Measuring the Lyapunov exponent using quantum mechanics

Details Measuring the Lyapunov exponent using quantum mechanics Measuring the Lyapunov exponent using quantum mechanics

2001-12-10

arxiv.org/abs/nlin/0112015v1

Nonlinear Sciences

Chaotic Dynamics

9 pages, 6 figures

Scientific paper

10.1103/PhysRevE.65.046209

We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the wave packet overlap function. We show that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the difference between the two Hamiltonians larger, the characteristic exponential decay time becomes the Lyapunov exponent of the classical system. We illustrate our theoretical findings by investigating numerically the overlap decay function of a two-dimensional dynamical system.

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