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Lyapunov exponents across the quantum-classical transition

Arjendu Pattanayak, Carleton College

(Session 6c : Friday from 2:00 - 2:30)

Abstract. Abstract: We calculate quantum lyapunov exponents for identical noise quantum trajectories for the damped driven double-well Duffing oscillator across a range of parameters, specifically as a function of effective hbar (=beta) as well as the system damping parameter Gamma. We demonstrate the recovery of the classical Lyapunov exponent in the limit of beta to 0. In general Lyapunov exponents decrease (chaos decreases) as beta increases (as the system becomes more quantal). However, we identify the following surprises: (a) Regions of anomalous increase of chaos (Lyapunov exponents increasing with beta); (b) Regions of anomalous 'quantum-induced' onset of chaos (Lyapunov exponent going from negative to positive with increasing beta); and (c) Regions of incomplete correspondence for values of Gamma where the classical system has windows of regularity embedded in a larger chaotic parameter regime. For these last regions, the classical results are not recovered for the smallest beta we can computationally access (beta =0.003). We discuss the meaning and consequences of these results, as well as prospects for experimental verification.