Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1202.3398

Self-consistent spin waves in magnetized BEC

Pavel A. Andreev

Published Feb 15, 2012• 0 citations
arXivHTMLPDF

Abstract

We obtain equations of quantum hydrodynamic (QHD) for magnetized spin-1 neutral Bose-Einstein condensate (BEC). System of QHD equations contains the equation of magnetic moment evolution (an analog of the Bloch equation). We account spin-spin interaction along with the short range interaction. We consider self-consistent field approximation of QHD equations. Starting from QHD equation we derive the Gross-Pitaevskii equation for magnetized BEC. We show that Gross-Pitaevskii equation exists under condition that the magnetic moment direction is not change. Using obtained QHD equations we study the dispersion of collective excitation. As in electrically polarized BEC [P. A. Andreev, L. S. Kuz'menkov, arXiv: 1201.2440], in the magnetically polarized BEC there is second wave mode (polarization mode or spin wave), in addition to the Bogoliubov's mode. Second wave solution appears due to the magnetic moment evolution. The influence of magnetization on dispersion of Bogoliubov's mode is found. We found strong difference of dispersion properties of waves in magnetized BEC from electrically polarized BEC.

DOI
10.48550/arxiv.1202.3398

Related papers

Quantum hydrodynamics description of spin-1 Bose–Einstein condensates

Mariya Iv. Trukhanova, Yuri N. Obukhov

Abstract We develop a novel model of the magnetized spin-1 Bose–Einstein condensate (BEC) of neutral atoms, using the method of many-particle quantum hydrodynamic (QHD) and propose an original derivation of the system of continual equations. We consider bosons with a spin-spin interaction and a short range interaction in the first order in the interaction radius, on the of basis of the self-consistent field approximation of the QHD equations. We demonstrate that the dynamics of the fluid velocity and magnetization is determined by a nontrivial modification of the Euler and Landau–Lifshitz equation, and show that a nontrivial modification of the spin density evolution equation contains the spin torque effect that arises from the self-interactions between spins of the bosons. The properties of the dispersion spectrum of collective excitations are described. We obtain the new contribution of the self-interaction of spins in the spin wave spectrum together with the influence of an external magnetic field and spin-spin interactions between polarized particles. The anisotropic spin wave instability is predicted.

arXiv:2101.03422•Physica Scripta•Nov 25, 2020•2 citations

Dispersion properties of transverse waves in electrically polarized BECs

Pavel A. Andreev, L S Kuzʼmenkov

Further development of the method of quantum hydrodynamics in application for Bose-Einstein condensates (BECs) is presented. To consider evolution of polarization direction along with particles movement we have developed corresponding set of quantum hydrodynamic equations. It includes equations of the polarization evolution and the polarization current evolution along with the continuity equation and the Euler equation (the momentum balance equation). Dispersion properties of the transverse waves including the electromagnetic waves propagating through the BECs are considered. To this end we consider full set of the Maxwell equations for description of electromagnetic field dynamics. This approximation gives us possibility to consider the electromagnetic waves along with the matter waves. We find a splitting of the electromagnetic wave dispersion on two branches. As a result we have four solutions, two for the electromagnetic waves and two for the matter waves, the last two are the concentration-polarization waves appearing as a generalization of the Bogoliubov mode. We also obtain that if the matter wave propagate perpendicular to external electric field when dipolar contribution does not disappear (as it follows from our generalization of the Bogoliubov spectrum). In this case exist a small dipolar frequency shift due to transverse electric field of perturbation.

arXiv:1208.1000•Journal of Physics B Atomic Molecular and Optical Physics•Oct 31, 2014•6 citations

