scholarly journals Symmetric bound states of Josephson vortices in BEC

2018 ◽  
Vol 96 (2) ◽  
pp. 208-212 ◽  
Author(s):  
Muhammad Irfan Qadir ◽  
Tehseen Zoma
Keyword(s):  
Bound States ◽  
Coupling Parameter ◽  
Bound State ◽  
Dark Soliton ◽  
Critical Value ◽  
One Dimensional ◽  
Josephson Vortices ◽  
Domain Of Existence ◽  
Existence And Stability ◽  
Bose Einstein

A system of two parallel coupled cigar-shaped Bose–Einstein condensates is considered in an effectively one-dimensional limit. The dynamics of the system is characterized by a pair of coupled nonlinear Gross–Pitaevskii equations. In particular, the existence and stability of symmetric bound states of Josephson vortices are investigated. It is realized that the symmetric bound state Josephson vortices solution persists stably in its whole domain of existence for the coupling strength. Nevertheless, the bound states solution converts into a dark soliton at a critical value of coupling parameter.

scholarly journals Bound states of atomic Josephson vortices

2017 ◽  
Vol 95 (4) ◽  
pp. 336-339 ◽  
Author(s):  
Muhammad Irfan Qadir ◽  
Usama Tahir
Keyword(s):  
Bound States ◽  
Coupling Parameter ◽  
Bound State ◽  
Dark Soliton ◽  
Critical Value ◽  
One Dimensional ◽  
Josephson Vortices ◽  
Existence And Stability ◽  
The Stability ◽  
Bose Einstein

We study the existence and stability of the bound state Josephson vortices solution in two parallel quasi one-dimensional coupled Bose–Einstein condensates. The system can be elucidated by linearly coupled Gross–Pitaevskii equations. The purpose of this study is to investigate the effects of altering the strength of coupling between the two condensates over the stability of the bound-state Josephson vortices. It is found that the stability of bound-state Josephson vortices depends on the value of coupling strength. However, at a critical value of coupling parameter, the Josephson vortices solution transforms into a coupled dark soliton.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION IN THE PRESENCE OF SHORT RANGE POTENTIALS

2006 ◽  
Vol 21 (02) ◽  
pp. 313-325 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
CLARA ROJAS
Keyword(s):  
Short Range ◽  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

scholarly journals Multi-dark soliton solutions for the (2+1)-dimensional multi-component Maccari system

2019 ◽  
Vol 33 (31) ◽  
pp. 1950390
Author(s):  
Tao Xu ◽  
Yong Chen ◽  
Zhijun Qiao
Keyword(s):  
Bound States ◽  
Arbitrary Order ◽  
Soliton Solutions ◽  
Bound State ◽  
Dark Soliton ◽  
Stationary Case ◽  
Kp Hierarchy ◽  
Short Waves ◽  
Dark Solitons ◽  
Two Component

Based on reduction of the KP hierarchy, the general multi-dark soliton solutions in Gram type determinant forms for the (2[Formula: see text]+[Formula: see text]1)-dimensional multi-component Maccari system are constructed. Especially, the two component coupled Maccari system comprising of two component short waves and single-component long waves are discussed in detail. Besides, the dynamics of one and two dark-dark solitons are analyzed. It is shown that the collisions of two dark-dark solitons are elastic by asymptotic analysis. Additionally, the two dark-dark solitons bound states are studied through two different cases (stationary and moving cases). The bound states can exist up to arbitrary order in the stationary case, however, only two-soliton bound state exists in the moving case. Besides, the oblique stationary bound state can be generated for all possible combinations of nonlinearity coefficients consisting of positive, negative and mixed cases. Nevertheless, the parallel stationary and the moving bound states are only possible when nonlinearity coefficients take opposite signs.

GENERATION AND EVOLUTION OF DARK-SOLITON TRAINS IN ONE-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

2006 ◽  
Vol 20 (07) ◽  
pp. 805-815
Author(s):  
QIANG TIAN ◽  
JINGPING WANG
Keyword(s):  
Dark Soliton ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Bose Einstein

Generation and evolution of dark-soliton trains are studied. We focus on the dynamics resulting from large initial excitations in one-dimensional Bose–Einstein condensates trapped by a harmonic potential numerically. We consider three different techniques of controllable creation of multisolition structures (soliton trains). Multisoliton effects are discussed.

scholarly journals Scattering State of Klein-Gordon Particles by q-Parameter Hyperbolic Poschl-Teller Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Akpan Ndem Ikot ◽  
Hillary P. Obong ◽  
Israel O. Owate ◽  
Michael C. Onyeaju ◽  
Hassan Hassanabadi
Keyword(s):  
Bound States ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Bound State ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Scattering State ◽  
Klein Gordon ◽  
The One

The one-dimensional Klein-Gordon equation for equal vector and scalar q-parameter hyperbolic Poschl-Teller potential is solved in terms of the hypergeometric functions. We calculate in detail the solutions of the scattering and bound states. By virtue of the conditions of equation of continuity of the wave functions, we obtained explicit expressions for the reflection and transmission coefficients and energy equation for the bound state solutions.

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