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Timescale for Macroscopic Equilibration in Isolated Quantum Systems: A Rigorous Derivation for Free Fermions
Takashi Hara1, Tatsuhiko Koike2
1Kyushu University, Faculty of Mathematics, Fukuoka 819-0395, Japan.
Physical Review Letters
|July 31, 2026
Summary
This study proves that translation-invariant free-fermion systems equilibrate in a timescale proportional to lattice size L. This optimal scaling, of order L, applies to systems with conserved quantities like particle number.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Statistical Mechanics
Background:
- Understanding equilibration dynamics in isolated quantum systems is a fundamental challenge.
- Translation-invariant free-fermion systems are crucial models for studying quantum dynamics.
- Previous studies lacked a definitive timescale for equilibration in such systems.
Purpose of the Study:
- To determine the equilibration timescale for translation-invariant free-fermion systems.
- To investigate the dependence of equilibration time on system size (L) and dimensionality (d).
- To establish theoretical bounds for equilibration in these quantum systems.
Main Methods:
- Analysis of translation-invariant free-fermion models on d-dimensional hypercubic lattices.
- Consideration of systems with uniform nearest-neighbor hopping.
- Derivation of equilibration time scaling from arbitrary pure initial states.
Main Results:
- Equilibration of coarse-grained density occurs within a timescale of order L.
- This O(L) scaling is proven to be optimal, with some initial states requiring this time.
- The results align with expectations for macroscopic systems possessing conserved quantities.
Conclusions:
- The equilibration timescale for these free-fermion systems is fundamentally limited by the system size L.
- This work provides a concrete timescale for thermalization in a significant class of quantum models.
- The findings have implications for understanding thermalization in quantum simulators and condensed matter systems.
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