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The European Physical Journal Special Topics

, Volume 227, Issue 3–4, pp 247–258 | Cite as

Decay of a thermofield-double state in chaotic quantum systems

From random matrices to spin systems
  • A. del Campo
  • J. Molina-Vilaplana
  • L. F. Santos
  • J. Sonner
Regular Article
Part of the following topical collections:
  1. Quantum Systems In and Out of Equilibrium - Fundamentals, Dynamics and Applications

Abstract

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This spreading can be analyzed with the spectral form factor, which is defined in terms of the analytic continuation of the partition function. The latter is equivalent to the survival probability of a thermofield double state under unitary dynamics. Using random matrices from the Gaussian unitary ensemble (GUE) as Hamiltonians for the time evolution, we obtain exact analytical expressions at finite N for the survival probability. Numerical simulations of the survival probability with matrices taken from the Gaussian orthogonal ensemble (GOE) are also provided. The GOE is more suitable for our comparison with numerical results obtained with a disordered spin chain with local interactions. Common features between the random matrix and the realistic disordered model in the chaotic regime are identified. The differences that emerge as the spin model approaches a many-body localized phase are also discussed.

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Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • A. del Campo
    • 1
  • J. Molina-Vilaplana
    • 2
  • L. F. Santos
    • 3
  • J. Sonner
    • 4
  1. 1.Department of PhysicsUniversity of MassachusettsBostonUSA
  2. 2.Department of Systems EngineeringTechnical University of CartagenaCartagenaSpain
  3. 3.Department of PhysicsYeshiva UniversityNew YorkUSA
  4. 4.Department of Theoretical PhysicsUniversity of GenevaGenève 4Switzerland

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