace produce the grand-canonical density matrix and a GAP/Scrooge wave-function distribution for the subsystem.