Treating Many-Body Quantum Systems by Means of Classical Mechanics

  • Andrey R. KolovskyEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 191)


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.


Hubbard Model Stability Island Bloch Oscillation Semiclassical Method Chaotic Component 
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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.L.V. Kirensky Institute of Physics of Siberian Branch of Russian Academy of ScienciesKrasnoyarskRussia

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