Krishnan, C and Mohan, V (2021) Hints of gravitational ergodicity: Berry’s ensemble and the universality of the semi-classical Page curve. In: Journal of High Energy Physics, 2021 (5).
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Abstract
Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this paper, we emphasize (1) that this peculiar manifestation of unitarity is not specific to black holes, and (2) that it can emerge from a single realization of an underlying unitary theory. To make things explicit, we consider a hard sphere gas leaking slowly from a small box into a bigger box. This is a quantum chaotic system in which we expect to see the Page curve in the full unitary description, while semi-classically, eigenstates are expected to behave as though they live in Berry’s ensemble. We reproduce the unitarity-compatible Page curve of this system, semi-classically. The computation has structural parallels to replica wormholes, relies crucially on ensemble averaging at each epoch, and reveals the interplay between the multiple time-scales in the problem. Working with the ensemble averaged state rather than the entanglement entropy, we can also engineer an information “paradox”. Our system provides a concrete example in which the ensemble underlying the semi-classical Page curve is an ergodic proxy for a time average, and not an explicit average over many theories. The questions we address here are logically independent of the existence of horizons, so we expect that semi-classical gravity should also be viewed in a similar light.
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal of High Energy Physics |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to the author. |
| Keywords: | Black Holes; Models of Quantum Gravity. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 10 Aug 2023 11:32 |
| Last Modified: | 10 Aug 2023 11:32 |
| URI: | https://eprints.iisc.ac.in/id/eprint/82704 |
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