Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates

Details Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates

1999-09-09

arxiv.org/abs/chao-dyn/9909014v2

Phys. Rev. Lett. {\bf 84}, 2841 (2000).

Physics

Condensed Matter

4 pages, 1 figure. Improved presentation. To be published in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.84.2841

We consider a classically chaotic system that is described by an Hamiltonian $H(Q,P;x)$ where x is a constant parameter. Our main interest is in the case of a gas-particle inside a cavity, where $x$ controls a deformation of the boundary or the position of a `piston'. The quantum-eigenstates of the system are $|n(x)>$. We describe how the parametric kernel $P(n|m)=||^2$ evolves as a function of $\delta x = (x-x_0)$. We explore both the perturbative and the non-perturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as of random-waves and random-matrix-theory (RMT) considerations.

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