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Transport properties of open chaotic ballistic systems and their statisticscan be expressed in terms of the scattering matrix connecting incoming andoutgoing wavefunctions. Here we calculate the dependence of correlationfunctions of arbitrarily many pairs of scattering matrices at differentenergies on the Ehrenfest time using trajectory based semiclassical methods.This enables us to verify the prediction from effective random matrix theorythat one part of the correlation function obtains an exponential dampingdepending on the Ehrenfest time, while also allowing us to obtain theadditional contribution which arises from bands of always correlatedtrajectories. The resulting Ehrenfest-time dependence, responsible e.g. forsecondary gaps in the density of states of Andreev billiards, can also be seento have strong effects on other transport quantities like the distribution ofdelay times.

Ehrenfest-time dependence of counting statistics for chaotic ballistic systems