A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas
We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb–Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on int...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/18/4/045010 |
| _version_ | 1827873684375732224 |
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| author | Jan C Zill Tod M Wright Karén V Kheruntsyan Thomas Gasenzer Matthew J Davis |
| author_facet | Jan C Zill Tod M Wright Karén V Kheruntsyan Thomas Gasenzer Matthew J Davis |
| author_sort | Jan C Zill |
| collection | DOAJ |
| description | We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb–Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on interaction strength, and analyze the effects of system size in the crossover from few-body to mesoscopic regimes for up to seven particles. We also obtain time-dependent nonequilibrium correlation functions for five particles following quenches of the interaction strength from two distinct initial states. One quench is from the noninteracting ground state and the other from a correlated ground state near the strongly interacting Tonks–Girardeau regime. The final interaction strength and conserved energy are chosen to be the same for both quenches. The integrability of the model highly constrains its dynamics, and we demonstrate that the time-averaged correlation functions following quenches from these two distinct initial conditions are both nonthermal and moreover distinct from one another. |
| first_indexed | 2024-03-12T16:40:43Z |
| format | Article |
| id | doaj.art-aad6550e9b514eb4b6944fb8506cf59b |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:40:43Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-aad6550e9b514eb4b6944fb8506cf59b2023-08-08T14:31:23ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118404501010.1088/1367-2630/18/4/045010A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gasJan C Zill0Tod M Wright1Karén V Kheruntsyan2Thomas Gasenzer3https://orcid.org/0000-0002-9363-7822Matthew J Davis4School of Mathematics and Physics, The University of Queensland , Brisbane QLD 4072, AustraliaSchool of Mathematics and Physics, The University of Queensland , Brisbane QLD 4072, AustraliaSchool of Mathematics and Physics, The University of Queensland , Brisbane QLD 4072, AustraliaKirchhoff-Institut für Physik, Universität Heidelberg , Im Neuenheimer Feld 227, D-69120 Heidelberg, Germany; ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, GermanySchool of Mathematics and Physics, The University of Queensland , Brisbane QLD 4072, Australia; JILA, University of Colorado , 440 UCB, Boulder, CO 80309, USAWe use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb–Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on interaction strength, and analyze the effects of system size in the crossover from few-body to mesoscopic regimes for up to seven particles. We also obtain time-dependent nonequilibrium correlation functions for five particles following quenches of the interaction strength from two distinct initial states. One quench is from the noninteracting ground state and the other from a correlated ground state near the strongly interacting Tonks–Girardeau regime. The final interaction strength and conserved energy are chosen to be the same for both quenches. The integrability of the model highly constrains its dynamics, and we demonstrate that the time-averaged correlation functions following quenches from these two distinct initial conditions are both nonthermal and moreover distinct from one another.https://doi.org/10.1088/1367-2630/18/4/045010Bethe ansatzone-dimensional quantum gasesfew-body systemsLieb–Liniger model0230Ik6785-d |
| spellingShingle | Jan C Zill Tod M Wright Karén V Kheruntsyan Thomas Gasenzer Matthew J Davis A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas New Journal of Physics Bethe ansatz one-dimensional quantum gases few-body systems Lieb–Liniger model 0230Ik 6785-d |
| title | A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas |
| title_full | A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas |
| title_fullStr | A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas |
| title_full_unstemmed | A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas |
| title_short | A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas |
| title_sort | coordinate bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one dimensional bose gas |
| topic | Bethe ansatz one-dimensional quantum gases few-body systems Lieb–Liniger model 0230Ik 6785-d |
| url | https://doi.org/10.1088/1367-2630/18/4/045010 |
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