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

Chinese Physics

Landau damping of collective modes in a harmonically trapped Bose–Einstein condensate

Xiaodong Ma, Yu Long Zhou, Ma Yong-Li, Guoxiang Huang

Published Jul 26, 2006• 10 citations
Publisher

Abstract

This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose–Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas–Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.

DOI
10.1088/1009-1963/15/8/040

Related papers

Analytical calculations on Landau damping of collective modes in anisotropic Bose-Einstein condensates

Xiaodong Ma, Yong-li Ma, Guoxiang Huang

We develop an analytical approach for calculating the Landau damping of collective modes in the Bose-Einstein condensate trapped by an anisotropic harmonic potential. Based on a variational ground-state wave function obtained by solving the time-independent Gross-Pitaevskii equation beyond Thomas-Fermi approximation, we solve the Bogoliubov--de Gennes equations describing thermal excited quasiparticles and provide divergence-free analytical solutions for the Bogoliubov amplitudes and coupling matrix elements that characterize the interaction between the collective modes and the quasiparticles. With these analytical results we evaluate the Landau damping rates of several collective modes for various anisotropic parameters of the trapping potential in terms of the formulas derived from a time-dependent mean-field theory. In addition, we discuss the dependence of the damping rates on temperature, particle number, trapping frequency, and anisotropic parameter of the system, and compare our theoretical results with experimental and numerical data reported in literature.

Physical Review A•Jan 31, 2007•5 citations

Landau Damping of Collective Modes in a Disc-Shaped Bose–Einstein Condensate

Xiaodong Ma, Ma Yong-Li, Guoxiang Huang

We investigate the Landau damping of collective modes in an anisotropic Bose–Einstein condensate (BEC). Based on divergence-free analytical solutions for the ground state wavefunction of the condensate and all eigenvalues and eigenfunctions for thermal excited quasiparticles, we make a detailed analytical calculation on coupling matrix elements. We evaluate the Landau damping of a quadrupole collective mode in the BEC with a disc-shaped trap and discuss its dependence on temperature and particle number of the system.

Chinese Physics Letters•Feb 19, 2007•3 citations

Landau damping of collective mode in a quasi-two-dimensional repulsive Bose—Einstein condensate

Xiaodong Ma, Zhan-Jin Yang, Junzhe Lu +1 more

We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hatree—Fock—Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system. We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode. We discuss the dependence of the Landau damping on temperature, on atom number in the condensate, on transverse trapping frequency and on the length of the condensate. The energy width of the collective mode is taken into account in our calculation. With little approximation, our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.

Chinese Physics B•Jul 1, 2011•5 citations

Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

M. Guilleumas, Лев П. Питаевский

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.

arXiv:cond-mat/9906214•Physical Review A•Dec 9, 1999•52 citations

Landau damping and frequency-shift of a monopole mode in a spherical rubidium Bose-Einstein condensate

Sheng Peng

The Landau damping and frequency- shift of a monopole mode in a spherical rubidium Bose- Einstein condensate are investigated by using the Hartree- Fock- Bogoliubov approximation. The damping rate and frequency- shift magnitude and their temperature dependence are analytically calculated by using the parameters of particle number and traping frequency in the study of numerical simulation and experiment in existence. In the calculation,the practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain the calculation formula for damping and frequency- shift,and the first approximation of Gaussian distribution function is employed for the ground- state wavefunction to eliminate the divergence of the three- mode coupling matrix elements. Our calculation results are directly and indirectly compared with the numerical simulation ones and experimental ones,respectively. And all the comparison illustrate that our method is reasonable.

Journal of Atomic and Molecular Physics•Jan 1, 2015•1 citation

Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose—Einstein Condensate

Zhan-Jin Yang, Zhao-Liang Chai, Chenxu Li +1 more

We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.

Communications in Theoretical Physics•May 1, 2012•6 citations
This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose–Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas–Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.
We develop an analytical approach for calculating the Landau damping of collective modes in the Bose-Einstein condensate trapped by an anisotropic harmonic potential. Based on a variational ground-state wave function obtained by solving the time-independent Gross-Pitaevskii equation beyond Thomas-Fermi approximation, we solve the Bogoliubov--de Gennes equations describing thermal excited quasiparticles and provide divergence-free analytical solutions for the Bogoliubov amplitudes and coupling matrix elements that characterize the interaction between the collective modes and the quasiparticles. With these analytical results we evaluate the Landau damping rates of several collective modes for various anisotropic parameters of the trapping potential in terms of the formulas derived from a time-dependent mean-field theory. In addition, we discuss the dependence of the damping rates on temperature, particle number, trapping frequency, and anisotropic parameter of the system, and compare our theoretical results with experimental and numerical data reported in literature.
We investigate the Landau damping of collective modes in an anisotropic Bose–Einstein condensate (BEC). Based on divergence-free analytical solutions for the ground state wavefunction of the condensate and all eigenvalues and eigenfunctions for thermal excited quasiparticles, we make a detailed analytical calculation on coupling matrix elements. We evaluate the Landau damping of a quadrupole collective mode in the BEC with a disc-shaped trap and discuss its dependence on temperature and particle number of the system.
We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hatree—Fock—Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system. We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode. We discuss the dependence of the Landau damping on temperature, on atom number in the condensate, on transverse trapping frequency and on the length of the condensate. The energy width of the collective mode is taken into account in our calculation. With little approximation, our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.
The Landau damping and frequency- shift of a monopole mode in a spherical rubidium Bose- Einstein condensate are investigated by using the Hartree- Fock- Bogoliubov approximation. The damping rate and frequency- shift magnitude and their temperature dependence are analytically calculated by using the parameters of particle number and traping frequency in the study of numerical simulation and experiment in existence. In the calculation,the practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain the calculation formula for damping and frequency- shift,and the first approximation of Gaussian distribution function is employed for the ground- state wavefunction to eliminate the divergence of the three- mode coupling matrix elements. Our calculation results are directly and indirectly compared with the numerical simulation ones and experimental ones,respectively. And all the comparison illustrate that our method is reasonable.
We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.