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Macroscopic irreversibility in quantum systems: Free expansion in a fermionic chain
1Gakushuin University, Department of Physics, Mejiro, Toshima-ku, Tokyo 171-8588, Japan.
Physical Review. E
|August 1, 2025
Summary
Quantum systems can exhibit irreversible behavior, like diffusion, even without randomness. This study proves that a free fermion chain evolves towards a uniform density distribution over time, demonstrating emergent irreversibility from any initial state.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- Quantum mechanical systems typically exhibit reversible time evolution.
- Emergence of irreversibility in quantum systems is often linked to randomness or specific initial states.
- The Energy Eigenstate Thermalization Hypothesis (ETH) describes thermalization in isolated quantum systems.
Purpose of the Study:
- To demonstrate the emergence of irreversible behavior in a quantum system governed by unitary time evolution.
- To prove that a free fermion chain evolves towards a uniform coarse-grained density distribution.
- To establish irreversibility without introducing randomness into the initial state or Hamiltonian.
Main Methods:
- Consideration of a free fermion chain with uniform nearest-neighbor hopping.
- Evolution of the system from an arbitrary initial state with a fixed macroscopic number of particles.
- Application of large deviation bounds for energy eigenstates, inspired by the strong ETH.
Main Results:
- The coarse-grained density distribution of the fermion chain approaches uniformity at large, typical times.
- This uniformity occurs with a probability extremely close to one.
- Demonstration of emergent ballistic diffusion, a form of irreversible behavior, from unitary quantum evolution.
Conclusions:
- Irreversible behavior can emerge in quantum systems from any initial state without added randomness.
- The findings provide a new perspective on the quantum-to-classical transition and thermalization.
- The study highlights the significance of large deviation bounds for understanding quantum dynamics.
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