The semiclassical continuity equation for open chaotic systems

Abstract

We consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical trajectories. The current density is related to the survival probability via the continuity equation, and we show that this relation is satisfied within the semiclassical approximation to all orders. For this we develop recursion relation arguments which connect the trajectory structures involved for the survival probability, which travel from one point in the bulk to another, to those structures involved for the current density, which travel from the bulk to the lead. The current density can also be linked, via another continuity equation, to a correlation function of the scattering matrix whose semiclassical approximation is expressed in terms of trajectories that start and end in the lead. We also show that this continuity equation holds to all orders.

Refereed version: Minor changes in presentation (especially in the Introduction) and minor corrections to the start of section 6. 21 pages, 1 figure in two parts

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Cited by in corpus (5)

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• Efficient semiclassical approach for time delays
• Quantum Corrections to Fidelity Decay in Chaotic Systems
• Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials
• Interplay between coherent and incoherent decay processes in chaotic systems: the role of quantum interference