Correlations in quantum time delay

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Abstract
The semiclassical periodic orbit content of the form factor K(lambda ), the Fourier transform of the autocorrelation function, for the quantum time delay is analyzed. In analogy to the case of bounded systems, three regimes can be identified. For small lambda isolated periodic orbits can be identified. For intermediate lambda, there is a lambda exp(-Gammalambda) regime, where Gamma is the classical escape rate. For large lambda, this changes into an exp( - gamma(qm)lambda) law, where now gamma(qm) is related to an inverse lifetime of the resonances. The transition between the latter two regimes is determined by the density of resonances. The theoretical analysis is supported by numerical data for the three disk scattering system.

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