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

Physical Review A

Thomas-Fermi description of the instability of quantum liquid droplets in the vapor phase

Jochen M. Schneider, Wilhelm Stocker

Published May 1, 1990• 1 citation
Publisher

Abstract

Using a schematic interaction we derive and solve temperature-dependent Thomas-Fermi equations for a quantum liquid droplet (nucleus, $^{3}\mathrm{He}$, or similar) in its vapor atmosphere. The results depend on the initial size of the droplet in the iterative numerical procedure, thereby simulating on the computer condensation and evaporation of the unstable droplets. The stationary but unstable droplet configuration is evidenced by a slowing down of the iterative change of the density. We also take into consideration bubble formation and instability for a chemical potential below the Maxwell liquid-vapor equilibrium value.

DOI
10.1103/physreva.41.5468

Related papers

On the Ground State Quantum Droplet for Large Chemical Potentials

Justin Holmer, Zhang, K. Z., P. G. Kevrekidis

In the present work we revisit the problem of the quantum droplet in atomic Bose-Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas-Fermi limit. We consider the problem as being separable into 3 distinct regions: an inner one, where the Thomas-Fermi approximation is valid, a sharp transition region where the density abruptly drops towards the (vanishing) background value and an outer region which asymptotes to the background value. We analyze the spatial extent of each of these regions, and develop a systematic effective description of the rapid intermediate transition region. Accordingly, we derive a uniformly valid description of the ground state that is found to very accurately match our numerical computations. As an additional application of our considerations, we show that this formulation allows for an analytical approximation of excited states such as the (trapped) dark soliton in the large density limit.

arXiv:2401.00213•Dec 30, 2023•0 citations

On the ground state of one-dimensional quantum droplets for large chemical potentials

Justin Holmer, Katherine Zhiyuan Zhang, P. G. Kevrekidis

Abstract In the present work we revisit the problem of the quantum droplet in atomic Bose–Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas–Fermi (TF) limit. We consider the problem as being separable into 3 distinct regions: an inner one, where the TF approximation is valid, a sharp transition region where the density abruptly drops towards the (vanishing) background value and an outer region which asymptotes to the background value. We analyze the spatial extent of each of these regions, and develop a systematic effective description of the rapid intermediate transition region. Accordingly, we derive a uniformly valid description of the ground state that is found to accurately match our numerical computations. As an additional application of our considerations, we show that this formulation allows for an analytical approximation of excited states such as the (trapped) dark soliton in the large density limit.

Journal of Physics A Mathematical and Theoretical•Oct 2, 2024•0 citations

Two-dimensional quantum droplets in dipolar Bose gases

Abdelâali Boudjemâa

Abstract We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole–dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.

arXiv:1709.07088•New Journal of Physics•Aug 30, 2019•22 citations

Three-dimensional Bose-Fermi droplets at nonzero temperatures

Maciej Lewkowicz, Mirosław Brewczyk, Mariusz Gajda +1 more

Using numerical methods, we study the formation of self-bound quantum Bose-Fermi droplets at nonzero temperatures. We describe an attractive atomic Bose-Fermi mixture using quantum hydrodynamics enriched by beyond-mean-field corrections and thermal fluctuations, together with a simplified self-consistent Hartree-Fock model. With these models, we determine that low-temperature droplets with finite lifetimes can exist in free space when the attraction between bosons and fermions is sufficiently strong. Additionally, Bose-Fermi droplets at nonzero temperatures can exist in a box potential in equilibrium with bosonic and fermionic vapor. We discuss the properties of Bose-Fermi droplets at nonzero temperatures in terms of the initial condensate fraction, total atom number, and interspecies attraction strength.

arXiv:2602.19925•Feb 23, 2026•0 citations

Universal scaling law for quantum droplet formation

Ian G. Moss

Given the right set of circumstances, ultracold quantum gases are able to change character and condense into a liquid state of quantum droplets. The size distribution of the droplets is determined dynamically in the condensation process. A semi-quantitative argument is presented which suggests that, at zero temperature, a multiple droplet system has is a preferred scale $\propto v^{-1/3}$, where $v$ is the rate of change of parameters at the time of droplet formation. Numerical simulations of two dimensional systems strongly support a power law $v^{-d}$, with an exponent $d\in(0.327,0.375)$.

