Semi-relativistic effects in spin-1/2 quantum plasmas

Abstract

Emerging possibilities for creating and studying novel plasma regimes, e.g. relativistic plasmas and dense systems, in a controlled laboratory environment also require new modeling tools for such systems. This motivates theoretical studies of the kinetic theory governing the dynamics of plasmas for which both relativistic and quantum effects occur simultaneously. Here, we investigate relativistic corrections to the Pauli Hamiltonian in the context of a scalar kinetic theory for spin-1/2 quantum plasmas. In particular, we formulate a quantum kinetic theory for the collective motion of electrons that takes into account effects such as spin-orbit coupling and Zitterbewegung. We discuss the implications and possible applications of our findings. Contents

Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation

“…Instead, the free current density displays a correction term that can be written as (E×M spin )/2mc 2 . This term was already obtained in the past from semi-relativistic kinetic models (Wigner equation) 22 . We will now attempt to provide a physical interpretation of these terms.…”

Phase-space methods for the spin dynamics in condensed matter systems

“…This approach was used to derive a Wigner equation that incorporates spin effects through the Zeeman interaction [24]. Semiclassical [25] and hydrodynamic [26] spin equations were also derived from those models, including other relativistic effects such as the spin-orbit coupling, the Darwin term, and the relativistic mass correction.…”

Balance equations in semi-relativistic quantum hydrodynamics

“…[32], where authors did not considered contribution from the relativistic part of kinetic energy in equations of collective motion. They aimed to neglect contribution from relativistic part of the quantum Bohm potential (the third term in formula (102)).…”