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:1812.04623

Maximizing Time Delays for Toy Models of Quantum Scattering

Erin Crawley

Published Dec 11, 2018• 0 citations
arXivHTMLPDF

Abstract

We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, $n$-site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for $n=1$. When $n=2$, we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.

DOI
10.48550/arxiv.1812.04623

Related papers

Time delay in simple one-dimensional systems

W. van Dijk, Ken Kiers A

The time delay or the time advance in the scattering of simple one-dimensional systems can be evaluated in a straightforward manner for certain potential models. It is found that when the interacting potential is attractive and has a strength such that it nearly supports an additional bound state, the time delay at small scattering energy is very large. On the other hand, if the potential supports a bound state with nearly zero binding energy, the time advance near threshold is anomalously large. The behavior of a wave packet scattering from the double delta-function potential is also investigated.

American Journal of Physics•Jun 1, 1992•30 citations

Delay time for a single resonance

M. Moshińsky, G. Monsiváis

Delay time is usually discussed in terms of a wavepacket going through a potential barrier and its time of reappearance on the other side of it, as compared with the corresponding problem in free motion. Wigner stressed though that an interaction should be described by an matrix and a particular case would be that of a single resonance. Long ago a dynamical model was developed for this case in which the interaction takes place at a point through boundary conditions. It is used here to discuss the passage to x > 0 of a plane wave initially constrained to the interval . Comparing our result with the corresponding problem of free-particle motion, at the classical time of flight of the particles, we obtain information on delay times for wide and narrow resonances. Note that our approach is different from the one using stationary states, i.e. when the time , originally introduced by Wigner. For completeness we also discuss the latter for our problem in the concluding section and compare the results with those obtained in this paper.

Journal of Physics G Nuclear and Particle Physics•May 1, 1997•3 citations

Time delays in reactions with intermediate and compound nuclear structure

E. Rosengaus, Pier A. Mello, M. Bauer

We present a simple model, analytically solvable, of the time evolution of the scattering of a wave packet, which exhibits and clarifies the compound nucleus process, and can be easily extended to the study of the time delays involved when intermediate structure is present.

American Journal of Physics•Nov 1, 1978•2 citations

Effects of coupling with a quantum oscillator on time-evolution of uncertainties of a quantum particle and entanglement entropy

Pei-Song He

The time evolution of a quantum particle’s product of uncertainties in position and momentum is calculated when it is coupled with an external source. We have used a simple toy model where the particle is subject to a harmonic potential and coupled with an equivalent harmonic oscillator via a linear term. It is found that the long-time-averaged product is an increasing function of the coupling strength. It diverges when one of the eigenmodes of the coupled system goes soft, with the singular term twice of that for the stationary state. Generally, there is a jump of finite size for this quantity when a small coupling is turned on, compared to the uncoupled case. Similar behaviors have also been found for the von Neumann entanglement entropy, which is calculated exactly using a covariance matrix formalism. We find that the mode-interference plays an important role in the main features of this work.

Modern Physics Letters B•Apr 25, 2023•1 citation

Time delay for dispersive systems in quantum scattering theory. I. The Friedrichs model

Rafael Tiedra de Aldecoa

We present a method for proving the existence of time delay (defined in terms of sojourn times) as well as its identity with Eisenbud-Wigner time delay in the case of the Friedrichs model. We show that this method applies to scattering by finite rank potentials.

arXiv:0804.1349•Apr 8, 2008•0 citations

The sojourn time of the inverted isotropic harmonic oscillators in a tilted magnetic field

Yanjie Wang, Wei Guo, Xiao‐Yin Pan

Abstract By employing the Feynman path integral approach, we investigate the sojourn time of a two-dimensional (2D) and a three-dimensional (3D) inverted isotropic harmonic oscillator under a tilted magnetic field. It is shown that the sojourn time in the 2D case behaves quite differently from the 3D case. In the 3D case, the sojourn time is a monotonically increasing function of the strength of the magnetic field, and its value approaches a finite value as the strength of the magnetic field approaches infinity. In the 2D case, the behavior of the sojourn time as a function of the strength and the angle θ of inclination of the magnetic field is much complicated. When the angle of inclination θ > π 4 , the system is unstable and the sojourn time is always finite. However, when 0 ≤ θ < π 4 , the system possesses a stable region with infinite large sojourn time as the strength of the magnetic field varies. The reason behind is explained via stability region analysis.

Physica Scripta•Jan 14, 2020•1 citation
We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, nnn-site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for n=1n=1n=1. When n=2n=2n=2, we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.
The time delay or the time advance in the scattering of simple one-dimensional systems can be evaluated in a straightforward manner for certain potential models. It is found that when the interacting potential is attractive and has a strength such that it nearly supports an additional bound state, the time delay at small scattering energy is very large. On the other hand, if the potential supports a bound state with nearly zero binding energy, the time advance near threshold is anomalously large. The behavior of a wave packet scattering from the double delta-function potential is also investigated.
Delay time is usually discussed in terms of a wavepacket going through a potential barrier and its time of reappearance on the other side of it, as compared with the corresponding problem in free motion. Wigner stressed though that an interaction should be described by an matrix and a particular case would be that of a single resonance. Long ago a dynamical model was developed for this case in which the interaction takes place at a point through boundary conditions. It is used here to discuss the passage to x > 0 of a plane wave initially constrained to the interval . Comparing our result with the corresponding problem of free-particle motion, at the classical time of flight of the particles, we obtain information on delay times for wide and narrow resonances. Note that our approach is different from the one using stationary states, i.e. when the time , originally introduced by Wigner. For completeness we also discuss the latter for our problem in the concluding section and compare the results with those obtained in this paper.
The time evolution of a quantum particle’s product of uncertainties in position and momentum is calculated when it is coupled with an external source. We have used a simple toy model where the particle is subject to a harmonic potential and coupled with an equivalent harmonic oscillator via a linear term. It is found that the long-time-averaged product is an increasing function of the coupling strength. It diverges when one of the eigenmodes of the coupled system goes soft, with the singular term twice of that for the stationary state. Generally, there is a jump of finite size for this quantity when a small coupling is turned on, compared to the uncoupled case. Similar behaviors have also been found for the von Neumann entanglement entropy, which is calculated exactly using a covariance matrix formalism. We find that the mode-interference plays an important role in the main features of this work.
Abstract By employing the Feynman path integral approach, we investigate the sojourn time of a two-dimensional (2D) and a three-dimensional (3D) inverted isotropic harmonic oscillator under a tilted magnetic field. It is shown that the sojourn time in the 2D case behaves quite differently from the 3D case. In the 3D case, the sojourn time is a monotonically increasing function of the strength of the magnetic field, and its value approaches a finite value as the strength of the magnetic field approaches infinity. In the 2D case, the behavior of the sojourn time as a function of the strength and the angle θ of inclination of the magnetic field is much complicated. When the angle of inclination θ > π 4 , the system is unstable and the sojourn time is always finite. However, when 0 ≤ θ < π 4 , the system possesses a stable region with infinite large sojourn time as the strength of the magnetic field varies. The reason behind is explained via stability region analysis.