TY - JOUR

T1 - Periodic orbits analysis of the form factor

T2 - From ballistic to diffusive systems

AU - Agam, Oded

AU - Fishman, Shmuel

PY - 1996

Y1 - 1996

N2 - The energy level correlator K(s) and the form factor K̂(t) are calculated for a hypercubic billiard with small hyperspheres placed at random in its interior. Various regimes, characterized by the elastic mean free path l, resulting from the scattering on impurities, are identified. The analysis extends from the ballistic regime, where l is much larger than the size of the system, via intermediate regimes, to the diffusive regime, where l is much smaller than its size. Semiclassical expressions for the density of states of chaotic and integrable systems in terms of classical periodic orbits are used. The diagonal approximation for K̂(t) is made for short times, while non-perturbative methods are used for long times. The analysis makes use of analytic properties of classical dynamical zeta function associated with the Perron-Frobenius operator. The general features are relevant for mesoscopic systems.

AB - The energy level correlator K(s) and the form factor K̂(t) are calculated for a hypercubic billiard with small hyperspheres placed at random in its interior. Various regimes, characterized by the elastic mean free path l, resulting from the scattering on impurities, are identified. The analysis extends from the ballistic regime, where l is much larger than the size of the system, via intermediate regimes, to the diffusive regime, where l is much smaller than its size. Semiclassical expressions for the density of states of chaotic and integrable systems in terms of classical periodic orbits are used. The diagonal approximation for K̂(t) is made for short times, while non-perturbative methods are used for long times. The analysis makes use of analytic properties of classical dynamical zeta function associated with the Perron-Frobenius operator. The general features are relevant for mesoscopic systems.

UR - http://www.scopus.com/inward/record.url?scp=0001020512&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/29/9/016

DO - 10.1088/0305-4470/29/9/016

M3 - Article

AN - SCOPUS:0001020512

SN - 0305-4470

VL - 29

SP - 2013

EP - 2038

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 9

ER -