Dynamical Fermionization and Emergent Bethe Rapidity Structure in the Spatial Density of Cold quenched Lieb-Liniger gas
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| Format: | Preprint |
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2024
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| author | Datta, Sumita Rejcek, James M Datta, Rajasee Olshanii, Maxim |
| author_facet | Datta, Sumita Rejcek, James M Datta, Rajasee Olshanii, Maxim |
| contents | We demonstrate that the nonequilibrium spatial density of a one-dimensional interacting Bose gas, following a geometric quench, directly encodes information about the underlying momentum (rapidity) distribution of the system.
Starting from the interacting ground state of a Lieb--Liniger gas confined in a hard-wall box of length $L_0$, we study its expansion into a larger box of length $L > L_0$ at fixed interaction strength. Using an ab initio quantum Monte Carlo approach based on the generalized Feynman--Kac representation, we compute the time evolution of the many-body density.
We show that, in the long-time limit, the density profile acquires a scaling form in the velocity variable $x/t$, approaching a stationary distribution whose shape reflects the underlying rapidity structure. The velocity-space density broadens systematically with increasing interaction strength and exhibits rapid convergence in the strongly interacting (Tonks--Girardeau) regime.
These results provide numerical evidence that ballistic expansion enables a direct mapping between spatial density profiles and the momentum-space structure of the integrable Lieb--Liniger model, offering a practical route to accessing Bethe rapidities through real-space observables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_11190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Fermionization and Emergent Bethe Rapidity Structure in the Spatial Density of Cold quenched Lieb-Liniger gas Datta, Sumita Rejcek, James M Datta, Rajasee Olshanii, Maxim Quantum Gases Quantum Physics We demonstrate that the nonequilibrium spatial density of a one-dimensional interacting Bose gas, following a geometric quench, directly encodes information about the underlying momentum (rapidity) distribution of the system. Starting from the interacting ground state of a Lieb--Liniger gas confined in a hard-wall box of length $L_0$, we study its expansion into a larger box of length $L > L_0$ at fixed interaction strength. Using an ab initio quantum Monte Carlo approach based on the generalized Feynman--Kac representation, we compute the time evolution of the many-body density. We show that, in the long-time limit, the density profile acquires a scaling form in the velocity variable $x/t$, approaching a stationary distribution whose shape reflects the underlying rapidity structure. The velocity-space density broadens systematically with increasing interaction strength and exhibits rapid convergence in the strongly interacting (Tonks--Girardeau) regime. These results provide numerical evidence that ballistic expansion enables a direct mapping between spatial density profiles and the momentum-space structure of the integrable Lieb--Liniger model, offering a practical route to accessing Bethe rapidities through real-space observables. |
| title | Dynamical Fermionization and Emergent Bethe Rapidity Structure in the Spatial Density of Cold quenched Lieb-Liniger gas |
| topic | Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2403.11190 |