Spectral form factor near the Ehrenfest time.
We calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor of a ballistic chaotic cavity using periodic orbit theory. For the case of broken time-reversal symmetry, when the quantum correction to the form factor involves two small-angle encounters of classical trajectories, our result differs from that previously obtained using field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. While we believe that the existing field-theoretic calculation is technically flawed, the question whether the field theoretic and periodic-orbit approaches agree when more than one small-angle encounter of classical orbits is involved remains unanswered.
Brouwer
Piet W
PW
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
Rahav
Saar
S
Tian
Chushun
C