Particle Fluctuations in Mesoscopic Bose Systems

Yukalov, V. I.

doi:10.3390/sym11050603

Cited by 10 publications

(11 citation statements)

References 42 publications

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“…Therefore, we may argue that the phase angle of any uniform BEC originating from SSB should be equal to Θ = πn. There is every likelihood that when condensates start to form, e.g., in a rectangle trap [33][34][35], those BEC with other phases leave the condensate, such that only those formations with with Θ = πn survive. The fact that even in the case of spatially inhomogeneous trapped Bose gases condensate has a fixed phase was experimentally observed many years ago [21].…”

Section: The Condensate Fraction and Its Phasementioning

confidence: 99%

Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

Rakhimov,

Khudoyberdiev,

Rani

et al. 2019

Preprint

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We study the thermodynamic properties of dimerized spin-gapped quantum magnets with and without exchange anisotropy (EA) and Dzyaloshinsky-Moriya (DM) anisotropies within the mean-field approximation. For this, we obtain the thermodynamic potential Ω of a triplon gas taking into account the strength of DM interaction up to second order. The minimization of Ω with respect to self-energies yields the equation for X 1,2 = Σ n ± Σ an − µ, which define the dispersion of quasiparticleswhere k is the bare dispersion of triplons. The minimization of Ω with respect to magnitude ρ 0 and phase Θ of triplon condensate leads to the coupled equations. We discuss also the restrictions on ρ 0 and Θ imposed by these equations for systems. The requirement of dynamical stability conditions in equilibrium, as well as the Hugenholtz-Pines theorem, particularly for isotropic Bose condensate, impose certain conditions to the physical solutions of these equations. It is shown that the phase angle of a purely homogenous Bose-Einstein condensate (BEC) without any anisotropy may only take values Θ = πn (n=0,±1, ±2..) while that of BEC with even a tiny DM interaction results in Θ = π/2 + 2πn. In contrast to Hartree-Fock-Popov approximation, which allows arbitrary phase angle, our approach predicts that the phase angle may have only discrete values. The consequences of this phase-locking for interference of two Bose condensates and to their possible Josephson junction is studied. In such quantum magnets, the emergence of a triplon condensate leads to a finite staggered magnetization M ⊥ , whose direction in the xy-plane is related to the condensate phase Θ.The possible Kibble-Zurek mechanism in dimerized magnets and its influence on M ⊥ also discussed.

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Section: The Condensate Fraction and Its Phasementioning

confidence: 99%

Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

Rakhimov,

Khudoyberdiev,

Rani

et al. 2019

Preprint

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“…Last but not least, it is possible to envision classifying the morphology of a Bose-Einstein condensate beyond that emanating from the variances of the position, momentum, and angular-momentum operators. Furthermore, in four spatial dimensions one could expect an additional richness of the variance [38].…”

Section: Discussionmentioning

confidence: 99%

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

Alon

2021

Symmetry

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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.

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“…is valid not for all dimensionalities. It is possible to show [14] that, depending on spatial dimensionality, particle fluctuations scale as…”

Section: Condensate Existence and Stabilitymentioning

confidence: 99%

“…in which µ 0 , µ 1 , and λ(r) are the Lagrange multipliers guaranteeing the validity of conditions ( 13), (14), and (15). The equations of motion can be written as the equation for the condensate function…”

Section: General Self-consistent Approachmentioning

confidence: 99%

Hartree–Fock–Bogolubov Method in the Theory of Bose-Condensed Systems

Yukalov

Yukalova

2020

Phys. Part. Nuclei

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The Hohenberg-Martin dilemma of conserving versus gapless theories for systems with Bose-Einstein condensate is considered. This dilemma states that, generally, a theory characterizing a system with broken global gauge symmetry, which is necessary for Bose-Einstein condensation, is either conserving, but has a gap in its spectrum, or is gapless, but does not obey conservation laws. In other words, such a system either displays a gapless spectrum, which is necessary for condensate existence, but is not conserving, which implies that it corresponds to an unstable system, or it respects conservation laws, describing a stable system, but the spectrum acquires a gap, which means that the condensate cannot appear. An approach is described, resolving this dilemma, and it is shown to give good quantitative agreement with experimental data. Calculations are accomplished in the Hartree-Fock-Bogolubov approximation.

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Particle Fluctuations in Mesoscopic Bose Systems

Cited by 10 publications

References 42 publications

Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

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

Hartree–Fock–Bogolubov Method in the Theory of Bose-Condensed Systems

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