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

Communications in Theoretical Physics

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

Zhan-Jin Yang, Zhao-Liang Chai, Chenxu Li, Xiaodong Ma

Published May 1, 2012• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/57/5/08

Related papers

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

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 and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate

Chai Zhao-Liang, Yu Long Zhou, Xiaodong Ma

The Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate are investigated by using the time-dependent Hartree-Fock-Bogoliubov approximation. Improving the previous approach, We have taken into account the practical relaxations of elementary excitations and the orthogonal relation among them. With such an approach, we provide a new calculation formula for Landau damping rate and frequency-shift. In addition, our previous method of eliminating the divergence in three-mode coupling matrix elements is also improved by zeroing the kinetic energy at the condensate boundary instead of minimizing the ground-state energy. Based on these improvements, both the Landau damping rate and the frequency-shift of the monopole mode are analytically calculated and their temperature dependences are also discussed. And all the theoretical results are in agree meat with experimental data.

Acta Physica Sinica•Jan 1, 2013•2 citations

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

Xiaodong Ma, Yu Long Zhou, Ma Yong-Li +1 more

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.

Chinese Physics•Jul 26, 2006•10 citations

Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate

M. Guilleumas, Лев П. Питаевский

We have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed.

arXiv:cond-mat/0208047•Physical Review A•May 27, 2003•22 citations

Landau damping in trapped Bose condensed gases

B Jackson, E. Zaremba

We study Landau damping in dilute Bose–Einstein condensed gases in both spherical and prolate ellipsoidal harmonic traps. We solve the Bogoliubov equations for the mode spectrum in both of these cases, and calculate the damping by summing over transitions between excited quasiparticle states. The results for the spherical case are compared to those obtained in the Hartree–Fock (HF) approximation, where the excitations take on a single-particle character, and excellent agreement between the two approaches is found. We have also taken the semiclassical limit of the HF approximation and obtain a novel expression for the Landau damping rate involving the time-dependent self-diffusion function of the thermal cloud. As a final approach, we study the decay of a condensate mode by making use of dynamical simulations in which both the condensate and thermal cloud are evolved explicitly as a function of time. A detailed comparison of all these methods over a wide range of sample sizes and trap geometries is presented.

arXiv:cond-mat/0305251•New Journal of Physics•Jul 7, 2003•28 citations
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.
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.
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.
The Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate are investigated by using the time-dependent Hartree-Fock-Bogoliubov approximation. Improving the previous approach, We have taken into account the practical relaxations of elementary excitations and the orthogonal relation among them. With such an approach, we provide a new calculation formula for Landau damping rate and frequency-shift. In addition, our previous method of eliminating the divergence in three-mode coupling matrix elements is also improved by zeroing the kinetic energy at the condensate boundary instead of minimizing the ground-state energy. Based on these improvements, both the Landau damping rate and the frequency-shift of the monopole mode are analytically calculated and their temperature dependences are also discussed. And all the theoretical results are in agree meat with experimental data.
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 have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed.
We study Landau damping in dilute Bose–Einstein condensed gases in both spherical and prolate ellipsoidal harmonic traps. We solve the Bogoliubov equations for the mode spectrum in both of these cases, and calculate the damping by summing over transitions between excited quasiparticle states. The results for the spherical case are compared to those obtained in the Hartree–Fock (HF) approximation, where the excitations take on a single-particle character, and excellent agreement between the two approaches is found. We have also taken the semiclassical limit of the HF approximation and obtain a novel expression for the Landau damping rate involving the time-dependent self-diffusion function of the thermal cloud. As a final approach, we study the decay of a condensate mode by making use of dynamical simulations in which both the condensate and thermal cloud are evolved explicitly as a function of time. A detailed comparison of all these methods over a wide range of sample sizes and trap geometries is presented.