Beyond the rotating wave
approximation: effective interactions and
quantum phase transitions
We study the distinctive features of quantum dynamics governed by
Hamiltonians which do no preserve the total number of excitations. In
particular we focus on the physical effects appearing exclusively due to
the presence of counter-rotating terms in the Hamiltonians describing
interaction of two or more quantum systems. Two interesting in
applications limits are analyzed:
1. Weak coupling regime: when the coupling constants is much lower
when all the typical system's frequencies. Here we show that a set of
effective resonant interactions describes the quantum dynamics.
2. Intermediate regime: when characteristic frequencies of the some
interacting subsystems are lower than the coupling constants, but the
other are higher. In this case quantum phase transitions naturally arise.