scholarly journals Bogoliubov theory of a Bose-Einstein condensate of rigid rotor molecules

2021 ◽  
Author(s):  
Joseph C Smith ◽  
Seth T Rittenhouse ◽  
Ryan M Wilson ◽  
Brandon March Peden
Keyword(s):  
Electric Fields ◽  
Density Wave ◽  
Mean Field ◽  
Einstein Condensate ◽  
Field Energy ◽  
Rigid Rotor ◽  
Bogoliubov Theory ◽  
Bose Einstein Condensate ◽  
Plane Component ◽  
Bose Einstein

Abstract We consider a BEC of rigid rotor molecules confined to quasi-2d through harmonic trapping. The molecules are subjected to an external electric field which polarizes the gas, and the molecules interact via dipole-dipole interactions. We present a description of the ground state and low-energy excitations of the system including an analysis of the mean-field energy, polarization, and stability. Under large electric fields the gas becomes fully polarized and we reproduce a well known density-wave instability which arises in polar BECs. Under smaller applied electric fields the gas develops an in-plane polarization leading to the emergence of a new global instability as the molecules “tilt”. The character of these instabilities is clarified by means of momentum-space density-density structure factors. A peak at zero momentum in the spin-spin structure factor for the in-plane component of the polarization indicates that the tilt instability is a global phonon-like instability.

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

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.

scholarly journals Two-component axionic dark matter halos

2020 ◽  
Vol 35 (26) ◽  
pp. 2050227 ◽  
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.

scholarly journals Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate

2019 ◽  
Vol 100 (2) ◽  
Author(s):  
G. Vasilakis ◽  
A. Roussou ◽  
J. Smyrnakis ◽  
M. Magiropoulos ◽  
W. von Klitzing ◽  
...  
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
The Mean ◽  
Bose Einstein

scholarly journals Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Milan Radonjic ◽  
Axel Pelster
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Weak Disorder ◽  
Field Approach ◽  
Bose Einstein Condensate ◽  
Adiabatic Switching ◽  
Long Time ◽  
Disorder Potential ◽  
Bose Einstein ◽  
Non Equilibrium

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially {equilibrated} Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part{, that actually corresponds to adiabatic switching on the disorder,} and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. {We also present an appropriate generalization to inhomogeneous trapped condensates.} Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

scholarly journals Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1344 ◽  
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Mean Field ◽  
Interaction Model ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
The Many ◽  
Harmonic Interaction ◽  
Bose Einstein

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.

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