Quantum compacton vacuum

Abstract

We study the properties of classical and quantum compacton chains by means of extensive numerical simulations. Such chains are strongly nonlinear and their classical dynamics remains chaotic at arbitrarily low energies. We show that the collective excitations of classical chains are described by sound waves which decay rate scales algebraically with the wave number with a generic exponent value. The properties of the quantum chains are studied by the quantum Monte Carlo method and it is found that the low energy excitations are well described by effective phonon modes with the sound velocity dependent on an effective Planck constant. Our results show that at low energies the quantum effects lead to a suppression of chaos and drive the system to a quasi-integrable regime of effective phonon modes.