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Equilibration Times in Closed Quantum Many-Body Systems

  • Henrik WilmingEmail author
  • Thiago R. de Oliveira
  • Anthony J. Short
  • Jens Eisert
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 195)

Abstract

For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter, we discuss the problem of equilibration and specifically provide insights into how long it takes to reach equilibrium in closed quantum systems. We first briefly discuss the connection of this problem with recent experiments and forthcoming quantum simulators. Then we provide a comprehensive discussion of equilibration from a heuristic point of view, with a focus on providing an intuitive understanding and connecting the problem with general properties of interacting many-body systems. Finally, we provide a concise review of the rigorous results on equilibration times that are known in the literature.

Notes

Acknowledgements

We would like to thank Lea F. Santos, C. Gogolin, and P. Reimann for comments on an earlier draft. H. W. and J. E. acknowledge funding from the Studienstiftung des Deutschen Volkes, the ERC (TAQ), the DFG (EI 519/14-1, EI 519/7-1, CRC 183), and the Templeton Foundation. T. R. O. is supported by the Brazilian National Institute for Science and Technology of Quantum Information (INCT-IQ) and the National Counsel of Technological and Scientific Development (CNPq).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Henrik Wilming
    • 1
    • 2
    Email author
  • Thiago R. de Oliveira
    • 3
  • Anthony J. Short
    • 4
  • Jens Eisert
    • 1
  1. 1.Dahlem Center for Complex Quantum SystemsFreie Universität BerlinBerlinGermany
  2. 2.Institute for Theoretical PhysicsETH ZurichZurichSwitzerland
  3. 3.Instituto de FísicaUniversidade Federal FluminenseNiteróiBrazil
  4. 4.H. H. Wills Physics LaboratoryUniversity of BristolBristolUK

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