Quantum Theory of Solid State Plasma Dielectric Response

Abstract

We review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired "second quantized" creation and annhilation field operators of interacting quantum many-body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron-hole pair excitations and plasmons.

Comment on ‘Discussion on novel attractive force between ions in quantum plasmas—failure of simulations based on a density functional approach’

“…A number of authors [29][30][31] raised serious concerns against its uncritical use that frequently disregards the applicability range of QHD. Our analysis presented in [28,32] answers just the question about 1 The longitudinal dielectric function follows from the dielectric tensor via l (k, ω) = i j k i k j (k, ω) i j /k 2 . 2 In non-equilibrium situations, such as ions embedded into streaming electrons, there exist additional attractive forces and wake effects, e.g.…”

“…have to be discarded since they are incompatible with the newly discovered SE attractive force that brings ions closer at atomic scales to form a high density superconducting plasma state with temperatures of the order of a few electron volts.' On page 3 SEA continue: 'the results of BPS [1] should be revised to include the energy associated with the quantum recoil effect in the DFT Hamiltonian in order to obtain a consistent output, similar to that of SE . .…”

“…Dense plasmas exhibiting quantum degeneracy of the electrons and Coulomb correlation effects are presently of high interest in many fields including condensed matter, astrophysics, warm dense matter and laser plasmas, e.g. [1][2][3][4][5]. Even for the simplest plasma system-hydrogen-interesting questions remain partly open, including details of the phase diagram, e.g.…”

“…While in the limit of a classical high-temperature plasma l s is given by the Debye radius, in a dense quantum plasma, it is given by the Thomas-Fermi length L TF . More general screened potentials are successfully computed using linear response theory to obtain the dynamic dielectric function, l (k, ω) (longitudinal density response), giving rise to 1 [20]…”

“…The potential (1) typically decays slower than the exponential Yukawa potential but faster than the Coulomb potential.…”