Quantum transients

Campo, Adolfo del; García–Calderón, Gastón; Muga, J. G.

doi:10.1016/j.physrep.2009.03.002

Cited by 117 publications

(160 citation statements)

References 252 publications

(657 reference statements)

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“…In particular, the use of δ-functional linear trapping potentials makes it possible to find exact solutions for various transfer problems [26,27]. The dynamical process of extracting matterwave pulses from a BEC reservoir with nonlinear tweezers, induced by an appropriate laser beam, was simulated in detail in Ref.…”

Section: Introductionmentioning

confidence: 99%

Transfer and scattering of wave packets by a nonlinear trap

Malomed

Frantzeskakis

2011

Phys. Rev. E

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In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers," as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "radiation." A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, which may be dragged by a nonlinear trap moving at a constant acceleration, are briefly considered too.

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Section: Introductionmentioning

confidence: 99%

Transfer and scattering of wave packets by a nonlinear trap

Malomed

Frantzeskakis

2011

Phys. Rev. E

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“…1, are introduced by an instantaneous process of switching the shutter, and are, in fact, a manifestation of the diffraction-in-time phenomenon. It is well known that these oscillations become less pronounced and eventually disappear as one switches the shutter "continuously" over longer and longer time intervals [10,18]. Here we note that the HFK construction provides a convenient framework for analyzing the disappearance (also known as apodization) of the diffraction pattern for initial states that are localized in the position space.…”

Section: A One Dimensionmentioning

confidence: 80%

“…[9,10] for reviews). In its one-dimensional formulation, the Moshinsky problem is concerned with time evolution of a quantum particle, whose wave function Ψ(ξ; t) is localized to the semiinfinite interval (−∞, x 1 ) at time t = 0, i.e., Ψ(ξ; 0) = 0 for ξ > x 1 .…”

Section: B Diffraction In Timementioning

confidence: 99%

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Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time

Goussev

2012

Phys. Rev. A

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Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.) arXiv:1201.1389v1 [quant-ph] 6 Jan 2012Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time Arseni GoussevMax Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187 Dresden, Germany (Dated: January 9, 2012)We address the phenomenon of diffraction of non-relativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatio-temporal properties of the opening. Our construction, based on the Huygens-Fresnel principle, describes the quantum phenomena of diffraction in space and diffraction in time, as well as the interplay between the two. We illustrate the method by calculating diffraction patterns for localized wave packets passing through various time-dependent openings in one and two spatial dimensions.

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“…While resonances are given by poles of any multiplicity located in the lower half plane symmetrically with respect to the imaginary axis, anti-bound states are given by simple poles on the negative imaginary axis [1,2]. Resonances and anti-bound states are particular cases of quantum transients [3].…”

Section: Introductionmentioning

confidence: 99%

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

2017

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We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the antibound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case.

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Quantum transients

Cited by 117 publications

References 252 publications

Transfer and scattering of wave packets by a nonlinear trap

Transfer and scattering of wave packets by a nonlinear trap

Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

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