Analytical solution of a free-fermion chain with time-dependent ramps
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912872745926656 |
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| author | Eisler, Viktor Bonsignori, Riccarda Scopa, Stefano |
| author_facet | Eisler, Viktor Bonsignori, Riccarda Scopa, Stefano |
| contents | We provide an exact analytical solution of the single-particle Schrödinger equation for a chain of non-interacting fermions subject to a time-dependent linear potential, with its slope varied as an arbitrary function of time. The resulting dynamics exhibit self-similar behavior, with a structure reminiscent of the domain wall melting problem, albeit characterized by a nontrivial time-dependent length scale and phase. Building on this solution, we derive hydrodynamic predictions for the evolution of particle density, current, and entanglement entropy along the chain. In the special case of a sudden quench, the system develops a breathing interface region, which may be interpreted as a realization of Wannier-Stark localization, as previously suggested on the basis of hydrodynamic arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical solution of a free-fermion chain with time-dependent ramps Eisler, Viktor Bonsignori, Riccarda Scopa, Stefano Statistical Mechanics Quantum Physics We provide an exact analytical solution of the single-particle Schrödinger equation for a chain of non-interacting fermions subject to a time-dependent linear potential, with its slope varied as an arbitrary function of time. The resulting dynamics exhibit self-similar behavior, with a structure reminiscent of the domain wall melting problem, albeit characterized by a nontrivial time-dependent length scale and phase. Building on this solution, we derive hydrodynamic predictions for the evolution of particle density, current, and entanglement entropy along the chain. In the special case of a sudden quench, the system develops a breathing interface region, which may be interpreted as a realization of Wannier-Stark localization, as previously suggested on the basis of hydrodynamic arguments. |
| title | Analytical solution of a free-fermion chain with time-dependent ramps |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2510.03112 |