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Parametric Evolution for a Deformed Cavity

Doron Cohen·Alex Barnett·Eric J. Heller
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Abstract

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.

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Doron Cohen, Alex Barnett, Eric J. Heller. 2001-01-02. Parametric Evolution for a Deformed Cavity. https://doi.org/10.1103/physreve.63.046207

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