Metastability, chaos and spectrum tomography for Bose-Hubbard rings and chains
arXiv:2603.23109 · doi:10.1103/dbpg-938z
Abstract
We analyze the metastability of Bose-Hubbard condensates for finite-size one-dimensional ring lattices and open chains, using a semiclassical tomographic perspective that emphasizes the relation of the many-body spectrum to the underlying classical phase-space structures. In order to address quantum ergodicity in far-from-equilibrium scenarios of experimental interest, we inspect both local aspects (via Bogoliubov analysis) and global aspects (mixed regular-chaotic dynamics). In particular, we highlight the roles of the two parameters that control metastability, clarify the essential differences between low- and high-dimensional chaos, and show how the dynamical instabilities diminish in the limit of the Gross-Pitaevskii equation. It is somewhat frustrating that with more degrees of freedom, the dynamically metastable islands become better distinct from the ergodic sea, while their borders become ill-defined topologically. This stands in opposition to the very structured phase-space of two-degree-of-freedom systems, as reflected in the tomographic quantum spectrum.
arXiv comment23 pages, 18 figures
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