Dipole-dipole interaction and polarization mode in BEC

Pavel A. Andreev, L. S. Kuz’menkov

We propose the construction of a set of quantum hydrodynamics equations for the Bose-Einstein condensate (BEC) where atoms have electric dipole moment (EDM). The contribution of the dipole-dipole interactions (DDI) to the Euler equation is estimated. Quantum equations for the evolution of medium polarization are constructed for the first time. The mathematical method we developed allows studying the effects of interactions on the evolution of polarization. The developed method may be applied to various physical systems in which dynamics is affected by DDI. A problem of elementary excitations in BEC, either affected or not affected by the uniform external electric field, is addressed using our method. We show that the evolution of polarization in BEC leads to the formation of a novel type of elementary excitations. Also, we consider the process of wave generation in polarized BEC by means of monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov's modes and polarization modes by the dipole beam.

arXiv:1106.0822•Jun 4, 2011•0 citations

Nematic tensor evolution in the partially-polarized spin-1 Bose–Einstein condensates

Mariya Iv. Trukhanova

We develop the complete hydrodynamical description of the spin-1 partially polarized Bose–Einstein condensate (BEC), based on the many-particle quantum hydrodynamic formalism. We derive the continuity equation, momentum balance equation, spin evolution and nematicity evolution equations considering the spin–spin dipole long-range interactions and short-range interactions between partially spin-polarized atoms of condensate. The nematic or quadrupolar tensor plays an important role in the experiments of spin-nematic squeezing. We predict the influence of the spin–spin dipole interactions and spin torque force on the dynamics of nematic tensor. The collective modes for phonons and magnons are predicted for the ferromagnetic phase of spinor condensate, where the spin–spin and short-range interactions modify the dispersion equation.

Modern Physics Letters B•Apr 9, 2021•0 citations

The quantum hydrodynamic description of quantum gases with different interactions

Pavel A. Andreev

We describe recent development of quantum hydrodynamics for ultracold Bose particle studying and consider different kinds of interactions. The method of derivation of equations describing the evolution of the neutral Bose particle system at low temperatures is described. Despite the fact that we consider the neutral particles we account the short-range interaction between particles. We consider the particles in the Bose-Einstein condensate (BEC) state. This method is called the method of quantum hydrodynamics, because natural for of the quantum mechanics rewritten in terms of material fields of observable quantities in three dimensional space is the set of equations, which look like the hydrodynamics equations. It can be shown that from the quantum hydrodynamics equations can be derived macroscopic non-linear Schrodinger equation. Most famous non-linear Schrodinger equation is the Gross-Pitaevskii (GP) equation, which contains nonlinearity of the third degree. There are generalizations of the GP equation. New term appears in the GP equation at account of the three-particle interaction. This term contains nonlinearity of the fifth degree. At more detailed account of the two particle interaction we come to the nonlocal non-linear Schrodinger equation. This equation contains spatial derivatives of the order parameter in the non-linear terms caused by the interaction. In this terminology the GP equation corresponds to the first order by the interaction radius. For the BEC of the neutral particles with anisotropic long-range dipole-dipole interaction the generalization of the GP equation was also suggested. Detailed analyses of the applicability conditions shows that this equation valid for the system of dipoles parallel to each other, which do not change their direction, and where the dipole-dipole interaction interferences translational motion of particles.

arXiv:1212.1890•Dec 9, 2012•0 citations

Hydrodynamics of the atomic Bose–Einstein condensate beyond the mean-field approximation

