Kuipers, Jack and Waltner, Daniel and Gutiérrez, Martha and Richter, Klaus (2009) The semiclassical continuity equation for open chaotic systems. Nonlinearity 22, pp. 1945-1964.
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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.
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter|
|Projects:||FOR 760: Scattering Systems with Complex Dynamics|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||25 May 2009 13:19|
|Last Modified:||20 Jun 2012 07:44|