A quantal entropy signature for the dynamics of pure states: studies on some model problems

Abstract

Von Neuman-Shannon entropy is zero for a pure state and remains so at every stage of its unitary evolution. However, a pseudo or quantal entropy (S_Q) of a pure state reveals significant dynamical features during a unitary evolution. S_Q can be identified, in a way with the entropy of 'basis mixing'. The quantum evolution of a pure state is generally shown to be accompanied by an early loss of information followed by an information gain at a later stage. This happens irrespective of the adiabaticity or the lack of it in the evolution process. Several model problems studied tend to suggest generality of this behaviour. These include, the photo-dissociation dynamics of a diatomic molecule modeled by a Morse oscillator, photo-dissociation of a randomly perturbed Morse oscillator, destabilization of a random linear oscillator perturbed by quartic anharmonicity, generalized Rabi oscillations in a three-level metastable system, etc. Adiabatically switching from a classically regular to a classically chaotic region of a suitable Hamiltonian which is known to generate quantum chaos is shown to leave a recognizable signature on the quantum dynamics of S_Q. This leads us to suggest that S_Q can perhaps be used as a dynamic descriptor for the onset of quantum chaos.