Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics

Christian Gogolin; Jens Eisert

2016

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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