Wavelet representation of hardcore bosons
| Autor: | Granet, Etienne |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2023) 123102 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/ad082c |
| Popis: | We consider the 1D Tonks-Girardeau gas with a space-dependent potential out of equilibrium. We derive the exact dynamics of the system when divided into $n$ boxes and decomposed into energy eigenstates within each box. It is a representation of the wave function that is mixed between real space and momentum space, whose basis elements are plane waves localized in a box, motivating the word "wavelet". In this representation we derive the emergence of generalized hydrodynamics in appropriate limits without assuming local relaxation. We emphasize in particular that a generalized hydrodynamic behaviour emerges in a high-momentum and short-time limit, besides the more common large-space and late-time limit, which is akin to a semi-classical expansion. In this limit, conserved charges do not require a large number of particles to be described by generalized hydrodynamics. Besides, we show that this wavelet representation provides an efficient numerical algorithm for a complete description of out-of-equilibrium dynamics of hardcore bosons. Comment: 35 pages |
| Databáze: | arXiv |
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