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Semiclassical approach to S-matrix energy correlations and time delay in chaotic systems.
- Source :
-
Physical review. E [Phys Rev E] 2022 Apr; Vol. 105 (4-1), pp. 044213. - Publication Year :
- 2022
-
Abstract
- The M-dimensional scattering matrix S(E) which connects incoming to outgoing waves in a chaotic systyem is always unitary, but shows complicated dependence on the energy. This is partly encoded in correlators constructed from traces of powers of S(E+ε)S^{†}(E-ε), averaged over E, and by the statistical properties of the time delay operator, Q(E)=-iℏS^{†}dS/dE. Using a semiclassical approach for systems with broken time-reversal symmetry, we derive two kinds of expressions for the energy correlators: one as a power series in 1/M whose coefficients are rational functions of ε, and another as a power series in ε whose coefficients are rational functions of M. From the latter we extract an explicit formula for Tr(Q^{m}) which is valid for all m and is in agreement with random matrix theory predictions.
Details
- Language :
- English
- ISSN :
- 2470-0053
- Volume :
- 105
- Issue :
- 4-1
- Database :
- MEDLINE
- Journal :
- Physical review. E
- Publication Type :
- Academic Journal
- Accession number :
- 35590583
- Full Text :
- https://doi.org/10.1103/PhysRevE.105.044213