期刊
SCIPOST PHYSICS
卷 11, 期 1, 页码 -出版社
SCIPOST FOUNDATION
DOI: 10.21468/SciPostPhys.11.1.008
关键词
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资金
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant [754411]
- European Research Council (ERC) [801770]
- European Union's Horizon 2020 research and innovation programme [824093]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [413495248 [VO 2437/1-1], 279384907 SFB 1245, 279384907 -SFB 1245]
In this paper, the authors extended the flow equations approach to compute observables other than energy for cold Bose gases, specifically focusing on one-dimensional systems with impurities. The results showed that the mean-field approximation is accurate under certain conditions and that perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions.
A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities [1,2]. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.
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