Treating Many-Body Quantum Systems by Means of Classical Mechanics

Kolovsky, Andrey R. EMERGENT COMPLEXITY FROM NONLINEARITY, IN PHYSICS, ENGINEERING AND THE LIFE SCIENCES, 191 37-48; 10.1007/978-3-319-47810-4_4 2017

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.