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

arXiv:1605.02220 · Journal of Statistical Mechanics Theory and Experiment

Nonequilibrium statistical mechanics in one-dimensional bose gases

F Baldovin, Alberto Cappellaro, Enzo Orlandini, Luca Salasnich

Published Jun 1, 2016• 7 citations
arXivHTMLPDF

Abstract

Abstract We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann–Vlasov equation with contact interaction, we derive an effective 1D Landau–Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas.

DOI
10.1088/1742-5468/2016/06/063303

Related papers

Quasi-One-Dimensional Bose Gases with a Large Scattering Length

G. E. Astrakharchik, D. Blume, S. Giorgini +1 more

Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).

arXiv:cond-mat/0308585•Physical Review Letters•Jan 22, 2004•81 citations

Bernstein–Greene–Kruskal and Case–Van Kampen Modes for the Landau–Vlasov Equation

Fernando Haas, Rodrigo Vidmar

The one-dimensional Landau–Vlasov equation describing ultracold dilute bosonic gases in the mean-field collisionless regime under strong transverse confinement is analyzed using traditional methods of plasma physics. Time-independent, stationary solutions are found using a similar approach as for the Bernstein–Greene–Kruskal nonlinear plasma modes. Linear stationary waves similar to the Case–Van Kampen plasma normal modes are also shown to be available. The new bosonic solutions have no decaying or growth properties, in the same sense as the analog plasma solutions. The results are applied for real ultracold bosonic gases accessible in contemporary laboratory experiments.

Atoms•Mar 1, 2022•1 citation

Collisionless dynamics in two-dimensional bosonic gases

Alberto Cappellaro, Flavio Toigo, Luca Salasnich

We study the dynamics of dilute and ultracold bosonic gases in a quasi-two-dimensional (quasi-2D) configuration and in the collisionless regime. We adopt the 2D Landau-Vlasov equation to describe a three-dimensional gas under very strong harmonic confinement along one direction. We use this effective equation to investigate the speed of sound in quasi-2D bosonic gases, i.e., the sound propagation around a Bose-Einstein distribution in collisionless 2D gases. We derive coupled algebraic equations for the real and imaginary parts of the sound velocity, which are then solved also taking into account the equation of state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless critical temperature we find that there is rapid growth of the imaginary component of the sound velocity, which implies a strong Landau damping. Quite remarkably, our theoretical results are in good agreement with very recent experimental data obtained with a uniform 2D Bose gas of $^{87}\mathrm{Rb}$ atoms.

arXiv:1807.02541•Physical Review A•Oct 3, 2018•19 citations

Beyond mean-field theory for attractive bosons under transverse harmonic confinement

Luca Salasnich

We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e., under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wavefunction which extends the Bethe ansatz proposed by McGuire (1964 J. Math. Phys. 5 622) by including a variational transverse Gaussian shape. We investigate the ground-state properties of the system comparing them with those of the one-dimensional (1D) attractive Bose gas. We find that the gas becomes ultra 1D as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the symmetry-breaking solitonic density profile of the ground state, which generalizes the one deduced by Calogero and Degasperis (Calogero F and Degasperis A 1975 Phys. Rev. A 11 265). This bright-soliton analytical solution shows near the collapse small deviations with respect to the three-dimensional (3D) mean-field numerical solution. Finally, we show that our variational Gauss–McGuire theory is always more accurate than the McGuire theory. In addition, we prove that, for small numbers of particles, the Gauss–McGuire theory is more reliable than the mean-field theory described by the 3D Gross–Pitaevskii equation.

arXiv:cond-mat/0602670•Journal of Physics B Atomic Molecular and Optical Physics•Mar 21, 2006•8 citations

Equilibrium and off-equilibrium trap-size scaling in one-dimensional ultracold bosonic gases

Massimo Campostrini B, Ettore Vicari

We study some aspects of equilibrium and off-equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles and study their scaling behavior with increasing the trap size. We focus on one-dimensional bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for an initial trap size. Renormalization-group scaling arguments and analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.

