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Quantum Simulation

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

arXiv
Authors: Tomotaka Kuwahara, Marius Lemm, Carla Rubiliani

Year

2025

Paper ID

17365

Status

Preprint

Abstract Read

~2 min

Abstract Words

111

Citations

N/A

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 n2xrangletlesssim t2d to langle n2xrangletlesssim td. 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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  • In this note, we study transport properties of the dynamics generated by translation-invariant and possibly long-ranged Hamiltonians of Bose-Hubbard type.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2511.07558 [2] arXiv https://arxiv.org/abs/2511.07558 [3] Publisher https://arxiv.org/abs/2511.07558

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