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.
From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
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abstract
Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of mutually interacting subsystem and heat bath, and assume that the whole system is initially in a pure state (which can be far from equilibrium) with small energy fluctuation. Under the "hypothesis of equal weights for eigenstates", we derive the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses.
fields
cond-mat.stat-mech 2verdicts
UNVERDICTED 2representative 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.
citing papers explorer
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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.
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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.