On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918008357650432 |
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| author | Lemm, Marius Rubiliani, Carla Zhang, Jingxuan |
| author_facet | Lemm, Marius Rubiliani, Carla Zhang, Jingxuan |
| contents | We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all power law exponents $α>d+1$ in $d$ dimensions, the sharp condition. (ii) The first thermodynamically stable Lieb-Robinson bound (LRB) for these Hamiltonians. To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work [arXiv:2310.14896]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_01786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians Lemm, Marius Rubiliani, Carla Zhang, Jingxuan Mathematical Physics Analysis of PDEs Quantum Physics We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all power law exponents $α>d+1$ in $d$ dimensions, the sharp condition. (ii) The first thermodynamically stable Lieb-Robinson bound (LRB) for these Hamiltonians. To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work [arXiv:2310.14896]. |
| title | On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians |
| topic | Mathematical Physics Analysis of PDEs Quantum Physics |
| url | https://arxiv.org/abs/2505.01786 |