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

中国物理B：英文版

Analytical method for yrast line states in the interacting two-component Bose-Einstein condensate

解炳昊, 景辉

Published Jun 13, 2005• 0 citations
Publisher

Abstract

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC),omitting the difference between the two components,has been studied using an analytical method.The energy eigenstates and eigenvalues for L=0,1,2,3 are given,We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions.Except for symmetric states,there are antisymmetric states for the permutation of the two components,which cannot reduce to those in a single condensate case when the value of L is odd.

DOI
10.1088/1009-1963/11/2/003

Related papers

Analytical method for yrast line states in the interacting two-component Bose-Einstein condensate

Bing-Hao Xie, Jing Hui

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC), omitting the difference between the two components, has been studied using an analytical method. The energy eigenstates and eigenvalues for L = 0, 1, 2, 3 are given. We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions. Except for symmetric states, there are antisymmetric states for the permutation of the two components, which cannot reduce to those in a single condensate case when the value of L is odd.

Chinese Physics•Jan 22, 2002•12 citations

Analytical method for low-angular-momentum yrast states in a two-component Bose-Einstein condensate

Bing-Hao Xie, Hui Jing, Shuo Jin +1 more

We study the energy eigenvalue problem and the yrast states for a harmonically trapped two-component weak-interacting Bose-Einstein condensate (BEC) using an analytical method. The yrast states and energy eigenvalues for $L=0,1,2,3$ are given in a special case. We illustrate the different eigenstate behaviors between even L and odd L for the two-component BEC. The odd-even effect of the yrast spectrum in the two-component BEC is also pointed out.

Physical Review A•May 16, 2002•3 citations

Analytical Method for Yrast Line States in Interacting Bose-Einstein Condensates

Ying Wu, Xiaoxue Yang, Yi Xiao

We propose a method to investigate the energy eigenvalue problem and corresponding yrast line for harmonically trapped interacting N-boson systems. This method is particularly simple and effective to obtain the explicit analytical expressions of low-L energy eigenstates with L denoting systems' total angular momentum but with an arbitrarily large N. We have derived the explicit analytical results for L = 0,1,....,9 and discussed the yrast line for these low- L energy eigenstates.

Physical Review Letters•Mar 12, 2001•94 citations

Effects of the Scattering Length on the Yrast Spectrum for a Two-Component Bose–Einstein Condensates

Yu Kun Yang, Luo Bin, Liu Kun +2 more

We study the energy eigenvalue and the yrast states for a harmonically two-component weak-interacting Bose–Einstein condensate (BEC) when the intra-species and interspecies scattering length are different. The energy shift for different energy eigenvalues related to intra- and interspecies scattering lengths is calculated with the perturbation method. The actual yrast spectrum is more complicated than that when intra-species and interspecies scattering length are equal. The degenerated features disappear and so do the perfect symmetric features.

Chinese Physics Letters•Dec 1, 2004•0 citations

Density profile diagrams of harmonically trapped two-component Bose–Einstein condensates

Liang Ji, Wen Wen

We present an analytical study for density profiles of two-component Bose–Einstein condensates (BECs) in an isotropic trap within the miscible regime. The analytical equations for the density profiles and the conditions for three different density configurations are presented, which allow us to explore the density profile diagrams of general two-component BECs depending on broad ranges of experimental parameters. Furthermore, we show that the obtained explicit expressions of the density profiles can also be applied to study the collective modes of the two-component BECs, and the frequencies of the two-component BECs clearly characterize the density configurations.

