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

Discrete and Continuous Dynamical Systems - S

Multiple dark solitons in Bose-Einstein condensates at finite temperatures

P. G. Kevrekidis, D. J. Frantzeskakis

Published Dec 29, 2010• 7 citations
Publisher

Abstract

We study analytically, as well as numerically, single- and multiple-dark matter-wave solitons in atomic Bose-Einstein condensates at finite temperatures. Our analysis is based on the study of the dissipative Gross-Pitaevskii equation, which incorporates a phenomenological damping term accounting for the interaction of the condensate with the thermal cloud. We illustrate how the negative Krein sign eigenmodes (associated with the the single- or multiple-dark soliton states) can give rise to Hopf bifurcations and oscillatory instabilities, whose ensuing dynamics is also elucidated. In all cases, the finite-temperature induced dynamics results in soliton decay, and the system eventually asymptotes to the ground state.

DOI
10.3934/dcdss.2011.4.1199

Related papers

Matter wave solitons at finite temperatures

B. Jackson, Carlo F. Barenghi, Nick P. Proukakis

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and N-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature. PACS numbers: 03.75.Lm, 05.45.Yv, 67.80.Gb 1.

•Jan 1, 2006•11 citations

Dark-bright solitons in Bose–Einstein condensates at finite temperatures

Vassos Achilleos, D Yan, P G Kevrekidis +1 more

We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.

arXiv:1110.3173•New Journal of Physics•May 1, 2012•38 citations

Matter wave solitons at finite temperatures

Brian Jackson, Carlo Barenghi, Nick P. Proukakis

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and N-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature. © Springer Science+Business Media, LLC 2007.

•Dec 31, 2007•0 citations

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

Yannan Shen, P. G. Kevrekidis, N. Whitaker +2 more

We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for both zero- and finite-temperature BECs to highlight the differences between the Hamiltonian and dissipative settings. For sufficiently small wave numbers of the periodic potential and weak linear potentials, the analytical results are found to be in good agreement with pertinent ones obtained via a Bogoliubov--de Gennes analysis and direct numerical simulations.

arXiv:1206.2993•Physical Review A•Sep 14, 2012•2 citations

Dark soliton decay in a Bose-Einstein condensate

Ashton S. Bradley, Karen Wright

We consider the decay of a dark soliton in a homogeneous BEC at finite temperature, with a particular emphasis on the effect of thermal noise on the stability of the soliton. We present an analytical treatment of a damped soliton in an unbounded system, comparing the predicted dynamics with numerical stochastic simulations of a spatially confined system. By varying the system temperature we study the relative importance of noise on the motion of the soliton. In the regime of low temperature the soliton is largely immune to thermal fluctuations, and is well described by the damped Gross-Pitaevskii equation. In this regime our analytical treatment is in close agreement with numerical simulations. For sufficiently high temperature, the thermal fluctuations have the interesting effect of increasing the stability of the soliton, extending its lifetime beyond the predictions of damped Gross-Pitaevskii theory.

•Aug 1, 2011•0 citations

Dark soliton decay in a Bose-Einstein condensate

Ashton S. Bradley, K J Wright

We consider the decay of a dark soliton in a homogeneous BEC at finite temperature, with a particular emphasis on the effect of thermal noise on the stability of the soliton.We present an analytical treatment of a damped soliton in an unbounded system, comparing the predicted dynamics with numerical stochastic simulations of a spatially confined system. By varying the system temperature we study the relative importance of noise on the motion of the soliton. In the regime of low temperature the soliton is largely immune to thermal fluctuations, and is well described by the damped Gross-Pitaevskii equation. In this regime our analytical treatment is in close agreement with numerical simulations. For sufficiently high temperature, the thermal fluctuations have the interesting effect of increasing the stability of the soliton, extending its lifetime beyond the predictions of damped Gross-Pitaevskii theory.

•Jan 1, 2011•0 citations
We study analytically, as well as numerically, single- and multiple-dark matter-wave solitons in atomic Bose-Einstein condensates at finite temperatures. Our analysis is based on the study of the dissipative Gross-Pitaevskii equation, which incorporates a phenomenological damping term accounting for the interaction of the condensate with the thermal cloud. We illustrate how the negative Krein sign eigenmodes (associated with the the single- or multiple-dark soliton states) can give rise to Hopf bifurcations and oscillatory instabilities, whose ensuing dynamics is also elucidated. In all cases, the finite-temperature induced dynamics results in soliton decay, and the system eventually asymptotes to the ground state.
We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and N-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature. PACS numbers: 03.75.Lm, 05.45.Yv, 67.80.Gb 1.
We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.
We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and N-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature. © Springer Science+Business Media, LLC 2007.
We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for both zero- and finite-temperature BECs to highlight the differences between the Hamiltonian and dissipative settings. For sufficiently small wave numbers of the periodic potential and weak linear potentials, the analytical results are found to be in good agreement with pertinent ones obtained via a Bogoliubov--de Gennes analysis and direct numerical simulations.
We consider the decay of a dark soliton in a homogeneous BEC at finite temperature, with a particular emphasis on the effect of thermal noise on the stability of the soliton. We present an analytical treatment of a damped soliton in an unbounded system, comparing the predicted dynamics with numerical stochastic simulations of a spatially confined system. By varying the system temperature we study the relative importance of noise on the motion of the soliton. In the regime of low temperature the soliton is largely immune to thermal fluctuations, and is well described by the damped Gross-Pitaevskii equation. In this regime our analytical treatment is in close agreement with numerical simulations. For sufficiently high temperature, the thermal fluctuations have the interesting effect of increasing the stability of the soliton, extending its lifetime beyond the predictions of damped Gross-Pitaevskii theory.
We consider the decay of a dark soliton in a homogeneous BEC at finite temperature, with a particular emphasis on the effect of thermal noise on the stability of the soliton.We present an analytical treatment of a damped soliton in an unbounded system, comparing the predicted dynamics with numerical stochastic simulations of a spatially confined system. By varying the system temperature we study the relative importance of noise on the motion of the soliton. In the regime of low temperature the soliton is largely immune to thermal fluctuations, and is well described by the damped Gross-Pitaevskii equation. In this regime our analytical treatment is in close agreement with numerical simulations. For sufficiently high temperature, the thermal fluctuations have the interesting effect of increasing the stability of the soliton, extending its lifetime beyond the predictions of damped Gross-Pitaevskii theory.