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Thermalization and ergodicity in one-dimensional many-body open quantum systems
Marko Znidaric1, Tomaz Prosen, Giuliano Benenti
1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Quantum chaotic systems thermalize to a universal state, independent of bath details. Integrable systems thermalize to bath-dependent states, differing from the grand canonical ensemble.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Understanding thermalization in quantum systems is crucial for quantum thermodynamics.
- The behavior of quantum systems coupled to external environments (baths) is key to studying their approach to equilibrium.
- Distinguishing between chaotic and integrable systems is fundamental in quantum dynamics.
Purpose of the Study:
- To investigate the thermalization dynamics of spin chains coupled to an external bath.
- To determine if quantum chaotic systems exhibit thermalization.
- To compare the thermalized states of chaotic and integrable systems.
Main Methods:
- Utilizing the time-dependent density-matrix renormalization-group (TD-DMRG) method.
- Analyzing the relaxation dynamics of spin chains.
- Comparing the resulting invariant states with the grand canonical ensemble.
Main Results:
- Evidence suggests that quantum chaotic systems do thermalize.
- Chaotic systems relax to an invariant ergodic state, well-approximated by the grand canonical state in the bulk.
- The bulk ergodic state in chaotic systems is independent of specific bath details.
- For integrable systems, the invariant state depends on the bath and deviates from the grand canonical state.
Conclusions:
- Quantum chaotic systems demonstrate thermalization, reaching a universal steady state.
- The thermalization process in integrable systems is sensitive to the coupling with the environment.
- These findings highlight fundamental differences in the thermalization mechanisms of chaotic versus integrable quantum systems.
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