A ballistic upper bound on the accumulation of bosonic on-site energies

• URL: http://arxiv.org/abs/2511.07558v1
• Date: Wed, 12 Nov 2025 01:03:15 GMT
• Title: A ballistic upper bound on the accumulation of bosonic on-site energies
• Authors: Tomotaka Kuwahara, Marius Lemm, Carla Rubiliani,
• Abstract summary: We study the dynamics generated by translation-invariant and possibly long-ranged Hamiltonians of Bose-Hubbard type.<n>For translation-invariant initial states with controlled boson density, we improve the known bound on the local repulsive energy at time $t$.<n>This shows that bosonic on-site energies accumulate at most ballistically.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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