Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases

Quantum droplets are ultradilute liquid states that emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.

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Impurities in a one-dimensional Bose gas: the flow equation approach

SciPost Physics ◽

10.21468/scipostphys.11.1.008 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Fabian Brauneis ◽

Hans-Werner Hammer ◽

Mikhail Lemeshko ◽

Artem Volosniev

Keyword(s):

Mean Field ◽

Interaction Strength ◽

Field Approximation ◽

Flow Equation ◽

Mean Field Approximation ◽

Bose Gases ◽

One Dimensional ◽

Flow Equations ◽

Impurity Interaction ◽

The Mean

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities[1,2]. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

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Uniqueness and Symmetry for the Mean Field Equation on Arbitrary Flat Tori

International Mathematics Research Notices ◽

10.1093/imrn/rnaa109 ◽

2020 ◽

Cited By ~ 1

Author(s):

Guangze Gu ◽

Changfeng Gui ◽

Yeyao Hu ◽

Qinfeng Li

Keyword(s):

Field Equation ◽

Level Sets ◽

Mean Field ◽

Flat Torus ◽

One Dimensional ◽

Uniqueness Of The Solution ◽

Flat Tori ◽

The Mean ◽

Symmetry Result ◽

Mean Field Equation

Abstract We study the following mean field equation on a flat torus $T:=\mathbb{C}/(\mathbb{Z}+\mathbb{Z}\tau )$: $$\begin{equation*} \varDelta u + \rho \left(\frac{e^{u}}{\int_{T}e^u}-\frac{1}{|T|}\right)=0, \end{equation*}$$where $ \tau \in \mathbb{C}, \mbox{Im}\ \tau>0$, and $|T|$ denotes the total area of the torus. We first prove that the solutions are evenly symmetric about any critical point of $u$ provided that $\rho \leq 8\pi $. Based on this crucial symmetry result, we are able to establish further the uniqueness of the solution if $\rho \leq \min{\{8\pi ,\lambda _1(T)|T|\}}$. Furthermore, we also classify all one-dimensional solutions by showing that the level sets must be closed geodesics.

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The 1/N-expansion as a perturbation about the mean field theory: A one-dimensional fermi model

Communications in Mathematical Physics ◽

10.1007/bf02100100 ◽

1996 ◽

Vol 179 (3) ◽

pp. 623-646 ◽

Cited By ~ 6

Author(s):

D. H. U. Marchetti ◽

P. A. Faria da Veiga ◽

T. R. Hurd

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

Fermi Model ◽

One Dimensional ◽

The Mean

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COLLAPSE OF K-Rb FERMI-BOSE MIXTURES IN OPTICAL LATTICES

International Journal of Modern Physics B ◽

10.1142/s0217979206036260 ◽

2006 ◽

Vol 20 (30n31) ◽

pp. 5199-5203

Author(s):

D. M. JEZEK ◽

H. M. CATALDO

Keyword(s):

Low Temperature ◽

Optical Lattice ◽

Optical Lattices ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

One Dimensional ◽

Different Types ◽

The Mean ◽

Number Of Particles

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

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RELAXATION UNDER OUTFLOW DYNAMICS WITH RANDOM SEQUENTIAL UPDATING

International Journal of Modern Physics C ◽

10.1142/s012918310500828x ◽

2005 ◽

Vol 16 (11) ◽

pp. 1771-1783 ◽

Cited By ~ 12

Author(s):

SYLWIA KRUPA ◽

KATARZYNA SZNAJD-WERON

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Mean Field ◽

Square Lattice ◽

One Dimensional ◽

Sequential Updating ◽

The Mean

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule.

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FRÖHLICH'S ONE-DIMENSIONAL SUPERCONDUCTOR WITH PARA-FERMI STATISTICS

Modern Physics Letters B ◽

10.1142/s0217984994001187 ◽

1994 ◽

Vol 08 (19) ◽

pp. 1195-1200 ◽

Cited By ~ 3

Author(s):

V. L. SAFONOV ◽

A. V. ROZHKOV

Keyword(s):

Density Wave ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Wave State ◽

One Dimensional ◽

Fermi Statistics ◽

The Mean ◽

A Charge ◽

Dimensional Crystal

The hypothesis that conduction electrons in a one-dimensional crystal obey para-Fermi statistics is discussed. Thermal properties of Fröhlich's model in the mean-field approximation are calculated within the framework of this hypothesis. It is shown that the temperature of the phase transition to a charge density wave state is greater in a system with parastatistics.

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NOTE ON ANALYTICAL STUDIES OF ONE-DIMENSIONAL HOLOGRAPHIC SUPERCONDUCTORS

Modern Physics Letters A ◽

10.1142/s0217732312500010 ◽

2012 ◽

Vol 27 (02) ◽

pp. 1250001 ◽

Cited By ~ 6

Author(s):

RAN LI

Keyword(s):

Equations Of Motion ◽

Mean Field ◽

Study Phase ◽

Coupling Term ◽

Analytical Treatment ◽

One Dimensional ◽

Holographic Superconductors ◽

Scalar Operator ◽

Sturm Liouville ◽

The Mean

We employ the variational method for the Sturm–Liouville eigenvalue problem to analytically study phase transition of one-dimensional holographic superconductors. It is shown that this method is not a very powerful method to analytically calculate the properties of holographic superconductors. From the analytical treatment of scalar operator condensate at critical temperature, we also show that the mean-field critical exponent 1/2 results from the coupling term between scalar field and vector field, which may be an universal property of holographic superconductors with a similar coupling term in their equations of motion.

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