Time-dependent point interactions and infinite walls: some results for wavepacket scattering

Kühn, Johann H.; Zanetti, F. M.; Azevedo, A. L.; Schmidt, Alexandre G. M.; Cheng, Bin Kang; Luz, M. G. E. da

doi:10.1088/1464-4266/7/3/011

Cited by 8 publications

(10 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Instead, these two systems exhibit phase-sensitive tunneling resonances for intermediate frequencies, which can be explained by an increase in the relative kinetic energy of incoming particles when the barrier approaches them. A moving potential barrier can also be used to tailor wave packets or to split an initial pulse into several well-separated coherent pulses, see [12,13].…”

Section: Introductionmentioning

confidence: 99%

Dynamical trapping and chaotic scattering of the harmonically driven barrier

et al. 2008

View full text Add to dashboard Cite

A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM-structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical trapping and chaotic scattering of the harmonically driven barrier

et al. 2008

View full text Add to dashboard Cite

show abstract

“…This corresponds to the most general possible BC (consistent with flux conservation) for a quantum particle interacting with an infinite wall in the half-line [174,233].…”

Section: C1 Few Usual Boundary Conditions For Quantum Graphsmentioning

confidence: 69%

“…(b) General point interactions are very diverse in their scattering properties. For instance, the intriguing aspects of transmission and reflection from point interactions have been discussed in distinct situations, such as, time-dependent potentials [174], nonlinear Schrödinger equation [175] and shredding by sparse barriers [176]. So, the mentioned procedure allows to have all the features of arbitrary zero-range potentials also in the context of quantum graphs.…”

Section: The Vertices As Zero-range Potentialsmentioning

confidence: 99%

“…Also, to illustrate the situation one can define only a reflection coefficient for the region V (see next), we assume for vertex B boundary conditions leading to a zero transmission amplitude, i.e., the reflection probability from vertex B is exactly 1. In this way we can generally write r B = exp[iφ B ], for φ B (k) a wavenumber dependent phase [174]. For A, we consider arbitrary boundary condition corresponding to generic r A and t A .…”

Section: Basic Aspectsmentioning

confidence: 99%

See 1 more Smart Citation

Green’s function approach for quantum graphs: An overview

et al. 2016

View full text Add to dashboard Cite

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function (G) framework. This approach is particularly interesting because G can be written as a sum over classical-like paths, where local quantum effects are taking into account through the scattering matrix amplitudes (basically, transmission and reflection amplitudes) defined on each one of the graph vertices. Hence, the exact G has the functional form of a generalized semiclassical formula, which through different calculation techniques (addressed in details here) always can be cast into a closed analytic expression. It allows to solve exactly arbitrary large (although finite) graphs in a recursive and fast way. Using the Green's function method, we survey many properties for open and closed quantum graphs as scattering solutions for the former and eigenspectrum and eigenstates for the latter, also considering quasi-bound states. Concrete examples, like cube, binary trees and Sierpiński-like topologies are presented. Along the work, possible distinct applications using the Green's function methods for quantum graphs are outlined.

show abstract

“…The propagator for general four parameter family of point interactions have been given in Albeverio et al [27]. Propagators for systems involving δ potentials are also studied from various points of view in references [28][29][30][31][32][33][34]. The propagator for derivatives of Dirac delta distribution for constant strengths has been recently studied in Lange [11].…”

Section: Introductionmentioning

confidence: 99%

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

2020

View full text Add to dashboard Cite

We study the time-dependent Schrödinger equation with finite number of Dirac δ and δ ′ potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrödinger equation for δ ′ potential with particular forms of the strengths.

show abstract

Time-dependent point interactions and infinite walls: some results for wavepacket scattering

Cited by 8 publications

References 53 publications

Dynamical trapping and chaotic scattering of the harmonically driven barrier

Dynamical trapping and chaotic scattering of the harmonically driven barrier

Green’s function approach for quantum graphs: An overview

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

Contact Info

Product

Resources

About