On the bright soliton in the Bose–Einstein condensate (to the third order in the interaction radius)

Andreev, Pavel A.; Trukhanova, Mariya Iv.

doi:10.1007/s11182-011-9548-9

Cited by 10 publications

(22 citation statements)

References 18 publications

(37 reference statements)

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“…Using the methods described in Ref.s [33], [34] we come to the particle concentration profile in well-known form of…”

Section: Bright Soliton In the Electrically Polarized Becmentioning

confidence: 99%

Nonintegral Form of the Gross–pitaevskii Equation for Polarized Molecules

Andreev

2013

Mod. Phys. Lett. B

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The Gross-Pitaevskii equation for polarized molecules is an integro-differential equation, consequently it is complicated for solving. We find a possibility to represent it as a non-integral nonlinear Schrodinger equation, but this equation should be coupled with two linear equations describing electric field. These two equations are the Maxwell equations. We recapture the dispersion of collective excitations in the three dimensional electrically polarized BEC with no evolution of the electric dipole moment directions. We trace the contribution of the electric dipole moment. We explicitly consider the contribution of the electric dipole moment in the interaction constant for the short-range interaction. We show that the spectrum of dipolar BEC reveals no instability at repulsive short-range interaction. Nonlinear excitations are also considered. We present dependence of the bright soliton characteristics on the electric dipole moment.

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“…Using the methods described in Ref.s [33], [34] we come to the particle concentration profile in well-known form of…”

Section: Bright Soliton In the Electrically Polarized Becmentioning

confidence: 99%

Nonintegral Form of the Gross–pitaevskii Equation for Polarized Molecules

Andreev

2013

Mod. Phys. Lett. B

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“…It corresponds to the repulsive SRI. Also, from (11) we obtain relation between n 1 and v 1 and their derivatives…”

Section: Bright-like Soliton In 1d Becmentioning

confidence: 99%

Bright-Like Soliton Solution in Quasi-One-Dimensional Bec in Third Order by Interaction Radius

Andreev

Kuz'menkov

2012

Mod. Phys. Lett. B

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Nonlinear Schrödinger equations and corresponding quantum hydrodynamic (QHD) equations are widely used in studying ultracold boson-fermion mixtures and superconductors. In this article, we show that a more exact account of interaction in Bose-Einstein condensate (BEC), in comparison with the Gross-Pitaevskii (GP) approximation, leads to the existence of a new type of solitons. We use a set of QHD equations in the third order by the interaction radius (TOIR), which corresponds to the GP equation in a first order by the interaction radius. The solution for the soliton in a form of expression for the particle concentration is obtained analytically. The conditions of existence of the soliton are studied. It is shown what solution exists if the interaction between the particles is repulsive. Particle concentration of order of 10 12 -10 14 cm −3 has been achieved experimentally for the BEC, the solution exists if the scattering length is of the order of 1 µm, which can be reached using the Feshbach resonance. It is one of the limit case of existence of new solution. The corresponding scattering length decrease with the increasing of concentration of particles. The investigation of effects in the TOIR approximation gives a more detail information on interaction potentials between the atoms and can be used for a more detail investigation into the potential structure.

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“…The MPQHD approach to systems of neutral particles, e.g. of ultracold boson-fermion mixtures, has been developed in [23] and applied later to describe linear and nonlinear characteristics of BEC and of boson-fermion mixtures [23,[48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles

2011

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In this paper we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Though we focused primarily on the two-dimension physical systems, the method is valid for three-dimension and one-dimension systems too. The presented method is based upon the Schrödinger equation. Fundamental QHD equations for charged and neutral particles were derived from the many-particle microscopic Schrödinger equation. The fact that particles possess the electric dipole moment (EDM) was taken into account. The explicated QHD approach was used to study dispersion characteristics of various physical systems. We analyzed dispersion of waves in a twodimension (2D) ion and hole gas placed into an external electric field which is orthogonal to the gas plane. Elementary excitations in a system of neutral polarized particles were studied for 1D, 2D and 3D cases. The polarization dynamics in systems of both neutral and charged particles is shown to cause formation of a new type of waves as well as changes in the dispersion characteristics of already known waves. We also analyzed wave dispersion in 2D exciton systems, in 2D electron-ion plasma and 2D electron-hole plasma. Generation of waves in 3D system neutral particles with EDM by means of the beam of electrons and neutral polarized particles is investigated.

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On the bright soliton in the Bose–Einstein condensate (to the third order in the interaction radius)

Cited by 10 publications

References 18 publications

Nonintegral Form of the Gross–pitaevskii Equation for Polarized Molecules

Nonintegral Form of the Gross–pitaevskii Equation for Polarized Molecules

Bright-Like Soliton Solution in Quasi-One-Dimensional Bec in Third Order by Interaction Radius

Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles

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