Spin current evolution in the separated spin-up and spin-down quantum hydrodynamics

TL;DR

This paper develops a quantum hydrodynamic model for particles with separated spin-up and spin-down states, deriving spin current evolution equations and analyzing wave propagation under various magnetic field strengths.

Contribution

It introduces a novel quantum hydrodynamic framework that treats spin-up and spin-down particles as separate species and derives their spin current evolution equations.

Findings

Derived spin current evolution equations within the quantum hydrodynamics framework.

Analyzed wave propagation in external magnetic fields, including quantum corrections.

Explored effects of weak and strong magnetic fields on spin current dynamics.

Abstract

We have developed the quantum hydrodynamic model that describes particles with spin-up and with spin-down in separate. We have derived the equation of the spin current evolution as a part of the set of the quantum hydrodynamics (QHD) equations that treat particles with different projection of spin on the preferable direction as two different species. We have studied orthogonal propagation of waves in the external magnetic field and determined the contribution of quantum corrections due to the Bohm potential and to magnetization energy of particles with different projections of spin in the spin current wave dispersion. We have analyzed the limits of weak and strong magnetic fields.