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Typicality versus thermality: an analytic distinction

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Abstract

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.

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Authors and Affiliations

  1. David Rittenhouse Laboratories, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Vijay Balasubramanian, Bartłomiej Czech, Klaus Larjo & Joan Simón

  2. Centre for Particle Theory and Department of Mathematical Sciences, Science Laboratories, South Road, Durham, DH1 3LE, UK

    Veronika E. Hubeny & Mukund Rangamani

  3. Department of Physics and Theoretical Physics Group, LBNL University of California, Berkeley, 94720, CA, USA

    Joan Simón

Authors
  1. Vijay Balasubramanian
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  2. Bartłomiej Czech
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  3. Veronika E. Hubeny
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  4. Klaus Larjo
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  5. Mukund Rangamani
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  6. Joan Simón
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Correspondence to Klaus Larjo.

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Balasubramanian, V., Czech, B., Hubeny, V.E. et al. Typicality versus thermality: an analytic distinction. Gen Relativ Gravit 40, 1863–1890 (2008). https://doi.org/10.1007/s10714-008-0606-8

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  • DOI: https://doi.org/10.1007/s10714-008-0606-8

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