Pavel A Andreev

Abstract Several hydrodynamic models of the atomic Bose–Einstein condensate (BEC) obtained beyond the mean-field approximation are discussed together from a single point of view. All these models are derived from the microscopic quantum description. The derivation is made within the many-particle quantum hydrodynamics method suggested by L Kuz’menkov. The derivation is demonstrated and discussed for the mean-field regime revealing the Gross–Pitaevskii equation as the simplest illustration. It appears in the first order by the interaction radius. Generalization of the hydrodynamic Euler equation obtained in the third order by the interaction radius is discussed. It includes the contribution of the isotropic short-range interaction (SRI) presented by the third space derivative of the square of concentration. The Euler equation also includes the contribution of the anisotropic part of the SRI proportional to the second order spherical function. A systematic account of the quantum fluctuations in terms of the many-particle quantum hydrodynamics method requires the extension of the set of hydrodynamic equations from the couple continuity and Euler equations to the set of four equations which also includes the pressure evolution equation and the evolution equation for the third rank tensor of the pressure flux. The pressure evolution equation contains no interaction contribution in the first order by the interaction radius. The source of the quantum fluctuations is in the interaction caused term existing in the third rank tensor evolution equation which is obtained in the first order by the interaction radius. The presented models are considered for the single-component BECs.

