2009/06/30 by Jack Kuipers
Mathematics · Physics and Astronomy · #Chaotic #Chaotic scattering #Correlation function (quantum field theory) #Probability density function #Quantum chaos and dynamical systems #Quantum many-body systems #Scattering #Semiclassical physics #Set (abstract data type) #Spectral Theory in Mathematical Physics #Trajectory #nlin.CD
paper · pdf · doi:10.1088/1751-8113/42/42/425101
published as J Phys A 42 (2009) 425101 · Refereed version. 26 pages, 3 figures in 6 parts
arxiv created 2009/09/21 · openalex publication_date 2009/09/30 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The addition of tunnel barriers to open chaotic systems, as well as representing more general physical systems, leads to much richer semiclassical dynamics. In particular, we present here a complete semiclassical treatment for these systems, in the regime where Ehrenfest time effects are negligible and for times shorter than the Heisenberg time. To start we explore the trajectory structures which contribute to the survival probability, and find results that are also in agreement with random matrix theory. Then we progress to the treatment of the probability current density and are able to show, using recursion relation arguments, that the continuity equation connecting the current density to the survival probability is satisfied to all orders in the semiclassical approximation. Following on, we also consider a correlation function of the scattering matrix, for which we have to treat a new set of possible trajectory diagrams. By simplifying the contributions of these diagrams, we show that the results obtained here are consistent with known properties of the scattering matrix. The correlation function can be trivially connected to the ac and dc conductances, quantities of particular interest for which finally we present a semiclassical expansion.