arXiv:1010.0806•Physical Review A•Dec 30, 2010•49 citations

Towards a kinetic theory of dark-soliton gases in one-dimensional superfluids a

C. Pereira, José Tito Mendonça, João D. Rodrigues +1 more

Abstract Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one-dimensional superfluids, such as Bose-Einstein condensates, involves the dynamics of dark solitons and, therefore, the description of a statistical ensemble of dark solitons, i.e. , soliton gases, is necessary. In this work, we propose a phase-space (kinetic) description of dark-soliton gases, introducing a kinetic equation that is formally similar to the Vlasov equation in plasma physics. We show that the proposed kinetic theory can capture the dynamical features of soliton gases and show that it sustains an acoustic mode, a fact that we corroborate with the help of direct numerical simulations. Our findings motivate the investigation of the microscopic structure of out-of-equilibrium and turbulent regimes in low-dimensional superfluids.

Europhysics Letters (EPL)•Jan 1, 2021•3 citations
Abstract We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann–Vlasov equation with contact interaction, we derive an effective 1D Landau–Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas.
Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).
The one-dimensional Landau–Vlasov equation describing ultracold dilute bosonic gases in the mean-field collisionless regime under strong transverse confinement is analyzed using traditional methods of plasma physics. Time-independent, stationary solutions are found using a similar approach as for the Bernstein–Greene–Kruskal nonlinear plasma modes. Linear stationary waves similar to the Case–Van Kampen plasma normal modes are also shown to be available. The new bosonic solutions have no decaying or growth properties, in the same sense as the analog plasma solutions. The results are applied for real ultracold bosonic gases accessible in contemporary laboratory experiments.
We study the dynamics of dilute and ultracold bosonic gases in a quasi-two-dimensional (quasi-2D) configuration and in the collisionless regime. We adopt the 2D Landau-Vlasov equation to describe a three-dimensional gas under very strong harmonic confinement along one direction. We use this effective equation to investigate the speed of sound in quasi-2D bosonic gases, i.e., the sound propagation around a Bose-Einstein distribution in collisionless 2D gases. We derive coupled algebraic equations for the real and imaginary parts of the sound velocity, which are then solved also taking into account the equation of state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless critical temperature we find that there is rapid growth of the imaginary component of the sound velocity, which implies a strong Landau damping. Quite remarkably, our theoretical results are in good agreement with very recent experimental data obtained with a uniform 2D Bose gas of 87Rb^{87}\mathrm{Rb}87Rb atoms.
We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e., under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wavefunction which extends the Bethe ansatz proposed by McGuire (1964 J. Math. Phys. 5 622) by including a variational transverse Gaussian shape. We investigate the ground-state properties of the system comparing them with those of the one-dimensional (1D) attractive Bose gas. We find that the gas becomes ultra 1D as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the symmetry-breaking solitonic density profile of the ground state, which generalizes the one deduced by Calogero and Degasperis (Calogero F and Degasperis A 1975 Phys. Rev. A 11 265). This bright-soliton analytical solution shows near the collapse small deviations with respect to the three-dimensional (3D) mean-field numerical solution. Finally, we show that our variational Gauss–McGuire theory is always more accurate than the McGuire theory. In addition, we prove that, for small numbers of particles, the Gauss–McGuire theory is more reliable than the mean-field theory described by the 3D Gross–Pitaevskii equation.
We study some aspects of equilibrium and off-equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles and study their scaling behavior with increasing the trap size. We focus on one-dimensional bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for an initial trap size. Renormalization-group scaling arguments and analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.
Abstract Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one-dimensional superfluids, such as Bose-Einstein condensates, involves the dynamics of dark solitons and, therefore, the description of a statistical ensemble of dark solitons, i.e. , soliton gases, is necessary. In this work, we propose a phase-space (kinetic) description of dark-soliton gases, introducing a kinetic equation that is formally similar to the Vlasov equation in plasma physics. We show that the proposed kinetic theory can capture the dynamical features of soliton gases and show that it sustains an acoustic mode, a fact that we corroborate with the help of direct numerical simulations. Our findings motivate the investigation of the microscopic structure of out-of-equilibrium and turbulent regimes in low-dimensional superfluids.