Many-body physics of identical particles is commonly believed to be a sovereign territory of Quantum Mechanics. The aim of this contribution is to show that it is actually not the case and one gets useful insights into a quantum many-body system by using the theory of classical dynamical systems. In the contribution we focus on one paradigmatic model of many-body quantum physics - the Bose– Hubbard model which, in particular, describes interacting ultracold Bose atoms in an optical lattice. We show how one can find/deduce the energy spectrum of the Bose–Hubbard model by using a kind of the semiclassical approach.
CITATION STYLE
Kolovsky, A. R. (2017). Treating many-body quantum systems by means of classical mechanics. In Springer Proceedings in Physics (Vol. 191, pp. 37–48). Springer Science and Business Media, LLC. https://doi.org/10.1007/978-3-319-47810-4_4
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