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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05057 |
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| _version_ | 1866916385444069376 |
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| author | Krapivsky, P. L. |
| author_facet | Krapivsky, P. L. |
| contents | We consider an impurity in a sea of zero-temperature fermions uniformly distributed throughout the space. The impurity scatters on fermions. On average, the momentum of impurity decreases with time as $t^{-1/(d+1)}$ in $d$ dimensions, and the momentum distribution acquires a scaling form in the long time limit. We solve the Lorentz-Boltzmann equation for the scaled momentum distribution of the impurity in three dimensions. The solution is a combination of confluent hypergeometric functions. In two spatial dimensions, the Lorentz-Boltzmann equation is analytically intractable, so we merely extract a few exact predictions about asymptotic behaviors when the scaled momentum of the impurity is small or large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Impurity in a zero-temperature three-dimensional Fermi gas Krapivsky, P. L. Quantum Gases Statistical Mechanics We consider an impurity in a sea of zero-temperature fermions uniformly distributed throughout the space. The impurity scatters on fermions. On average, the momentum of impurity decreases with time as $t^{-1/(d+1)}$ in $d$ dimensions, and the momentum distribution acquires a scaling form in the long time limit. We solve the Lorentz-Boltzmann equation for the scaled momentum distribution of the impurity in three dimensions. The solution is a combination of confluent hypergeometric functions. In two spatial dimensions, the Lorentz-Boltzmann equation is analytically intractable, so we merely extract a few exact predictions about asymptotic behaviors when the scaled momentum of the impurity is small or large. |
| title | Impurity in a zero-temperature three-dimensional Fermi gas |
| topic | Quantum Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2403.05057 |