Classical Hamiltonian time crystals–general theory and simple examples
We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the available mechanical free energy that is simultaneously a time d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aba8d3 |
| _version_ | 1797750364735275008 |
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| author | Jin Dai Antti J Niemi Xubiao Peng |
| author_facet | Jin Dai Antti J Niemi Xubiao Peng |
| author_sort | Jin Dai |
| collection | DOAJ |
| description | We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the available mechanical free energy that is simultaneously a time dependent solution of Hamilton’s equation. The mathematical description of such a timecrystalline spontaneous symmetry breaking builds on concepts of equivariant Morse theory in the space of Hamiltonian flows. As an example we analyze a general family of timecrystalline Hamiltonians that is designed to model polygonal, piecewise linear closed strings. The vertices correspond to the locations of pointlike interaction centers; the string is akin a chain of atoms, that are joined together by covalent bonds, modeled by the links of the string. We argue that the timecrystalline character of the string can be affected by its topology. For this we show that a knotty string is usually more timecrystalline than a string with no self-entanglement. We also reveal a relation between phase space topology and the occurrence of timecrystalline dynamics. For this we show that in the case of three point particles, the presence of a time crystal can relate to a Dirac monopole that resides in the phase space. Our results propose that physical examples of Hamiltonian time crystals can be realized in terms of closed, knotted molecular rings. |
| first_indexed | 2024-03-12T16:31:43Z |
| format | Article |
| id | doaj.art-a5f052efa16641238d137760cdfcf8ac |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:31:43Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a5f052efa16641238d137760cdfcf8ac2023-08-08T15:27:30ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122808500610.1088/1367-2630/aba8d3Classical Hamiltonian time crystals–general theory and simple examplesJin Dai0Antti J Niemi1https://orcid.org/0000-0003-3408-5834Xubiao Peng2Nordita, Stockholm University , Roslagstullsbacken 23, SE-106 91 Stockholm, SwedenNordita, Stockholm University , Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden; Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours , Parc de Grandmont, F37200, Tours, France; School of Physics, Beijing Institute of Technology , Haidian District, Beijing 100081, People’s Republic of ChinaSchool of Physics, Beijing Institute of Technology , Haidian District, Beijing 100081, People’s Republic of ChinaWe focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the available mechanical free energy that is simultaneously a time dependent solution of Hamilton’s equation. The mathematical description of such a timecrystalline spontaneous symmetry breaking builds on concepts of equivariant Morse theory in the space of Hamiltonian flows. As an example we analyze a general family of timecrystalline Hamiltonians that is designed to model polygonal, piecewise linear closed strings. The vertices correspond to the locations of pointlike interaction centers; the string is akin a chain of atoms, that are joined together by covalent bonds, modeled by the links of the string. We argue that the timecrystalline character of the string can be affected by its topology. For this we show that a knotty string is usually more timecrystalline than a string with no self-entanglement. We also reveal a relation between phase space topology and the occurrence of timecrystalline dynamics. For this we show that in the case of three point particles, the presence of a time crystal can relate to a Dirac monopole that resides in the phase space. Our results propose that physical examples of Hamiltonian time crystals can be realized in terms of closed, knotted molecular rings.https://doi.org/10.1088/1367-2630/aba8d3time crystalsHamiltonian dynamicspresymplectic geometryequivariant Morse theory |
| spellingShingle | Jin Dai Antti J Niemi Xubiao Peng Classical Hamiltonian time crystals–general theory and simple examples New Journal of Physics time crystals Hamiltonian dynamics presymplectic geometry equivariant Morse theory |
| title | Classical Hamiltonian time crystals–general theory and simple examples |
| title_full | Classical Hamiltonian time crystals–general theory and simple examples |
| title_fullStr | Classical Hamiltonian time crystals–general theory and simple examples |
| title_full_unstemmed | Classical Hamiltonian time crystals–general theory and simple examples |
| title_short | Classical Hamiltonian time crystals–general theory and simple examples |
| title_sort | classical hamiltonian time crystals general theory and simple examples |
| topic | time crystals Hamiltonian dynamics presymplectic geometry equivariant Morse theory |
| url | https://doi.org/10.1088/1367-2630/aba8d3 |
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