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 -