V A Gopar et al 2008 J. Phys. A: Math. Theor. 41 015103 doi:10.1088/1751-8113/41/1/015103
Chaotic scattering with direct processes: a generalization of Poisson's kernel for non-unitary scattering matrices
V A Gopar1,2, M Martínez-Mares3 and R A Méndez-Sánchez4
Show affiliationsThe problem of chaotic scattering in the presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in the absence of such processes for non-unitary scattering matrices 
. When prompt responses are absent, 
is uniformly distributed according to its invariant measure in the space of 
matrices with zero average 
. When direct processes occur, the distribution of 
is non-uniform and is characterized by an average 
. In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well-known Poisson kernel, we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied, for transport experiments in chaotic systems where gains or losses are present, for example in microwave chaotic cavities or graphs, and acoustic or elastic resonators.
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- Dates
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Issue 1 (11 January 2008)
Received 25 September 2007, in final form 13 November 2007
Published 12 December 2007
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Chaotic scattering with direct processes: a generalization of Poisson's kernel for non-unitary scattering matrices
V A Gopar et al 2008 J. Phys. A: Math. Theor. 41 015103
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