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

Abstract

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 $P(n|m)=|<n(x)|m(x_0)>{|}^2$ 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.

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

References in corpus (2)

• Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
• Quantum-Classical Correspondence in Energy Space: Two Interacting Spin-Particles

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