Time Scales in the Approach to Equilibrium of Macroscopic Quantum Systems

2013/07/31 by Sheldon Goldstein, Takashi Hara, Hal Tasaki · 99 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Statistical physics #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1103/physrevlett.111.140401

published in Physical Review Letters 111(14), 140401 (American Physical Society) · 5 pages, 1 figure. Some small improvements in version 2. This version will appear in Phys. Rev. Lett

arxiv created 2013/09/05 · openalex publication_date 2013/10/01 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove two theorems concerning the time evolution in general isolated quantum systems. The theorems are relevant to the issue of the time scale in the approach to equilibrium. The first theorem shows that there can be pathological situations in which the relaxation takes an extraordinarily long time, while the second theorem shows that one can always choose an equilibrium subspace, the relaxation to which requires only a short time for any initial state.

Citations

• Approach to thermal equilibrium of macroscopic quantum systems
• Foundation of Statistical Mechanics under experimentally realistic conditions

Cited by

• Tunable many-body burst in isolated quantum systems
• Typical fast thermalization processes in closed many-body systems
• Classical Lieb-Robinson Bound for Estimating Equilibration Timescales of Isolated Quantum Systems