Self-consistent inclusion of disorder in the BCS-BEC crossover near the critical temperature
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911568215670784 |
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| author | Iskin, M. |
| author_facet | Iskin, M. |
| contents | We develop a systematic theoretical approach to incorporate the effects of a static white-noise disorder into the BCS-BEC crossover near the critical temperature ($T_c$) of the superfluid transition. Starting from a functional-integral formulation in momentum-frequency space, we derive an effective thermodynamic potential that fully accounts for Gaussian fluctuations of the order-parameter field and its coupling to the disorder potential. The effective action, expanded to second order in both the disorder potential and the bosonic field, naturally involves third- and fourth-order terms arising from the logarithmic expansion near $T_c$. By providing a controlled description of pairing fluctuations and disorder effects, this formalism correctly recovers the well-established BCS and BEC limits. This ensures a consistent physical foundation for analyzing the entire BCS-BEC crossover, effectively anchoring the intermediate regime between these two analytically robust endpoints. The approach applies equally to continuum and lattice systems and provides a natural framework for generalizations to multiband models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-consistent inclusion of disorder in the BCS-BEC crossover near the critical temperature Iskin, M. Superconductivity Quantum Gases Strongly Correlated Electrons We develop a systematic theoretical approach to incorporate the effects of a static white-noise disorder into the BCS-BEC crossover near the critical temperature ($T_c$) of the superfluid transition. Starting from a functional-integral formulation in momentum-frequency space, we derive an effective thermodynamic potential that fully accounts for Gaussian fluctuations of the order-parameter field and its coupling to the disorder potential. The effective action, expanded to second order in both the disorder potential and the bosonic field, naturally involves third- and fourth-order terms arising from the logarithmic expansion near $T_c$. By providing a controlled description of pairing fluctuations and disorder effects, this formalism correctly recovers the well-established BCS and BEC limits. This ensures a consistent physical foundation for analyzing the entire BCS-BEC crossover, effectively anchoring the intermediate regime between these two analytically robust endpoints. The approach applies equally to continuum and lattice systems and provides a natural framework for generalizations to multiband models. |
| title | Self-consistent inclusion of disorder in the BCS-BEC crossover near the critical temperature |
| topic | Superconductivity Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2512.11073 |