Parametric Evolution for a Deformed Cavity

Details Parametric Evolution for a Deformed Cavity Parametric Evolution for a Deformed Cavity

2000-08-30

arxiv.org/abs/nlin/0008040v2

Phys. Rev. E 63, 046207 (2001).

Nonlinear Sciences

Chaotic Dynamics

13 pages, 8 figures, improved introduction, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.63.046207

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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