Ground-state solution of Bose–Einstein condensate by directly minimizing the energy functional

We consider a two-component dark matter halo (DMH) of a galaxy containing ultra-light axions (ULA) of different mass. The DMH is described as a Bose–Einstein condensate (BEC) in its ground state. In the mean-field (MF) limit, we have derived the integro-differential equations for the spherically symmetrical wave functions of the two DMH components. We studied, numerically, the radial distribution of the mass density of ULA and constructed the parameters which could be used to distinguish between the two- and one-component DMH. We also discuss an interesting connection between the BEC ground state of a one-component DMH and Black Hole temperature and entropy, and Unruh temperature.

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Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential

Asymptotic Analysis ◽

10.3233/asy-211748 ◽

2021 ◽

pp. 1-26

Author(s):

Tianfang Wang ◽

Wen Zhang ◽

Jian Zhang

Keyword(s):

Dirac Equation ◽

Coulomb Potential ◽

Ground State ◽

Continuous Dependence ◽

Energy Functional ◽

Ground State Solution ◽

State Solution ◽

Nonlinear Dirac Equation ◽

Relationship Of ◽

Least Energy

In this paper we study the Dirac equation with Coulomb potential − i α · ∇ u + a β u − μ | x | u = f ( x , | u | ) u , x ∈ R 3 where a is a positive constant, μ is a positive parameter, α = ( α 1 , α 2 , α 3 ), α i and β are 4 × 4 Pauli–Dirac matrices. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions, we prove that the problem possesses a ground state solution which is exponentially decay, and the least energy has continuous dependence about μ. Moreover, we are able to obtain the asymptotic property of ground state solution as μ → 0 + , this result can characterize some relationship of the above problem between μ > 0 and μ = 0.

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Ground-state Properties of a Bose-Einstein Condensate in an Optomechanical Cavity

Acta Sinica Quantum Optica ◽

10.3788/asqo20152103.0241 ◽

2015 ◽

Vol 21 (3) ◽

pp. 241-245

Author(s):

贾树芳 JIA Shu-fang ◽

梁九卿 LIANG Jiu-qing

Keyword(s):

Ground State ◽

Einstein Condensate ◽

Bose Einstein Condensate ◽

Ground State Properties ◽

Bose Einstein ◽

Optomechanical Cavity

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MODULATION OF ORDER PARAMETER OF EXCITON BOSE-EINSTEIN CONDENSATE IN A RING

International Journal of Modern Physics B ◽

10.1142/s0217979204027475 ◽

2004 ◽

Vol 18 (27n29) ◽

pp. 3797-3802 ◽

Cited By ~ 3

Author(s):

S.-R. ERIC YANG ◽

Q-HAN PARK ◽

J. YEO

Keyword(s):

Ground State ◽

Order Parameter ◽

Weak Magnetic Field ◽

Random Potential ◽

Einstein Condensate ◽

Einstein Condensation ◽

Random Potentials ◽

Bose Einstein Condensate ◽

The Mean ◽

Bose Einstein

We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with a random variation of the effective exciton potential along the circumference. We derive a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate, which is valid even in the presence of a weak magnetic field. For several types of the random potentials our numerical solution of the ground state of the GPE displays a necklace-like structure. This is a consequence of the interplay between the random potential and a strong nonlinear repulsive term of the GPE. We have investigated how the mean distance between modulation peaks depends on properties of the random potentials.

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