arXiv:2504.21641•Apr 30, 2025•0 citations

Quantum liquid droplets in Bose mixtures with weak disorder

Karima Abbas, Abdelâali Boudjemâa

We study the properties of self-bound liquid droplets of three-dimensional Bose mixtures in a weak random potential with Gaussian correlation function at both zero and finite temperatures. Using the Bogoliubov theory, we derive useful formulas for the ground-state energy, the equilibrium density, the depletion, and the anomalous density of the droplet. The quantum fluctuation induced by the disorder known as the glassy fraction is also systematically computed. At finite temperature, we calculate the free energy, the thermal equilibrium density, and the critical temperature in terms of the disorder parameters. We show that when the strength and the correlation length of the disorder potential exceed a certain critical value, the droplet evaporates and is eventually entirely destroyed. We calculate the density profiles of this exotic state by means of numerical simulations of the corresponding generalized disorder Gross-Pitaevskii equation. Our predictions reveal that as the strength of the disorder gets larger, the atomic density varies rapidly in the plateau region. We point out in addition that the peculiar interplay of the disorder and the repulsive Lee-Huang-Yang corrections play a pivotal role in the collective modes of the self-bound droplet.

arXiv:2303.04760•Physical Review A•Mar 7, 2023•13 citations
Using a schematic interaction we derive and solve temperature-dependent Thomas-Fermi equations for a quantum liquid droplet (nucleus, 3He^{3}\mathrm{He}3He, or similar) in its vapor atmosphere. The results depend on the initial size of the droplet in the iterative numerical procedure, thereby simulating on the computer condensation and evaporation of the unstable droplets. The stationary but unstable droplet configuration is evidenced by a slowing down of the iterative change of the density. We also take into consideration bubble formation and instability for a chemical potential below the Maxwell liquid-vapor equilibrium value.
In the present work we revisit the problem of the quantum droplet in atomic Bose-Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas-Fermi limit. We consider the problem as being separable into 3 distinct regions: an inner one, where the Thomas-Fermi approximation is valid, a sharp transition region where the density abruptly drops towards the (vanishing) background value and an outer region which asymptotes to the background value. We analyze the spatial extent of each of these regions, and develop a systematic effective description of the rapid intermediate transition region. Accordingly, we derive a uniformly valid description of the ground state that is found to very accurately match our numerical computations. As an additional application of our considerations, we show that this formulation allows for an analytical approximation of excited states such as the (trapped) dark soliton in the large density limit.
Abstract In the present work we revisit the problem of the quantum droplet in atomic Bose–Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas–Fermi (TF) limit. We consider the problem as being separable into 3 distinct regions: an inner one, where the TF approximation is valid, a sharp transition region where the density abruptly drops towards the (vanishing) background value and an outer region which asymptotes to the background value. We analyze the spatial extent of each of these regions, and develop a systematic effective description of the rapid intermediate transition region. Accordingly, we derive a uniformly valid description of the ground state that is found to accurately match our numerical computations. As an additional application of our considerations, we show that this formulation allows for an analytical approximation of excited states such as the (trapped) dark soliton in the large density limit.
Abstract We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole–dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.
Using numerical methods, we study the formation of self-bound quantum Bose-Fermi droplets at nonzero temperatures. We describe an attractive atomic Bose-Fermi mixture using quantum hydrodynamics enriched by beyond-mean-field corrections and thermal fluctuations, together with a simplified self-consistent Hartree-Fock model. With these models, we determine that low-temperature droplets with finite lifetimes can exist in free space when the attraction between bosons and fermions is sufficiently strong. Additionally, Bose-Fermi droplets at nonzero temperatures can exist in a box potential in equilibrium with bosonic and fermionic vapor. We discuss the properties of Bose-Fermi droplets at nonzero temperatures in terms of the initial condensate fraction, total atom number, and interspecies attraction strength.
Given the right set of circumstances, ultracold quantum gases are able to change character and condense into a liquid state of quantum droplets. The size distribution of the droplets is determined dynamically in the condensation process. A semi-quantitative argument is presented which suggests that, at zero temperature, a multiple droplet system has is a preferred scale ∝v−1/3\propto v^{-1/3}∝v−1/3, where vvv is the rate of change of parameters at the time of droplet formation. Numerical simulations of two dimensional systems strongly support a power law v−dv^{-d}v−d, with an exponent d∈(0.327,0.375)d\in(0.327,0.375)d∈(0.327,0.375).
We study the properties of self-bound liquid droplets of three-dimensional Bose mixtures in a weak random potential with Gaussian correlation function at both zero and finite temperatures. Using the Bogoliubov theory, we derive useful formulas for the ground-state energy, the equilibrium density, the depletion, and the anomalous density of the droplet. The quantum fluctuation induced by the disorder known as the glassy fraction is also systematically computed. At finite temperature, we calculate the free energy, the thermal equilibrium density, and the critical temperature in terms of the disorder parameters. We show that when the strength and the correlation length of the disorder potential exceed a certain critical value, the droplet evaporates and is eventually entirely destroyed. We calculate the density profiles of this exotic state by means of numerical simulations of the corresponding generalized disorder Gross-Pitaevskii equation. Our predictions reveal that as the strength of the disorder gets larger, the atomic density varies rapidly in the plateau region. We point out in addition that the peculiar interplay of the disorder and the repulsive Lee-Huang-Yang corrections play a pivotal role in the collective modes of the self-bound droplet.