Quantum hydrodynamics of the spinor Bose-Einstein condensate at non-zero temperatures
Pavel A. Andreev,
I. N. Mosaki,
Mariya Iv. Trukhanova
Abstract:Finite temperature hydrodynamic model is derived for the spin-1 ultracold bosons by the manyparticle quantum hydrodynamic method. It is presented as the two fluid model of the BEC and normal fluid. The linear and quadratic Zeeman effects are included. Scalar and spin-spin like shortrange interactions are considered in the first order by the interaction radius. It is also represented as the set of two nonlinear Pauli equations. The spectrum of the bulk collective excitations is considered for the ferromagnetic … Show more
“…Definition (1) is the first step of derivation of the hydrodynamic equations from the microscopic many-particle Schrodinger equation in the coordinate representation by the quantum hydrodynamic method suggested by L. S. Kuz'menkov and S. G. Maksimov [30], [31], [32]. This method is applied to the spin-1 ultracold bosons [33]. We consider the ferromagnetic phase of spin-1 BECs, while there are other phases such as polar phase, partially polarized BECs, antiferromagnetic phase (which includes the nematic ordering of the system [34]).…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…It leads to the following set of hydrodynamic equations. First, it is the continuity equations for the BEC and for the normal fluid [33]…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…where subindex a stands for B and n. Vector v a is the hydrodynamic velocity field. The velocity field is the ratio of the momentum density to the mass m and concentration n. The momentum density is defined via the many-particle wave function similarly to the concentration (1) [33]. The spinor BEC is characterized by the spin vector field…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…For the finite temperature it is derived in Ref. [33]. Hydrodynamic model ( 2)-( 11) is equivalent to the set of non-linear Schrodinger equations…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…The spin field is the unit field for the ferromagnetic phase s = {cos Φ(r) sin Θ(r), sin Φ(r) sin Θ(r), cos Θ(r)}. (33) Functions Φ(r) and Θ(r) depend in general on the three dimensional coordinate r. They are functions of time as well. However, we are focused on the static regime, where there is plane symmetry.…”
Section: Skyrmions In Spin-1 Ultracold Bosonsmentioning
Quantum hydrodynamic of skyrmions in spinor ultracold bosons at the finite temperature is described. The limit regime of BEC appearing at the zero temperature is discussed either. The skyrmions are found as the solution of the spin evolution equation for the ferromagnetic phase of spin-1 ultracold bosons. It is demonstrated that the quantum part of the spin current gives major contribution in the formation of the skyrmions. The interplay between the quantum (spin) vorticity and the classic vorticity is considered for the finite temperatures. Bosons are presented as two fluids associated with the Bose-Einstein condensate and the normal fluid. All effects are considered for the ferromagnetic phase.
“…Definition (1) is the first step of derivation of the hydrodynamic equations from the microscopic many-particle Schrodinger equation in the coordinate representation by the quantum hydrodynamic method suggested by L. S. Kuz'menkov and S. G. Maksimov [30], [31], [32]. This method is applied to the spin-1 ultracold bosons [33]. We consider the ferromagnetic phase of spin-1 BECs, while there are other phases such as polar phase, partially polarized BECs, antiferromagnetic phase (which includes the nematic ordering of the system [34]).…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…It leads to the following set of hydrodynamic equations. First, it is the continuity equations for the BEC and for the normal fluid [33]…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…where subindex a stands for B and n. Vector v a is the hydrodynamic velocity field. The velocity field is the ratio of the momentum density to the mass m and concentration n. The momentum density is defined via the many-particle wave function similarly to the concentration (1) [33]. The spinor BEC is characterized by the spin vector field…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…For the finite temperature it is derived in Ref. [33]. Hydrodynamic model ( 2)-( 11) is equivalent to the set of non-linear Schrodinger equations…”
Section: Hydrodynamic Equations For Spin-1 Bec and Normal Fluid In Th...mentioning
confidence: 99%
“…The spin field is the unit field for the ferromagnetic phase s = {cos Φ(r) sin Θ(r), sin Φ(r) sin Θ(r), cos Θ(r)}. (33) Functions Φ(r) and Θ(r) depend in general on the three dimensional coordinate r. They are functions of time as well. However, we are focused on the static regime, where there is plane symmetry.…”
Section: Skyrmions In Spin-1 Ultracold Bosonsmentioning
Quantum hydrodynamic of skyrmions in spinor ultracold bosons at the finite temperature is described. The limit regime of BEC appearing at the zero temperature is discussed either. The skyrmions are found as the solution of the spin evolution equation for the ferromagnetic phase of spin-1 ultracold bosons. It is demonstrated that the quantum part of the spin current gives major contribution in the formation of the skyrmions. The interplay between the quantum (spin) vorticity and the classic vorticity is considered for the finite temperatures. Bosons are presented as two fluids associated with the Bose-Einstein condensate and the normal fluid. All effects are considered for the ferromagnetic phase.
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