A Note on the Calculation of the Long-Wavelength Limit of the Bosonic Excitation Spectrum

Rovenchak, Andrij

doi:10.1515/zna-2014-0211

Cited by 2 publications

(1 citation statement)

References 29 publications

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“…This correction does not contribute in the long-wavelength limit (figure 3). The behavior of the elementary excitation spectrum in the long-wavelength limit was solved in [48] of the method of two-time temperature Green's functions. At least a two-parametric deformation should be sought for to consider anharmonic terms ∆H in Hamiltonian (2.3) in a proper way.…”

Section: -11mentioning

confidence: 99%

The theory of a many boson system with the deformed Heisenberg algebra

Vakarchuk¹,

Panochko²

2015

Condens. Matter Phys.

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We propose to consider nonlinear fluctuations in the theory of liquid 4 He deforming the commutation relations between the generalized coordinates and momenta. Generalized coordinates are coefficients of density fluctuations of Bose particles. The deformation parameter takes into account the effects of three-and four-particle correlations in the behavior of a system. This parameter is defined from the experimental values of the elementary excitation spectrum and the structure factor extrapolated to T = 0 K. The numerical estimation of the ground state energy and the Bose condensate fraction is made. The elementary excitation spectrum and the potential of interaction between the helium atoms are recovered.

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Section: -11mentioning

confidence: 99%

The theory of a many boson system with the deformed Heisenberg algebra

Vakarchuk¹,

Panochko²

2015

Condens. Matter Phys.

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Effective Hamiltonian and excitation spectrum of harmonically trapped bosons

Rovenchak

2016

Low Temperature Physics

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An approach is proposed to obtain an effective Hamiltonian of a harmonically trapped Bose-system. Such a Hamiltonian is quadratic in the creation-annihilation operators and certain approximations allow to simplify higher (three and four operator) products to the required form. After the Hamiltonian diagonalization, the expression for the excitation spectrum is obtained containing in particular temperature-dependent corrections. Numerical calculations are made for a one-dimensional system. Some prospects towards the extension of the suggested approach to study binary bosonic mixtures are briefly discussed.

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A Note on the Calculation of the Long-Wavelength Limit of the Bosonic Excitation Spectrum

Cited by 2 publications

References 29 publications

The theory of a many boson system with the deformed Heisenberg algebra

The theory of a many boson system with the deformed Heisenberg algebra

Effective Hamiltonian and excitation spectrum of harmonically trapped bosons

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