The quantum Frenkel-Kontorova model: a squeezed state approach

The squeezed state is used to study the one-dimensional quantum mechanical Frenkel Kontorova model. A set of coupled equations for the particle’s expectation value and the fluctuations for the ground state are derived. It is shown that quantum fluctuations renormalize the standard map to an effective sawtooth map. The mechanism underling provides an alternative and simple explanation of dynamical localization in quantum chaos.