Traveling discontinuity at the quantum butterfly front
We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of informati...
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| Format: | Article |
| Language: | English |
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SciPost
2023-08-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.2.042 |
| _version_ | 1797756375444488192 |
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| author | Camille Aron, Éric Brunet, Aditi Mitra |
| author_facet | Camille Aron, Éric Brunet, Aditi Mitra |
| author_sort | Camille Aron, Éric Brunet, Aditi Mitra |
| collection | DOAJ |
| description | We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone. |
| first_indexed | 2024-03-12T18:00:28Z |
| format | Article |
| id | doaj.art-7e398bf993be4bffbab770e3c7822b6f |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-12T18:00:28Z |
| publishDate | 2023-08-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-7e398bf993be4bffbab770e3c7822b6f2023-08-02T12:16:54ZengSciPostSciPost Physics2542-46532023-08-0115204210.21468/SciPostPhys.15.2.042Traveling discontinuity at the quantum butterfly frontCamille Aron, Éric Brunet, Aditi MitraWe formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.https://scipost.org/SciPostPhys.15.2.042 |
| spellingShingle | Camille Aron, Éric Brunet, Aditi Mitra Traveling discontinuity at the quantum butterfly front SciPost Physics |
| title | Traveling discontinuity at the quantum butterfly front |
| title_full | Traveling discontinuity at the quantum butterfly front |
| title_fullStr | Traveling discontinuity at the quantum butterfly front |
| title_full_unstemmed | Traveling discontinuity at the quantum butterfly front |
| title_short | Traveling discontinuity at the quantum butterfly front |
| title_sort | traveling discontinuity at the quantum butterfly front |
| url | https://scipost.org/SciPostPhys.15.2.042 |
| work_keys_str_mv | AT camillearonericbrunetaditimitra travelingdiscontinuityatthequantumbutterflyfront |