Heating rate of driven bosons with unbounded local energy
In plain words
For spins driven fast, heating is known to be exponentially slow in the drive frequency. For quantum bosons, where many particles can occupy one site, no such result has been proven.
Precise statement
Rigorous bounds give heating time $t_{h}>\sim \exp(c\hbar\omega/J)$ for periodically driven lattice systems with bounded local energy scale $J$ (Mori, Kuwahara, Saito 2016; Abanin, De Roeck, Ho, Huveneers 2017). Classical rotor chains with unbounded local energy show exponentially long heating times controlled by the prethermal temperature (Rajak, Citro, Dalla Torre 2018; Sadia, Dalla Torre, Rajak 2022). For the driven Bose-Hubbard model at fixed filling and energy density, determine $t_{h}(\omega)$, the parameter that controls it (local occupation or prethermal temperature), and whether a rigorous bound exists. Answer: the asymptotic form (exponential, stretched exponential, or power law) with its controlling parameter.
What would settle it
A derivation or rigorous bound matched by quantum simulations over a range of $\omega$ spanning several decades of $t_{h}$.
Status in the literature
Classical unbounded rotor chains prethermalize with exponentially slow heating (numerics 2018-2022); no rigorous bound or quantum bosonic result exists.