Rate of energy absorption for a driven chaotic cavity

Abstract

We consider the response of a chaotic cavity in d dimensions to periodic driving. We are motivated by older studies of one-body dissipation in nuclei, and also by anticipated mesoscopic applications. For calculating the rate of energy absorption due to time-dependent deformation of the confining potential, we introduce an improved version of the wall formula. Our formulation takes into account that a special class of deformations causes no heating in the zero-frequency limit. We also derive a mesoscopic version of the Drude formula, and explain that it can be regarded as a special example of our calculations. Specifically we consider a quantum dot driven by electro-motive force which is induced by a time-dependent homogeneous magnetic field.

24 pages, 15 figures, mesoscopic Drude section much improved, to be published in J. Phys. A

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• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
• Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems
• Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions
• Escape from intermittent repellers- Periodic orbit theory for crossover from exponential to algebraic decay

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