TY - JOUR

T1 - Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates

AU - Cohen, Doron

AU - Heller, Eric J.

PY - 2000/3/27

Y1 - 2000/3/27

N2 - We consider a classically chaotic system that is described by a Hamiltonian H (Q, P; x), where x is a constant parameter. Specifically, we discuss 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 δx = x - x 0. We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.

AB - We consider a classically chaotic system that is described by a Hamiltonian H (Q, P; x), where x is a constant parameter. Specifically, we discuss 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 δx = x - x 0. We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.

UR - http://www.scopus.com/inward/record.url?scp=0000085137&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.84.2841

DO - 10.1103/PhysRevLett.84.2841

M3 - Article

AN - SCOPUS:0000085137

VL - 84

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 13

M1 - 2841

ER -