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:2601.12848

Anisotropic dispersion relation of ultralight Bose gases in modified Newtonian dynamics

Ning Liu

cond-mat.quant-gasastro-ph.GAcond-mat.stat-mechquant-phSubmitted Jan 19, 2026• Announced Jan 20, 2026• Revised Apr 30, 2026 (v3)
v1 · Jan 19, 2026v2 · Jan 31, 2026v3 · Apr 30, 2026
arXivHTMLPDF

Abstract

We investigate the dispersion relation of collective modes in ultralight Bose gases under Modified Newtonian Dynamics (MOND). Starting from the coupled Gross-Pitaevskii and MOND Poisson equations, we derive an anisotropic dispersion relation that depends on the angle between the perturbation wavevector and the background gravitational field. This anisotropy arises directly from the nonlinear structure of the MOND field equation and leads to a direction-dependent Jeans instability, with critical wavelengths and masses varying with orientation. Our results provide a distinctive signature of MOND in a quantum astrophysical context and suggest that ultralight Bose gases can serve as novel probes of modified gravity.

Journal reference
Physics Letters A 590, 131863(2026)
DOI
10.1016/j.physleta.2026.131863
Comments
14 pages,3 figures

Related papers

Ground State and Collective Modes of Bose-Einstein Condensates in Newtonian and MOND-inspired gravitational potentials

Ning Liu

We analytically and numerically study the ground state and collective dynamics of Bose-Einstein condensates in two traps: a Newtonian potential and a logarithmic potential inspired by Modified Newtonian Dynamics (MOND). In the ground state, the MOND potential supports bound states only in the deep-MOND regime, where the condensate becomes significantly larger than its Newtonian counterpart. The size increases with repulsive coupling parameter $β$ in both potentials. A clear scaling law of the size with $β^{1/3}$ emerges in the MOND case and is confirmed numerically over a wide parameter range, while for the Newtonian potential no simple scaling law exists as the Thomas-Fermi approximation ceases to be valid. For the dynamics, we derive and solve equations for the monopole collective mode. The larger MOND-bound condensate oscillates at a lower frequency, which scales as $β^{-1/3}$ in the strong-interaction limit. These scaling laws provide insights for quantum-simulation experiments aiming to probe modified-gravity scenarios with cold atoms.

cond-mat.quant-gasCross-listedarXiv:2601.01039•Jan 6, 2026•0 citations

Collective Excitations of Self-Gravitating Bose–Einstein Condensates: Breathing Mode and Appearance of Anisotropy under Self-Gravity

Kenta Asakawa, Hideki Ishihara, Makoto Tsubota

Abstract We investigate the collective mode of a self-gravitating Bose–Einstein condensate (BEC) described by the Gross–Pitaevskii–Poisson (GPP) equations. The self-gravitating BEC has garnered considerable attention in cosmology and astrophysics, being proposed as a plausible candidate for dark matter. Our inquiry delves into the breathing and anisotropic collective modes by numerically solving the GPP equations and using the variational method. The breathing mode demonstrates a reduction in period with increasing total mass due to the density dependence of the self-gravitating BEC, attributed to the density-dependent nature of self-gravitating BECs, aligning quantitatively with our analytical findings. Additionally, we investigate an anisotropic collective mode in which the quadrupole mode intertwines with the breathing mode. The period of the quadrupole mode exhibits similar total mass dependence to that of the breathing mode. The characteristics of these periods differ from those of a conventional BEC confined by an external potential. Despite the differences in density dependence, the ratio of their periods equals that of the BEC confined by an isotropic harmonic potential. Furthermore, an extension of the variational method to a spheroidal configuration enables the isolation of solely the quadrupole mode from the anisotropic collective mode.

arXiv:2307.14018•Progress of Theoretical and Experimental Physics•May 28, 2024•3 citations

Impact of Three-Body Interactions and Nonlinear Dispersion on the Dynamics of Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Potential

Emmanuel Kengne, Ahmed Lakhssassi

A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.

Chinese Journal of Physics•Feb 1, 2015•4 citations

Two-Dimensional Soliton Interaction for Multi-component Bose–Einstein Condensates

Sheng-Chang Li, Duan Wen-Shan

For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.

Communications in Theoretical Physics•Sep 1, 2008•3 citations

Variational approach to the snake instability of a Bose-Einstein condensate soliton

U. Tanyeri, M. A. Gürkan, Ahmet Keleş +1 more

Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.

arXiv:2507.04926•Physical Review A•Dec 23, 2025•0 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
We investigate the dispersion relation of collective modes in ultralight Bose gases under Modified Newtonian Dynamics (MOND). Starting from the coupled Gross-Pitaevskii and MOND Poisson equations, we derive an anisotropic dispersion relation that depends on the angle between the perturbation wavevector and the background gravitational field. This anisotropy arises directly from the nonlinear structure of the MOND field equation and leads to a direction-dependent Jeans instability, with critical wavelengths and masses varying with orientation. Our results provide a distinctive signature of MOND in a quantum astrophysical context and suggest that ultralight Bose gases can serve as novel probes of modified gravity.
We analytically and numerically study the ground state and collective dynamics of Bose-Einstein condensates in two traps: a Newtonian potential and a logarithmic potential inspired by Modified Newtonian Dynamics (MOND). In the ground state, the MOND potential supports bound states only in the deep-MOND regime, where the condensate becomes significantly larger than its Newtonian counterpart. The size increases with repulsive coupling parameter βββ in both potentials. A clear scaling law of the size with β1/3β^{1/3}β1/3 emerges in the MOND case and is confirmed numerically over a wide parameter range, while for the Newtonian potential no simple scaling law exists as the Thomas-Fermi approximation ceases to be valid. For the dynamics, we derive and solve equations for the monopole collective mode. The larger MOND-bound condensate oscillates at a lower frequency, which scales as β−1/3β^{-1/3}β−1/3 in the strong-interaction limit. These scaling laws provide insights for quantum-simulation experiments aiming to probe modified-gravity scenarios with cold atoms.
Abstract We investigate the collective mode of a self-gravitating Bose–Einstein condensate (BEC) described by the Gross–Pitaevskii–Poisson (GPP) equations. The self-gravitating BEC has garnered considerable attention in cosmology and astrophysics, being proposed as a plausible candidate for dark matter. Our inquiry delves into the breathing and anisotropic collective modes by numerically solving the GPP equations and using the variational method. The breathing mode demonstrates a reduction in period with increasing total mass due to the density dependence of the self-gravitating BEC, attributed to the density-dependent nature of self-gravitating BECs, aligning quantitatively with our analytical findings. Additionally, we investigate an anisotropic collective mode in which the quadrupole mode intertwines with the breathing mode. The period of the quadrupole mode exhibits similar total mass dependence to that of the breathing mode. The characteristics of these periods differ from those of a conventional BEC confined by an external potential. Despite the differences in density dependence, the ratio of their periods equals that of the BEC confined by an isotropic harmonic potential. Furthermore, an extension of the variational method to a spheroidal configuration enables the isolation of solely the quadrupole mode from the anisotropic collective mode.
A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.
For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.
Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.
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.