Pseudorelativistic effects on solitons in quantum semiconductor plasma

Abstract

A theory for nonlinear excitations in quantum plasmas is presented for narrow-gap semiconductors by considering the combined effects of quantum and pseudorelativity. The system is governed by a coupled Klein-Gordon equation for the collective wave functions of the conduction electrons and Poisson's equation for the electrostatic potential. This gives a closed system, including the effects of charge separation, quantum tunneling, and pseudorelativity. By choosing the typical parameters of semiconductor InSb, the quasistationary soliton solution, which is a multipeaked dark soliton, is obtained numerically and shows depleted electron densities correlated with a localized potential. The dynamical simulation result shows that the dark soliton is stable and has a multipeaked profile, which is consistent with the quasistationary solution. The present model and results may be useful in understanding the nonlinear properties of semiconductor plasma on an ultrafast time scale.

Simulating thermal boundary conditions of spin–lattice models with weighted averages

“…It was shown that the absolute free energy can be measured very accurately using the free energy perturbation method in both population annealing and parallel tempering [11,15]. It can be shown from statistical mechanics that the average energy, entropy, free energy and the spin overlap distribution should be averaged as…”

Ground state of a bosonic massive charged particle in the presence of external fields in a Gödel-type spacetime

“…[4]. Another interesting work addresses the study of nonlinear quantum electrostatic waves in a pseudorelativistic quantum semiconductor plasm [5]. In this description, the authors considered the substitution p 0 → p 0 − eA 0 and p → p, and they showed that the system is governed by the Klein-Gordon equation for the collective wave functions of the conducting electrons and Poisson's equation for the electrostatic potential.…”

Effective photon mass and exact translating quantum relativistic structures

“…(64) assuming decaying boundary conditions, plus the use of the dispersion relation (7), the KGE (13), the radial equation (26), the definition (27), and the normalization condition (34). In such way, we finally derive the simple expression…”

“…Examples are provided by the analysis of the Zitterbewegung (trembling motion) of Klein-Gordon particles in extremely small spatial scales, and its simulation by classical systems, 16 the KGE as a model for the Weibel instability in relativistic quantum plasmas, 17 the description of standing EM solitons in degenerate relativistic plasmas, 18 the KGE as the starting point for the wave kinetics of relativistic quantum plasmas, 19 the KGE in the presence of a strong rotating electric field and the QED cascade, 20 the Klein-Gordon-Maxwell multistream model for quantum plasmas, 21 the negative energy waves and quantum relativistic Buneman instabilities, 22 the separation of variables of the KGE in a curved space-time in open cosmological universes, 23 the resolution of the KGE equation in the presence of Kratzer 24 and Coulombtype 25 potentials, the KGE with a short-range separable potential and interacting with an intense plane-wave EM field, 26 electrostatic one-dimensional propagating nonlinear structures and pseudo-relativistic effects on solitons in quantum semiconductor plasma, 27 the square-root KGE, 28 hot nonlinear quantum mechanics, 29 a quantum-mechanical free-electron laser model based on the single electron KGE, 30 and the inverse bremsstrahlung in relativistic quantum plasmas. Very often, the treatment of charged particle dynamics described by the Klein-Gordon or Dirac equations assumes a circularly polarized electromagnetic (CPEM) wave, [31][32][33][34][35][36][37][38][39][40] mainly due to the analytical simplicity.…”