Typicality versus thermality: an analytic distinction |
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Authors: | Vijay Balasubramanian Bartłomiej Czech Veronika E Hubeny Klaus Larjo Mukund Rangamani Joan Simón |
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Institution: | (1) David Rittenhouse Laboratories, University of Pennsylvania, Philadelphia, PA 19104, USA;(2) Centre for Particle Theory and Department of Mathematical Sciences, Science Laboratories, South Road, Durham, DH1 3LE, UK;(3) Department of Physics and Theoretical Physics Group, LBNL University of California, Berkeley, 94720, CA, USA |
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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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Keywords: | Typicality Thermality Variances between microstates |
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