Adiabatic quantization of Andreev quantum billiard levels.
We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent lambda), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods T(n), which in turn generate a ladder of excited states epsilon (nm)=(m+1/2)pi(h) /T(n). The largest quantized period is the Ehrenfest time T(0)=lambda(-1)ln(N). Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/sqrt[N], much below the width W of the constriction.
Silvestrov
P G
PG
Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
Goorden
M C
MC
Beenakker
C W J
CW