A ballistic upper bound on the accumulation of bosonic on-site energies
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915610756120576 |
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| author | Kuwahara, Tomotaka Lemm, Marius Rubiliani, Carla |
| author_facet | Kuwahara, Tomotaka Lemm, Marius Rubiliani, Carla |
| contents | In this note, we study transport properties of the dynamics generated by translation-invariant and possibly long-ranged Hamiltonians of Bose-Hubbard type. For translation-invariant initial states with controlled boson density, we improve the known bound on the local repulsive energy at time $t$ from $\langle n^2_x\rangle_t\lesssim t^{2d}$ to $\langle n^2_x\rangle_t\lesssim t^d$. This shows that bosonic on-site energies accumulate at most ballistically. Extending the result to higher moments would have powerful implications for bosonic Lieb-Robinson bounds. While previous approaches focused on controlling particle transport, our proof develops novel ASTLOs (adiabatic space-time localization observables) that are able to track the growth of local boson-boson correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A ballistic upper bound on the accumulation of bosonic on-site energies Kuwahara, Tomotaka Lemm, Marius Rubiliani, Carla Mathematical Physics Analysis of PDEs Quantum Physics In this note, we study transport properties of the dynamics generated by translation-invariant and possibly long-ranged Hamiltonians of Bose-Hubbard type. For translation-invariant initial states with controlled boson density, we improve the known bound on the local repulsive energy at time $t$ from $\langle n^2_x\rangle_t\lesssim t^{2d}$ to $\langle n^2_x\rangle_t\lesssim t^d$. This shows that bosonic on-site energies accumulate at most ballistically. Extending the result to higher moments would have powerful implications for bosonic Lieb-Robinson bounds. While previous approaches focused on controlling particle transport, our proof develops novel ASTLOs (adiabatic space-time localization observables) that are able to track the growth of local boson-boson correlations. |
| title | A ballistic upper bound on the accumulation of bosonic on-site energies |
| topic | Mathematical Physics Analysis of PDEs Quantum Physics |
| url | https://arxiv.org/abs/2511.07558 |