Caustics in quantum many-body dynamics
We describe a new class of nonequilibrium quantum many-body phenomena in the form of networks of caustics that dominate the many-body wave function in the semiclassical regime following a sudden quench. It includes the light cone-like propagation of correlations as a particular case. Caustics are si...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.013105 |
| _version_ | 1797210815046090752 |
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| author | W. Kirkby Y. Yee K. Shi D. H. J. O'Dell |
| author_facet | W. Kirkby Y. Yee K. Shi D. H. J. O'Dell |
| author_sort | W. Kirkby |
| collection | DOAJ |
| description | We describe a new class of nonequilibrium quantum many-body phenomena in the form of networks of caustics that dominate the many-body wave function in the semiclassical regime following a sudden quench. It includes the light cone-like propagation of correlations as a particular case. Caustics are singularities formed by the birth and death of waves and form a hierarchy of universal patterns whose natural mathematical description is via catastrophe theory. Examples in classical waves range from rainbows and gravitational lensing in optics to tidal bores and rogue waves in hydrodynamics. Quantum many-body caustics are discretized by second quantization (“quantum catastrophes”) and live in Fock space, which can potentially have many dimensions. We illustrate these ideas using the Bose Hubbard dimer and trimer models, which are simple enough that the caustic structure can be elucidated from first principles and yet run the full range from integrable to nonintegrable dynamics. The dimer gives rise to discretized versions of fold and cusp catastrophes whereas the trimer allows for higher catastrophes including the codimension-3 hyperbolic and elliptic umbilics, which are organized by, and projections of, an 8-dimensional corank-2 catastrophe known as X_{9}. These results describe a hitherto unrecognized form of universality in quantum dynamics organized by singularities that manifest as strong fluctuations in mode population probabilities. |
| first_indexed | 2024-04-24T10:16:35Z |
| format | Article |
| id | doaj.art-c072a1f44e6e4fcdbcb0bd399264872b |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:16:35Z |
| publishDate | 2022-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-c072a1f44e6e4fcdbcb0bd399264872b2024-04-12T17:17:53ZengAmerican Physical SocietyPhysical Review Research2643-15642022-02-014101310510.1103/PhysRevResearch.4.013105Caustics in quantum many-body dynamicsW. KirkbyY. YeeK. ShiD. H. J. O'DellWe describe a new class of nonequilibrium quantum many-body phenomena in the form of networks of caustics that dominate the many-body wave function in the semiclassical regime following a sudden quench. It includes the light cone-like propagation of correlations as a particular case. Caustics are singularities formed by the birth and death of waves and form a hierarchy of universal patterns whose natural mathematical description is via catastrophe theory. Examples in classical waves range from rainbows and gravitational lensing in optics to tidal bores and rogue waves in hydrodynamics. Quantum many-body caustics are discretized by second quantization (“quantum catastrophes”) and live in Fock space, which can potentially have many dimensions. We illustrate these ideas using the Bose Hubbard dimer and trimer models, which are simple enough that the caustic structure can be elucidated from first principles and yet run the full range from integrable to nonintegrable dynamics. The dimer gives rise to discretized versions of fold and cusp catastrophes whereas the trimer allows for higher catastrophes including the codimension-3 hyperbolic and elliptic umbilics, which are organized by, and projections of, an 8-dimensional corank-2 catastrophe known as X_{9}. These results describe a hitherto unrecognized form of universality in quantum dynamics organized by singularities that manifest as strong fluctuations in mode population probabilities.http://doi.org/10.1103/PhysRevResearch.4.013105 |
| spellingShingle | W. Kirkby Y. Yee K. Shi D. H. J. O'Dell Caustics in quantum many-body dynamics Physical Review Research |
| title | Caustics in quantum many-body dynamics |
| title_full | Caustics in quantum many-body dynamics |
| title_fullStr | Caustics in quantum many-body dynamics |
| title_full_unstemmed | Caustics in quantum many-body dynamics |
| title_short | Caustics in quantum many-body dynamics |
| title_sort | caustics in quantum many body dynamics |
| url | http://doi.org/10.1103/PhysRevResearch.4.013105 |
| work_keys_str_mv | AT wkirkby causticsinquantummanybodydynamics AT yyee causticsinquantummanybodydynamics AT kshi causticsinquantummanybodydynamics AT dhjodell causticsinquantummanybodydynamics |