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 STABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS

2014 ◽  
Vol 54 (2) ◽  
pp. 133-138 ◽  
Author(s):  
Andreas Löhle ◽  
Holger Cartarius ◽  
Daniel Haag ◽  
Dennis Dast ◽  
Jörg Main ◽  
...  
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Branch Points ◽  
Mean Field Limit ◽  
Bose Einstein Condensate ◽  
Stability Change ◽  
The Difference ◽  
Bose Einstein

A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) with a <em>PT</em> symmetric external potential. If the strength of the in- and outcoupling is increased two <em>PT</em> broken states bifurcate from the <em>PT</em> symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a <em>PT</em> symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.

scholarly journals Morphology of an Interacting Three-Dimensional Trapped Bose–Einstein Condensate from Many-Particle Variance Anisotropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1237
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Wave Packet ◽  
Infinite Number ◽  
Mean Field ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose–Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose–Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.

scholarly journals Nonperturbative dynamical many-body theory of a Bose-Einstein condensate

2005 ◽  
Vol 72 (6) ◽  
Author(s):  
Thomas Gasenzer ◽  
Jürgen Berges ◽  
Michael G. Schmidt ◽  
Marcos Seco
Keyword(s):  
Einstein Condensate ◽  
Many Body ◽  
Many Body Theory ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Body Theory

scholarly journals Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Hiroyuki Tajima ◽  
Junichi Takahashi ◽  
Simeon Mistakidis ◽  
Eiji Nakano ◽  
Kei Iida
Keyword(s):  
Spectral Function ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Quantum Gas ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
Three Body ◽  
Bose Einstein ◽  
The Impact

The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

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 Entropy Production Within a Pulsed Bose–Einstein Condensate

2016 ◽  
Vol 71 (10) ◽  
pp. 875-881 ◽  
Author(s):  
Christoph Heinisch ◽  
Martin Holthaus
Keyword(s):  
Einstein Condensate ◽  
Many Body ◽  
Initial State ◽  
Site Model ◽  
Bose Einstein Condensate ◽  
Body Dynamics ◽  
Adiabatic Motion ◽  
The Many ◽  
Bose Einstein ◽  
Loss Of Coherence

AbstractWe suggest to subject anharmonically trapped Bose–Einstein condensates to sinusoidal forcing with a smooth, slowly changing envelope, and to measure the coherence of the system after such pulses. In a series of measurements with successively increased maximum forcing strength, one then expects an adiabatic return of the condensate to its initial state as long as the pulses remain sufficiently weak. In contrast, once the maximum driving amplitude exceeds a certain critical value there should be a drastic loss of coherence, reflecting significant heating induced by the pulse. This predicted experimental signature is traced to the loss of an effective adiabatic invariant, and to the ensuing breakdown of adiabatic motion of the system’s Floquet state when the many-body dynamics become chaotic. Our scenario is illustrated with the help of a two-site model of a forced bosonic Josephson junction, but should also hold for other, experimentally accessible configurations.

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