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This research advances the theoretical framework of quantum hydrodynamics by rigorously deriving spin-orbit coupling forces through Hamilton's action principle applied to the Pauli equation. By distinguishing between standard spin-hydrodynamic forces and novel SOC-induced orbital forces, the study clarifies fundamental mechanisms driving spin transport phenomena like the spin Hall effect. The work provides a new definition for transport spin current and proposes a particle-based numerical scheme applicable to planar SOC configurations.
Madelung hydrodynamics of spin-orbit coupling: action principles, currents, and correlations
arXiv:2601.10698v3 Announce Type: replace Abstract: We exploit the variational and Hamiltonian structures of quantum hydrodynamics with spin to unfold the correlation and torque mechanisms accompanying spin-orbit coupling (SOC) in electronic motion. Using Hamilton's action principle for the Pauli equation, we isolate SOC-induced quantum forces that act on the orbital Madelung--Bohm trajectories and complement the usual force terms known to appear in quantum hydrodynamics with spin. While the latter spin-hydrodynamic forces relate to the quantum geometric tensor (QGT), SOC-induced orbital forces originate from a particular current operator that contributes prominently to the spin current. This distinction between force terms reveals two fundamentally different mechanisms generating quantum spin-orbit correlations. Leveraging the Hamiltonian structure of the hydrodynamic system, we also elucidate spin transport features such as the correlation-induced quantum torques and the current shift in the spin Hall effect. This Hall shift leads to a new definition of the transport spin current thereby addressing an open question in spintronics. Finally, we illustrate the framework via the Madelung--Rashba equations for planar SOC configurations and propose a particle-based scheme for numerical implementation.
Abstract:We exploit the variational and Hamiltonian structures of quantum hydrodynamics with spin to unfold the correlation and torque mechanisms accompanying spin-orbit coupling (SOC) in electronic motion. Using Hamilton's action principle for the Pauli equation, we isolate SOC-induced quantum forces that act on the orbital Madelung--Bohm trajectories and complement the usual force terms known to appear in quantum hydrodynamics with spin. While the latter spin-hydrodynamic forces relate to the quantum geometric tensor (QGT), SOC-induced orbital forces originate from a particular current operator that contributes prominently to the spin current. This distinction between force terms reveals two fundamentally different mechanisms generating quantum spin-orbit correlations. Leveraging the Hamiltonian structure of the hydrodynamic system, we also elucidate spin transport features such as the correlation-induced quantum torques and the current shift in the spin Hall effect. This Hall shift leads to a new definition of the transport spin current thereby addressing an open question in spintronics. Finally, we illustrate the framework via the Madelung--Rashba equations for planar SOC configurations and propose a particle-based scheme for numerical implementation.
Extended and fully revised. 27 pages including appendix. Comments welcome
Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph)
arXiv:2601.10698 [quant-ph]
(or arXiv:2601.10698v3 [quant-ph] for this version)
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