Problem with the single-particle description and the spectra of intrinsic modes of degenerate boson-fermion systems

Andreev, Pavel A.; Kuz'menkov, L. S.

doi:10.1103/physreva.78.053624

Cited by 64 publications

(105 citation statements)

References 52 publications

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“…A generalization of this model appears at more detail consideration of the short-range interaction up to the third order by the interaction radius Ref. [32]. Corresponding generalization of the Bogoloubov spectrum can be found in Ref.…”

Section: Modelmentioning

confidence: 98%

“…The method of many-particle quantum hydrodynamics [31] allows to derive the Gross-Pitaevskii equation for BECs of neutral atoms [32]. The Gross-Pitaevskii equation appears in the first order by the interaction radius.…”

Section: Modelmentioning

confidence: 99%

“…This formula was derived in Ref. [32] (see formula (25)). We also present it here n 2 (r, r ′ , t) = n(r, t)n(r ′ , t)…”

Section: Modelmentioning

confidence: 99%

See 2 more Smart Citations

Simultaneous dipole and quadrupole moment contribution in the Bogoliubov spectrum: Application of the non-integral Gross–Pitaevskii equation

Andreev

2017

Mod. Phys. Lett. B

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We present the Gross-Pitaevskii equation for Bose-Einstein condensates (BECs) possessing the electric dipole and the electric quadrupole moments in a non-integral form. These equations are coupled with the Maxwell equations. The model under consideration includes the dipole-dipole, the dipole-quadrupole, and the quadrupole-quadrupole interactions in terms of the electric field created by the dipoles and quadrupoles. We apply this model to obtain the Bogoliubov spectrum for three dimensional BECs with a repulsive short-range interaction. We obtain an extra term in the Bogoliubov spectrum in compare with the dipolar BECs. We show that the quadrupole-quadrupole interaction gives a positive contribution in the Bogoliubov spectrum. Hence this spectrum is stable.

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Section: Modelmentioning

confidence: 98%

Section: Modelmentioning

confidence: 99%

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Simultaneous dipole and quadrupole moment contribution in the Bogoliubov spectrum: Application of the non-integral Gross–Pitaevskii equation

Andreev

2017

Mod. Phys. Lett. B

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“…Furthermore, Kuzmenkov and his coworkers developed MPQHD further to analyze spin effects [14,15] and Bose-Einstein-Condensates [16]. In addition, applications of MPQHD were discussed for electrons in graphene [17] and plasma effects [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

The Connection between Bohmian Mechanics and Many-Particle Quantum Hydrodynamics

Renziehausen

Barth

2020

Found Phys

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Bohm developed the Bohmian mechanics (BM), in which the Schrödinger equation is transformed into two differential equations: a continuity equation and an equation of motion similar to the Newtonian equation of motion. This transformation can be executed both for single-particle systems and for many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum mechanics for the derivation of manyparticle quantum hydrodynamics (MPQHD) including one differential equation for the mass balance and two differential equations for the momentum balance, and we extended their analysis in a prework (K. Renziehausen, I. Barth in Prog. Theor. Exp. Phys. 2018:013A05, 2018) for the case that the particle ensemble consists of different particle sorts. The purpose of this paper is to show how the differential equations of MPQHD can be derived for such a particle ensemble with the differential equations of BM as a starting point. Moreover, our discussion clarifies that the differential equations of MPQHD are more suitable for an analysis of many-particle systems than the differential equations of BM because the differential equations of MPQHD depend on a single position vector only while the differential equations of BM depend on the complete set of all particle coordinates.

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“…There is also interaction proportional to δ(r i − r j ), which corresponds to the Zitterbewegung effect. Through studies of specific physical processes, such as dispersion of waves, interaction of charged beams with plasmas, equations of quantum hydrodynamics have been used in modern literature, and these equations can be derived from both the manyparticle Schrödinger equation to be truncated for particular system of particles [1], [2], [3], [44] and from the Schrödinger equation for one particle in an external field [45]- [47].…”

Section: Introductionmentioning

confidence: 99%

Balance equations in semi-relativistic quantum hydrodynamics

Ivanov

Andreev

Kuz'menkov

2014

Int. J. Mod. Phys. B

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Аннотация. Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i. e. described by the Darwin Lagrangian on microscopic level) hydrodynamical equations is given after a brief review of method development. It provides better distinguishing between classic and quantum semi-relativistic effects. Derivation of the classical equations is interesting since it is made by a natural, but not very widespread method. This derivation contains explicit averaging of the microscopic dynamics. Derivation of corresponding quantum hydrodynamic equations is presented further. Equations are obtained in the five-momentum approximation including the continuity equation, Euler and energy balance equations. It is shown that relativistic corrections lead to presence of new quantum terms in expressions for a force field, a work field etc. The semi-relativistic generalization of the quantum Bohm potential is obtained. Quantum part of the energy current, which is an analog of the quantum Bohm potential for the energy evolution equation, is derived. The Langmuir wave dispersion in semi-relativistic quantum plasmas, corresponding to the Darwin Lagrangian, is also considered to demonstrate contribution of semi-relativistic effects on basic plasma phenomenon.

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Problem with the single-particle description and the spectra of intrinsic modes of degenerate boson-fermion systems

Cited by 64 publications

References 52 publications

Simultaneous dipole and quadrupole moment contribution in the Bogoliubov spectrum: Application of the non-integral Gross–Pitaevskii equation

Simultaneous dipole and quadrupole moment contribution in the Bogoliubov spectrum: Application of the non-integral Gross–Pitaevskii equation

The Connection between Bohmian Mechanics and Many-Particle Quantum Hydrodynamics

Balance equations in semi-relativistic quantum hydrodynamics

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