scholarly journals Scattering of a flat top solitons of cubic - quintic nonlinear Shrödinger equation by a linear delta potential

2017 ◽  
Vol 819 ◽  
pp. 012023
Author(s):  
B A Umarov ◽  
N A B Aklan
Keyword(s):  
Delta Potential ◽  
Shrodinger Equation

scholarly journals Quantum scattering on a delta potential in ghost-free theory

2018 ◽  
Vol 782 ◽  
pp. 688-693 ◽  
Author(s):  
Jens Boos ◽  
Valeri P. Frolov ◽  
Andrei Zelnikov
Keyword(s):  
Quantum Scattering ◽  
Delta Potential ◽  
Free Theory

scholarly journals Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

2018 ◽  
Vol 52 (2) ◽  
pp. 567-593 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Stephan Knapp
Keyword(s):  
Particle System ◽  
Rigorous Derivation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Delta Potential ◽  
Intermediate Particle ◽  
Stochastic Particle System ◽  
Aggregation Equation ◽  
Discretization Schemes ◽  
Theoretical Results

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

scholarly journals Quantum chaos for point scatterers on flat tori

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120509 ◽  
Author(s):  
Henrik Ueberschär
Keyword(s):  
Wave Function ◽  
Strong Coupling ◽  
Quantum Chaos ◽  
Recent Progress ◽  
Three Dimensional ◽  
Point Scatterer ◽  
Open Problems ◽  
Survey Article ◽  
Delta Potential ◽  
Flat Tori

This survey article deals with a delta potential—also known as a point scatterer—on flat two- and three-dimensional tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so-called weak and strong coupling regimes. We report on recent progress as well as a number of open problems in this field.

Rotational excitations of diatomic molecule with delta potential barrier

2018 ◽  
Vol 17 (04) ◽  
pp. 1850022
Author(s):  
Sonia Lumb ◽  
Shalini Lumb ◽  
Vinod Prasad
Keyword(s):  
Diatomic Molecule ◽  
Applied Field ◽  
Morse Potential ◽  
Short Range ◽  
Delta Function ◽  
Energy Spectra ◽  
Matrix Elements ◽  
Delta Potential ◽  
Homonuclear Diatomic Molecule ◽  
Delta Functions

The interatomic interactions in a diatomic molecule can be fairly modeled by the Morse potential. Short range interactions of the molecule with the neighboring environment can be analyzed by modifying this potential by delta functions. Energy spectra and radial matrix elements have been calculated using an accurate nine-point finite-difference method for such an interacting homonuclear diatomic molecule. The effect of the strength and position of a single delta function interaction on the alignment of this molecule has been studied. The dependence of alignment on the strength of applied field has also been analyzed.

scholarly journals Geometric Effects of a Quarter of Corrugated Torus

2018 ◽  
Vol 4 (1) ◽  
pp. 3 ◽  
Author(s):  
Run Cheng ◽  
Yong-Long Wang ◽  
Hua Jiang ◽  
Xiao-Jun Liu ◽  
Hong-Shi Zong
Keyword(s):  
Thin Layer ◽  
Resonant Tunneling ◽  
Transmission Probability ◽  
Quantization Scheme ◽  
Geometric Effects ◽  
Shrodinger Equation

In the spirit of the thin-layer quantization scheme, we give the effective Shrödinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the attractive wells reconstructed by the corrugation not being at identical depths, which is strikingly different from that of a corrugated nanotube, especially in the inner side of the torus. By numerically calculating the transmission probability, we find that the resonant tunneling peaks and the transmission gaps are merged and broadened by the corrugation of the inner side of torus. These results show that the quarter corrugated torus can be used not only to connect two tubes with different radiuses in different directions, but also to filter the particles with particular incident energies.

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