Physics – Condensed Matter – Quantum Gases
Scientific paper
2011-12-21
Physics
Condensed Matter
Quantum Gases
Scientific paper
A simple four-mode Bose-Hubbard model with two distinct dynamical time scales can be considered as a paradigm for thermal contact between mesoscopic quantum systems. Among the perturbations around excited stationary states of the system is a slow collective excitation that is not present in the Bogoliubov spectrum. This extra mode is basically resonant energy exchange, as between two weakly coupled oscillators, but it is nontrivially modified by nonlinearity. It is similar enough to second sound in liquid Helium II that it may aptly be called a second Josephson oscillation. In this paper we extend the analysis of this system into the fully quantum regime, by comparing the exact energy spectrum for cases of up to 40 particles with the results of an analytical adiabatic theory. Apart from the intrinsic interest of this system as a toy model for quantum thermodynamics, the accuracy of our adiabatic theory shows that good free quasiparticle approximations may be constructed around highly excited states of many-body systems, by a conceptually straightforward redoubling of Bogoliubov theory.
Anglin James R.
Strzys M. P.
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