Critical Dynamics in Short-Range Quadratic Hamiltonians
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912258599157760 |
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| author | Hopjan, Miroslav Vidmar, Lev |
| author_facet | Hopjan, Miroslav Vidmar, Lev |
| contents | We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time. We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$. This result has notable implications: it says that superdiffusive transport in $d_l\geq 2$ and diffusive transport in $d_l\geq 3$ cannot be critical in the sense defined above. Our findings clarify previous results on disordered and quasiperiodic models and, through Fibonacci potential models in two and three dimensions, provide non-trivial examples of critical dynamics in systems with $d_l\neq1$ and $d_s\neq1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical Dynamics in Short-Range Quadratic Hamiltonians Hopjan, Miroslav Vidmar, Lev Statistical Mechanics Disordered Systems and Neural Networks Quantum Gases Quantum Physics We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time. We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$. This result has notable implications: it says that superdiffusive transport in $d_l\geq 2$ and diffusive transport in $d_l\geq 3$ cannot be critical in the sense defined above. Our findings clarify previous results on disordered and quasiperiodic models and, through Fibonacci potential models in two and three dimensions, provide non-trivial examples of critical dynamics in systems with $d_l\neq1$ and $d_s\neq1$. |
| title | Critical Dynamics in Short-Range Quadratic Hamiltonians |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2503.02828 |