Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1908.06920 · Acta Physica Polonica A

Reflection Time Difference as a Probe of S-Matrix Zeroes in Chaotic Resonance Scattering

Yan V. Fyodorov

Published Nov 1, 2019• 14 citations
arXivHTMLPDF

Abstract

Motivated by recent interest in the zeroes of S-matrix entries in the complex energy plane, the Heidelberg model of resonance scattering is used to introduce the notion of reflection time difference.As is shown, it plays the same role for the zeroes as the Wigner time delay plays for the S-matrix poles.
DOI
10.12693/aphyspola.136.785

Related papers

Time delay and resonances in potential scattering

Werner O. Amrein, Kalyan B. Sinha

We present stationary expressions for the on-shell time delay operator and for its trace in quantum-mechanical potential scattering. The trace of this operator is shown to represent the time delay for a monoenergetic and well-collimated beam of initial states. For exponentially decaying potentials the total scattering cross section and the trace of the on-shell time delay operator have analytic extensions to complex energies, with poles at most at the usual resonance poles (poles of the analytically continued S -matrix) in the lower half plane and at their mirror images with respect to the real axis. At real energies close to such a pole both the scattering cross section and the time delay are approximately of Breit–Wigner type, the sign of the time delay being related to that of the virial. These results corroborate the idea that a resonance should show up through a peak in the scattering cross section and a large (though positive) time delay.

Journal of Physics A Mathematical and General•Jul 5, 2006•15 citations

Open orbits and the semiclassical dwell time

Caio Lewenkopf, Raúl O. Vallejos

The Wigner delay time is addressed semiclassically using Miller's S -matrix expressed in terms of open orbits. This leads to a very appealing expression, in terms of classical paths, for the energy averaged Wigner time delay in chaotic scattering. The same approach also puts in evidence the semiclassical incapability to correctly assess the time delay higher moments. This limitation suggests that the use of the semiclassical approximation to quantify fluctuations in scattering phenomena, like in mesoscopic physics, has to be considered with great caution.

arXiv:cond-mat/0310025•Journal of Physics A Mathematical and General•Dec 9, 2003•16 citations

Delay time experienced by a particle undergoing resonant scattering: The case of the 3D square well

Raúl C. Mun̄oz

A formalism to calculate the time delay experienced by a particle undergoing scattering is presented. The formalism is a natural extension of Wigner’s delay time to wave packets which do not exhibit a well defined angular momentum. The delay depends only on the partial wave phase shifts characterizing the scattering event. The formalism is tested by applying it to the 3D square well. The results are shown to agree with the known properties of resonant scattering as deduced from a study of the poles of the scattering matrix in the complex energy plane.

The Journal of Chemical Physics•Dec 15, 1985•0 citations

Time-energy coherent states and adiabatic scattering

J. E. Avron, Alexander Elgart, Gian Michele Graf +1 more

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state ρ(H0) the energy shift determines the outgoing state.

arXiv:math-ph/0202021•Journal of Mathematical Physics•Jul 1, 2002•27 citations

Concerning the Notion of "Time Interval" in S -Matrix Theory

M. L. Goldberger, Kenneth Watson

The notion of time duration is considered within the framework of $S$-matrix theory. It is shown that Wigner's definition of the time delay, $\ensuremath{-}i\ensuremath{\hbar}[(\frac{d\mathrm{ln}S}{\mathrm{dE}})]$, for a scattering process permits one to define time duration in a "coarse-grained" sense.

Physical Review•Sep 15, 1962•41 citations

Random Matrix Theory for Chaotic Wave Scattering and Transport

Yan V. Fyodorov, Dmitry V. Savin

We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.

nlin.CDCross-listedarXiv:2606.10957•Jun 10, 2026
We present stationary expressions for the on-shell time delay operator and for its trace in quantum-mechanical potential scattering. The trace of this operator is shown to represent the time delay for a monoenergetic and well-collimated beam of initial states. For exponentially decaying potentials the total scattering cross section and the trace of the on-shell time delay operator have analytic extensions to complex energies, with poles at most at the usual resonance poles (poles of the analytically continued S -matrix) in the lower half plane and at their mirror images with respect to the real axis. At real energies close to such a pole both the scattering cross section and the time delay are approximately of Breit–Wigner type, the sign of the time delay being related to that of the virial. These results corroborate the idea that a resonance should show up through a peak in the scattering cross section and a large (though positive) time delay.
The Wigner delay time is addressed semiclassically using Miller's S -matrix expressed in terms of open orbits. This leads to a very appealing expression, in terms of classical paths, for the energy averaged Wigner time delay in chaotic scattering. The same approach also puts in evidence the semiclassical incapability to correctly assess the time delay higher moments. This limitation suggests that the use of the semiclassical approximation to quantify fluctuations in scattering phenomena, like in mesoscopic physics, has to be considered with great caution.
A formalism to calculate the time delay experienced by a particle undergoing scattering is presented. The formalism is a natural extension of Wigner’s delay time to wave packets which do not exhibit a well defined angular momentum. The delay depends only on the partial wave phase shifts characterizing the scattering event. The formalism is tested by applying it to the 3D square well. The results are shown to agree with the known properties of resonant scattering as deduced from a study of the poles of the scattering matrix in the complex energy plane.
Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state ρ(H0) the energy shift determines the outgoing state.
The notion of time duration is considered within the framework of SSS-matrix theory. It is shown that Wigner's definition of the time delay, $\ensuremath{-}i\ensuremath{\hbar}[(\frac{d\mathrm{ln}S}{\mathrm{dE}})]$, for a scattering process permits one to define time duration in a "coarse-grained" sense.
We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.