arXiv:2007.15045•Laser Physics Letters•Apr 19, 2021•5 citations
We obtain equations of quantum hydrodynamic (QHD) for magnetized spin-1 neutral Bose-Einstein condensate (BEC). System of QHD equations contains the equation of magnetic moment evolution (an analog of the Bloch equation). We account spin-spin interaction along with the short range interaction. We consider self-consistent field approximation of QHD equations. Starting from QHD equation we derive the Gross-Pitaevskii equation for magnetized BEC. We show that Gross-Pitaevskii equation exists under condition that the magnetic moment direction is not change. Using obtained QHD equations we study the dispersion of collective excitation. As in electrically polarized BEC [P. A. Andreev, L. S. Kuz'menkov, arXiv: 1201.2440], in the magnetically polarized BEC there is second wave mode (polarization mode or spin wave), in addition to the Bogoliubov's mode. Second wave solution appears due to the magnetic moment evolution. The influence of magnetization on dispersion of Bogoliubov's mode is found. We found strong difference of dispersion properties of waves in magnetized BEC from electrically polarized BEC.
Abstract We develop a novel model of the magnetized spin-1 Bose–Einstein condensate (BEC) of neutral atoms, using the method of many-particle quantum hydrodynamic (QHD) and propose an original derivation of the system of continual equations. We consider bosons with a spin-spin interaction and a short range interaction in the first order in the interaction radius, on the of basis of the self-consistent field approximation of the QHD equations. We demonstrate that the dynamics of the fluid velocity and magnetization is determined by a nontrivial modification of the Euler and Landau–Lifshitz equation, and show that a nontrivial modification of the spin density evolution equation contains the spin torque effect that arises from the self-interactions between spins of the bosons. The properties of the dispersion spectrum of collective excitations are described. We obtain the new contribution of the self-interaction of spins in the spin wave spectrum together with the influence of an external magnetic field and spin-spin interactions between polarized particles. The anisotropic spin wave instability is predicted.
Further development of the method of quantum hydrodynamics in application for Bose-Einstein condensates (BECs) is presented. To consider evolution of polarization direction along with particles movement we have developed corresponding set of quantum hydrodynamic equations. It includes equations of the polarization evolution and the polarization current evolution along with the continuity equation and the Euler equation (the momentum balance equation). Dispersion properties of the transverse waves including the electromagnetic waves propagating through the BECs are considered. To this end we consider full set of the Maxwell equations for description of electromagnetic field dynamics. This approximation gives us possibility to consider the electromagnetic waves along with the matter waves. We find a splitting of the electromagnetic wave dispersion on two branches. As a result we have four solutions, two for the electromagnetic waves and two for the matter waves, the last two are the concentration-polarization waves appearing as a generalization of the Bogoliubov mode. We also obtain that if the matter wave propagate perpendicular to external electric field when dipolar contribution does not disappear (as it follows from our generalization of the Bogoliubov spectrum). In this case exist a small dipolar frequency shift due to transverse electric field of perturbation.
We propose the construction of a set of quantum hydrodynamics equations for the Bose-Einstein condensate (BEC) where atoms have electric dipole moment (EDM). The contribution of the dipole-dipole interactions (DDI) to the Euler equation is estimated. Quantum equations for the evolution of medium polarization are constructed for the first time. The mathematical method we developed allows studying the effects of interactions on the evolution of polarization. The developed method may be applied to various physical systems in which dynamics is affected by DDI. A problem of elementary excitations in BEC, either affected or not affected by the uniform external electric field, is addressed using our method. We show that the evolution of polarization in BEC leads to the formation of a novel type of elementary excitations. Also, we consider the process of wave generation in polarized BEC by means of monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov's modes and polarization modes by the dipole beam.
We develop the complete hydrodynamical description of the spin-1 partially polarized Bose–Einstein condensate (BEC), based on the many-particle quantum hydrodynamic formalism. We derive the continuity equation, momentum balance equation, spin evolution and nematicity evolution equations considering the spin–spin dipole long-range interactions and short-range interactions between partially spin-polarized atoms of condensate. The nematic or quadrupolar tensor plays an important role in the experiments of spin-nematic squeezing. We predict the influence of the spin–spin dipole interactions and spin torque force on the dynamics of nematic tensor. The collective modes for phonons and magnons are predicted for the ferromagnetic phase of spinor condensate, where the spin–spin and short-range interactions modify the dispersion equation.
We describe recent development of quantum hydrodynamics for ultracold Bose particle studying and consider different kinds of interactions. The method of derivation of equations describing the evolution of the neutral Bose particle system at low temperatures is described. Despite the fact that we consider the neutral particles we account the short-range interaction between particles. We consider the particles in the Bose-Einstein condensate (BEC) state. This method is called the method of quantum hydrodynamics, because natural for of the quantum mechanics rewritten in terms of material fields of observable quantities in three dimensional space is the set of equations, which look like the hydrodynamics equations. It can be shown that from the quantum hydrodynamics equations can be derived macroscopic non-linear Schrodinger equation. Most famous non-linear Schrodinger equation is the Gross-Pitaevskii (GP) equation, which contains nonlinearity of the third degree. There are generalizations of the GP equation. New term appears in the GP equation at account of the three-particle interaction. This term contains nonlinearity of the fifth degree. At more detailed account of the two particle interaction we come to the nonlocal non-linear Schrodinger equation. This equation contains spatial derivatives of the order parameter in the non-linear terms caused by the interaction. In this terminology the GP equation corresponds to the first order by the interaction radius. For the BEC of the neutral particles with anisotropic long-range dipole-dipole interaction the generalization of the GP equation was also suggested. Detailed analyses of the applicability conditions shows that this equation valid for the system of dipoles parallel to each other, which do not change their direction, and where the dipole-dipole interaction interferences translational motion of particles.
Abstract Several hydrodynamic models of the atomic Bose–Einstein condensate (BEC) obtained beyond the mean-field approximation are discussed together from a single point of view. All these models are derived from the microscopic quantum description. The derivation is made within the many-particle quantum hydrodynamics method suggested by L Kuz’menkov. The derivation is demonstrated and discussed for the mean-field regime revealing the Gross–Pitaevskii equation as the simplest illustration. It appears in the first order by the interaction radius. Generalization of the hydrodynamic Euler equation obtained in the third order by the interaction radius is discussed. It includes the contribution of the isotropic short-range interaction (SRI) presented by the third space derivative of the square of concentration. The Euler equation also includes the contribution of the anisotropic part of the SRI proportional to the second order spherical function. A systematic account of the quantum fluctuations in terms of the many-particle quantum hydrodynamics method requires the extension of the set of hydrodynamic equations from the couple continuity and Euler equations to the set of four equations which also includes the pressure evolution equation and the evolution equation for the third rank tensor of the pressure flux. The pressure evolution equation contains no interaction contribution in the first order by the interaction radius. The source of the quantum fluctuations is in the interaction caused term existing in the third rank tensor evolution equation which is obtained in the first order by the interaction radius. The presented models are considered for the single-component BECs.