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Typical equilibrium state of an embedded quantum system.
Grégoire Ithier1, Saeed Ascroft1, Florent Benaych-Georges2
1Department of Physics, Royal Holloway, University of London, TW20 0EX, Egham, United Kingdom.
Physical Review. E
|January 20, 2018
Summary
We analytically calculate a partition function for quantum systems interacting with large quantum environments. This function characterizes the stationary state, offering a thermodynamic ensemble applicable to quantum dynamics and typicality.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- The dynamics of quantum systems interacting with large quantum environments often exhibit typicality, meaning their time evolution is independent of specific interaction details.
- Previous work established this typicality for certain random interactions in embedded quantum systems.
Purpose of the Study:
- To analytically derive a partition function for the stationary state of a quantum system coupled to a large quantum environment.
- To demonstrate that this partition function provides a generalized thermodynamic ensemble.
Main Methods:
- Leveraging the property of typicality in quantum system dynamics.
- Analytical calculation of a partition function based on eigenvector overlaps of bare and dressed Hamiltonians.
- Focusing on the long-time (stationary) regime of the quantum system.
Main Results:
- A novel partition function characterizing the stationary state of an embedded quantum system was derived.
- This partition function unifies microcanonical and canonical ensembles as special cases.
- The analytical predictions were validated through numerical simulations.
Conclusions:
- The derived partition function offers a powerful tool for understanding the thermodynamics of open quantum systems.
- Typicality in quantum dynamics simplifies the analysis of stationary states in complex quantum environments.
- This framework provides a unified approach to thermodynamic ensembles in quantum statistical mechanics.
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