Modern Physics Letters B•Dec 6, 2019•0 citations

On two-component Bose-Einstein condensates in a ring

Marcus Sköld

A Bose-Einstein condensate is a type of gas consisting of one or more types of particles called bosons which are cooled to a temperature very close the absolute zero. Under these conditions the particles all start to occupy their lowest quantum state. Once in these states it is necessary to use quantum physics to describe the behaviour of the particles by the means of a wave function which describes the probability of finding the particles in different locations. In this thesis we will study a gas consisting of two components. The wave function satisfies the Schrödinger equation, which is a linear partial differential equation. The gas will be considered to be confined within a thin ring with a cross section small enough to treat it as one dimensional. By using the mean field approximation we're able to consider a much simpler model than the individual particle interaction and reduce the many-body problem to a one-body problem. However, the linear Schrödinger equation is replaced by the non-linear Schrödinger equation. We will also investigate the mean-field yrast spectrum, where these states are the ones with minimum energy for a given angular momentum. The existence of a minimum gives the possibility of having persistent currents as argued in previous research. In order to identify the yrast states, we first look for critical points of the energy under the constraints of total probability mass and angular momentum using a special Ansatz. We then try to determine if they are minimizers using analytic and numerical methods.

•Jan 1, 2019•0 citations
The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC),omitting the difference between the two components,has been studied using an analytical method.The energy eigenstates and eigenvalues for L=0,1,2,3 are given,We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions.Except for symmetric states,there are antisymmetric states for the permutation of the two components,which cannot reduce to those in a single condensate case when the value of L is odd.
The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC), omitting the difference between the two components, has been studied using an analytical method. The energy eigenstates and eigenvalues for L = 0, 1, 2, 3 are given. We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions. Except for symmetric states, there are antisymmetric states for the permutation of the two components, which cannot reduce to those in a single condensate case when the value of L is odd.
We study the energy eigenvalue problem and the yrast states for a harmonically trapped two-component weak-interacting Bose-Einstein condensate (BEC) using an analytical method. The yrast states and energy eigenvalues for L=0,1,2,3L=0,1,2,3L=0,1,2,3 are given in a special case. We illustrate the different eigenstate behaviors between even L and odd L for the two-component BEC. The odd-even effect of the yrast spectrum in the two-component BEC is also pointed out.
We study the energy eigenvalue and the yrast states for a harmonically two-component weak-interacting Bose–Einstein condensate (BEC) when the intra-species and interspecies scattering length are different. The energy shift for different energy eigenvalues related to intra- and interspecies scattering lengths is calculated with the perturbation method. The actual yrast spectrum is more complicated than that when intra-species and interspecies scattering length are equal. The degenerated features disappear and so do the perfect symmetric features.
We present an analytical study for density profiles of two-component Bose–Einstein condensates (BECs) in an isotropic trap within the miscible regime. The analytical equations for the density profiles and the conditions for three different density configurations are presented, which allow us to explore the density profile diagrams of general two-component BECs depending on broad ranges of experimental parameters. Furthermore, we show that the obtained explicit expressions of the density profiles can also be applied to study the collective modes of the two-component BECs, and the frequencies of the two-component BECs clearly characterize the density configurations.
A Bose-Einstein condensate is a type of gas consisting of one or more types of particles called bosons which are cooled to a temperature very close the absolute zero. Under these conditions the particles all start to occupy their lowest quantum state. Once in these states it is necessary to use quantum physics to describe the behaviour of the particles by the means of a wave function which describes the probability of finding the particles in different locations. In this thesis we will study a gas consisting of two components. The wave function satisfies the Schrödinger equation, which is a linear partial differential equation. The gas will be considered to be confined within a thin ring with a cross section small enough to treat it as one dimensional. By using the mean field approximation we're able to consider a much simpler model than the individual particle interaction and reduce the many-body problem to a one-body problem. However, the linear Schrödinger equation is replaced by the non-linear Schrödinger equation. We will also investigate the mean-field yrast spectrum, where these states are the ones with minimum energy for a given angular momentum. The existence of a minimum gives the possibility of having persistent currents as argued in previous research. In order to identify the yrast states, we first look for critical points of the energy under the constraints of total probability mass and angular momentum using a special Ansatz. We then try to determine if they are minimizers using analytic and numerical methods.