Semiclassical Spectrum of Small Bose-Hubbard Chains: A Normal Form Approach

Abstract

We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance normal form theory. The derivation takes into account the 1:1 resonance between frequencies of a linearized classical system, and brings nonlinear terms into a corresponding normal form. The obtained expressions reproduce the exact low-energy spectrum of the system remarkably well even for a small number of particles N corresponding to fillings of just two particles per site. Such small fillings are often used in current experiments, and it is inspiring to get insight into this quantum regime using essentially classical calculations.

Minor corrections to the coefficients of the effective Hamiltonian in Eqs 14,15,18,19. Figs 1,2 are slightly modified, correspondingly

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Cited by in corpus (7)

• Coherent tunneling via adiabatic passage in a three-well Bose-Hubbard system
• Analytical results for Josephson dynamics of ultracold Bosons
• Dynamics of interacting bosons using the Herman-Kluk semiclassical initial value representation
• Time-dependent Semiclassics for Ultracold Bosons
• Understanding quantum work in a quantum many-body system
• Phase-space mixing in dynamically unstable, integrable few-mode quantum systems
• Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy