Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory

Bose–Einstein condensates of repulsive Bose atoms in a one-dimensional harmonic trap are investigated within the framework of a mean field theory. We solve the one-dimensional nonlinear Gross–Pitaevskii (GP) equation that describes atomic Bose–Einstein condensates. As a result, we acquire a family of exact breather solutions of the GP equation. We numerically calculate the number density [Formula: see text] of atoms that is associated with these solutions. The first discovery of the calculation is that at the instant of the saddle point, the density profile exhibits a sharp peak with extremely narrow width. The second discovery of the calculation is that in the center of the trap ([Formula: see text] m), the number density is a U-shaped function of the time [Formula: see text]. The third discovery of the calculation is that the surface plot of the density [Formula: see text] likes a saddle surface. The fourth discovery of the calculation is that as the number [Formula: see text] of atoms increases, the Bose–Einstein condensate in a one-dimensional harmonic trap becomes stabler and stabler.

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QUANTUM CORRECTIONS TO THE DYNAMICS OF THE BOSE–EINSTEIN CONDENSATE IN A DOUBLE-WELL POTENTIAL

International Journal of Modern Physics B ◽

10.1142/s0217979212500439 ◽

2012 ◽

Vol 26 (06) ◽

pp. 1250043 ◽

Cited By ~ 2

Author(s):

YAN XU ◽

WEI FAN ◽

BING CHEN

Keyword(s):

Mean Field Theory ◽

Mean Field ◽

Einstein Condensate ◽

Matter Wave ◽

Quantum Corrections ◽

Bose Einstein Condensate ◽

Bose Einstein ◽

Dynamical Instabilities ◽

Double Well Potential ◽

Correction Terms

The dynamics of the Bose–Einstein condensate (BEC) in a double-well potential is often investigated under the mean-field theory (MFT). This works successfully for large particle numbers with dynamical stability. But for dynamical instabilities, quantum corrections to the MFT becomes important [J. R. Anglin and A. Vardi, Phys. Rev. A64, 013605 (2001)]. Recently the adiabatic dynamics of the double-well BEC is investigated under the MFT in terms of a dark variable [C. Ottaviani et al., Phys. Rev. A81, 043621 (2010)], which generalizes the adiabatic passage techniques in quantum optics to the nonlinear matter-wave case. We give a fully quantized version of it using second-quantization and introduce new correction terms from higher order interactions beyond the on-site interaction, which are interactions between the tunneling particle and the particle in the well and interactions between the tunneling particles. If only the on-site interaction is considered, this reduces to the usual two-mode BEC.

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Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-021-01616-9 ◽

2021 ◽

Vol 240 (1) ◽

pp. 383-417

Author(s):

Nikolai Leopold ◽

David Mitrouskas ◽

Robert Seiringer

Keyword(s):

Mean Field ◽

Einstein Condensate ◽

Back Reaction ◽

Many Body ◽

Field Limit ◽

Mean Field Limit ◽

Phonon Field ◽

Bose Einstein Condensate ◽

Weakly Couple ◽

Bose Einstein

AbstractWe consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

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Two-component axionic dark matter halos

Modern Physics Letters A ◽

10.1142/s0217732320502272 ◽

2020 ◽

Vol 35 (26) ◽

pp. 2050227 ◽

Cited By ~ 1

Author(s):

Gennady P. Berman ◽

Vyacheslav N. Gorshkov ◽

Vladimir I. Tsifrinovich ◽

Marco Merkli ◽

Vladimir V. Tereshchuk

Keyword(s):

Dark Matter ◽

Ground State ◽

Mass Density ◽

Mean Field ◽

Einstein Condensate ◽

Dark Matter Halo ◽

Bose Einstein Condensate ◽

Interesting Connection ◽

Two Component ◽

Bose Einstein

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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