Langmuir waves in semi-relativistic spinless quantum plasmas

Abstract

Many particle quantum hydrodynamics based on the Darwin Hamiltonian (the Hamiltonian corresponding to the Darwin Lagrangian) is considered. A force field appearing in corresponding Euler equation is considered in details. Contributions from different terms of the Darwin Hamiltonian in the Euler equation are traced. For example, the relativistic correction to the kinetic energy of particles leads to several terms in the Euler equation, these terms have different form. One of them has a form similar to a term appearing from the Darwin term. Hence, the two different mechanisms give analogous contributions in wave dispersion. Microscopic analog of the Biot-Savart law, called the current-current interaction and describing an interaction of moving charges via the magnetic field, is also included in our description. The semi-relativistic generalization of the quantum Bohm potential is obtained. Contribution of the relativistic effects in the spectrum of plasma collective excitations is considered.

Separated spin evolution quantum hydrodynamics of degenerate electrons with spin–orbit interaction and extraordinary wave spectrum

“…(2012), along with the Darwin term. However, the Darwin term is considered in reduced form corresponding to the single-particle motion only, but for a system of identical particles it makes a different contribution (see the discussion in Ivanov, Andreev & Kuz’menkov 2015). The complete result for the Darwin term or the Darwin interaction contribution is presented in Ivanov et al.…”

“…The complete result for the Darwin term or the Darwin interaction contribution is presented in Ivanov et al. (2015). There is another quantum-relativistic force which appears via the simultaneous consideration of the Coulomb interaction and the semi-relativistic part of the kinetic energy (Ivanov, Andreev & Kuz’menkov 2014; Ivanov et al.…”

“…There is another quantum-relativistic force which appears via the simultaneous consideration of the Coulomb interaction and the semi-relativistic part of the kinetic energy (Ivanov, Andreev & Kuz’menkov 2014; Ivanov et al. 2015). Let us call it the CI-SPKE.…”

“…The Darwin interaction force and the CI-SPKE force give contributions which are equal to each other in the linear approximation of hydrodynamic equations (Ivanov et al. 2015).…”

“…The semi-relativistic part of the quantum Bohm potential is derived in Ivanov et al. (2014, 2015) along with the current–current interaction (CCI). The CCI leads to three kinds of terms in the Euler equation: the first of them is , the classic semi-relativistic forces, and the quantum semi-relativistic forces (Ivanov et al.…”