Statistics of time delay and scattering correlation functions in chaotic systems. I. Random matrix theory

Journal Article · Mon Jun 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4922746· OSTI ID:22479692

Novaes, Marcel ^[1]

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1. Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)

We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.

• OSTI ID: 22479692
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
CORRELATION FUNCTIONS
POLYNOMIALS
RANDOMNESS
S MATRIX
SCATTERING
SEMICLASSICAL APPROXIMATION
STATISTICS
T INVARIANCE
TIME DELAY