A dynamical mechanism for the Page curve from quantum chaos
Abstract If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zer...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/132059 |
| _version_ | 1811097153189183488 |
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| author | Liu, Hong Vardhan, Shreya |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Liu, Hong Vardhan, Shreya |
| author_sort | Liu, Hong |
| collection | MIT |
| description | Abstract
If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the “operator gas” approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the “gas” can “jump” outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation. |
| first_indexed | 2024-09-23T16:55:11Z |
| format | Article |
| id | mit-1721.1/132059 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:55:11Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1320592023-01-10T19:54:18Z A dynamical mechanism for the Page curve from quantum chaos Liu, Hong Vardhan, Shreya Massachusetts Institute of Technology. Center for Theoretical Physics Abstract If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the “operator gas” approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the “gas” can “jump” outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation. 2021-09-20T17:41:43Z 2021-09-20T17:41:43Z 2021-03-08 2021-03-14T05:04:16Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/132059 Journal of High Energy Physics. 2021 Mar 08;2021(3):88 PUBLISHER_CC en https://doi.org/10.1007/JHEP03(2021)088 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Liu, Hong Vardhan, Shreya A dynamical mechanism for the Page curve from quantum chaos |
| title | A dynamical mechanism for the Page curve from quantum chaos |
| title_full | A dynamical mechanism for the Page curve from quantum chaos |
| title_fullStr | A dynamical mechanism for the Page curve from quantum chaos |
| title_full_unstemmed | A dynamical mechanism for the Page curve from quantum chaos |
| title_short | A dynamical mechanism for the Page curve from quantum chaos |
| title_sort | dynamical mechanism for the page curve from quantum chaos |
| url | https://hdl.handle.net/1721.1/132059 |
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