Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Thomas EnglKlaus Richter

Abstract

We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons.

References

Jul 15, 1991·Physical Review. a·S C Creagh, R G Littlejohn
Sep 1, 1993·Physical Review. a·H A Weidenmüller
Jan 15, 2011·Physical Review Letters·Tilman ZiboldMarkus K Oberthaler

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Citations

May 4, 2016·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Thomas EnglKlaus Richter
Dec 15, 2016·Physical Review. E·Peter Jason, Magnus Johansson
May 6, 2017·Physical Review Letters·Maram AkilaThomas Guhr
Oct 9, 2018·Physical Review Letters·Josef RammenseeKlaus Richter
Apr 19, 2017·Physical Review. E·Qian Wang, H T Quan
Jan 13, 2019·Physical Review Letters·Bruno BertiniTomaž Prosen
Oct 21, 2020·Physical Review. E·Javier de la CruzJorge G Hirsch
May 20, 2021·Physical Review. E·Goran Nakerst, Masudul Haque

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