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 Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1342
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Infinite Number ◽  
Mean Field ◽  
Solvable Model ◽  
Time Dependent ◽  
Angular Momentum Operator ◽  
Many Body ◽  
The Many ◽  
Bose Einstein ◽  
Number Of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

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 IDEAL-MODIFIED BOSONIC GAS TRAPPED IN AN ARBITRARY THREE-DIMENSIONAL POWER-LAW POTENTIAL

2012 ◽  
Vol 27 (31) ◽  
pp. 1250181 ◽  
Author(s):  
E. CASTELLANOS ◽  
C. LÄMMERZAHL
Keyword(s):  
Dispersion Relation ◽  
Power Law ◽  
Three Dimensional ◽  
Particle Dispersion ◽  
Einstein Condensate ◽  
Gravity Models ◽  
Condensation Temperature ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose–Einstein condensate trapped in a generic three-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. In addition, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.

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.

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.

λ-Transition to the Bose-Einstein Condensate

1995 ◽  
Vol 50 (10) ◽  
pp. 921-930 ◽  
Author(s):  
Siegfried Grossmann ◽  
Martin Holthaus
Keyword(s):  
Heat Capacity ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Harmonic Oscillator Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Analytical Expressions ◽  
Grand Canonical

Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statis­tics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discon­tinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.

scholarly journals Three-Dimensional Skyrmions with Arbitrary Topological Number in a Ferromagnetic Spin-1 Bose-Einstein Condensate

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Huan-Bo Luo ◽  
Lu Li ◽  
Wu-Ming Liu
Keyword(s):  
Magnetic Field ◽  
Vortex Ring ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Laser Beams ◽  
Quantization Axis ◽  
Density Distributions ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Topological Number

AbstractWe propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.

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