arXiv subjects

Eric J. Heller

Publications and source records attributed to Eric J. Heller.

74 records · Page 5Linked to original sources

arXiv2000

Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on ω= (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency ω. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like ω^4 as ω-> 0, for rotations like ω^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.

nlin.CD↗

arXiv2000

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

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 $δx = (x-x_0)$. 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.

chao-dyn↗