Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain
arXiv:2401.15263 · doi:10.1103/8cdf-sth8
Abstract
We consider a free fermion chain with uniform nearest-neighbor hopping and let it evolve from an arbitrary initial state with a fixed macroscopic number of particles. We then prove that, at a sufficiently large and typical time, the measured coarse-grained density distribution is almost uniform with (quantum mechanical) probability extremely close to one. This establishes the emergence of irreversible behavior, i.e., a ballistic diffusion, in a system governed by quantum mechanical unitary time evolution. It is conceptually important that irreversibility from any initial state is proved here without introducing any randomness to the initial state or the Hamiltonian, while the known examples, both classical and quantum, rely on certain randomness or apply to limited classes of initial states. The essential new ingredient in the proof is the large deviation bound for every energy eigenstate, which is reminiscent of the strong ETH (energy eigenstate thermalization hypothesis).
5 pages, no figures. This is the final version to be published in PRE as a Letter. There are also some new references. There is a 20-minute video that explains the main results of the present work: https://youtu.be/HQzzCxok18A
References in corpus (19)
- Chaos and Quantum Thermalization
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Alternatives to Eigenstate Thermalization
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
- Initial state dependence of the quench dynamics in integrable quantum systems
- Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
- Generalization of von Neumann's Approach to Thermalization
- Equilibration towards generalized Gibbs ensembles in non-interacting theories
- Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field
- Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
- Generalized thermalization in quantum-chaotic quadratic Hamiltonians
- Boltzmann entropy of a freely expanding quantum ideal gas
- Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
- A rigourous demonstration of the validity of Boltzmann's scenario for the spatial homogenization of a freely expanding gas and the equilibration of the Kac ring
- Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system