We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics
2016
Key concepts
- equilibrium
- mechanics
- statistical mechanics
- many-body localisation
- physics
- typicality
- closed systems
- Review
- local operations and classical communication
- quantum mechanical
- maximum entropy principle
- dynamics
- thermalisation
- equilibration
- eigenstate thermalisation hypothesis
- von Neumann
- pure state
- Schrödinger equation
Scholarcy highlights
- AppendixA Remarks on the foundations of statistical mechanics
- The microscopic description of quantum mechanical systems following the dynamical equations of motion is still in some tension with the picture arising from the ensemble description of quantum statistical mechanics
- We have elaborated on a question that is at the heart of the foundations of quantum statistical mechanics: This is the question of how pure states evolving unitarily according to the Schrödinger equation can give rise to a wealth of phenomena that can rightfully be called thermodynamic
- It turns out that the equilibrium properties can be captured by suitable maximum entropy principles implied by quantum mechanical dynamics alone
- If a part of the system can be naturally identified as a bath and its complement as a distinguished subsystem, a weak interaction naturally leads to decoherence in the energy eigenbasis, and under additional conditions even equilibration to a thermal state can be guaranteed
- We have reviewed systems where an absence of thermalisation is anticipated and the role played by many-body localisation played in this context
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