Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918374548701184 |
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| author | Park, Takamori Huang, Xiaoyang Savary, Lucile Balents, Leon |
| author_facet | Park, Takamori Huang, Xiaoyang Savary, Lucile Balents, Leon |
| contents | We systematically derive the dissipationless quantum kinetic equation for a multi-band free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band-diagonalize the dynamics. Expanding to the second order in gradients, which is beyond the semiclassical limit, we give a complete analysis of the band-resolved thermodynamics and transport properties, especially those arising from the quantum geometric tensor. We apply our framework to a Bloch band theory under electric fields near equilibrium and find the linear and nonlinear transport coefficients. We also obtain the dynamical density-density response functions in the metallic case, including quantum metric corrections. Our results and approach can be applied very generally to multi-band problems even in situations with spatially varying Hamiltonians and distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response Park, Takamori Huang, Xiaoyang Savary, Lucile Balents, Leon Mesoscale and Nanoscale Physics Statistical Mechanics Strongly Correlated Electrons We systematically derive the dissipationless quantum kinetic equation for a multi-band free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band-diagonalize the dynamics. Expanding to the second order in gradients, which is beyond the semiclassical limit, we give a complete analysis of the band-resolved thermodynamics and transport properties, especially those arising from the quantum geometric tensor. We apply our framework to a Bloch band theory under electric fields near equilibrium and find the linear and nonlinear transport coefficients. We also obtain the dynamical density-density response functions in the metallic case, including quantum metric corrections. Our results and approach can be applied very generally to multi-band problems even in situations with spatially varying Hamiltonians and distributions. |
| title | Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response |
| topic | Mesoscale and Nanoscale Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2504.10447 |