Galvano- and thermo-magnetic effects at low and high temperatures within non-Markovian quantum Langevin approach

Abstract

The quantum Langevin formalism is used to study the charge carrier transport in a twodimensional sample. The center of mass of charge carriers is visualized as a quantum particle, while an environment acts as a heat bath coupled to it through the particle-phonon interaction.The dynamics of the charge carriers is limited by the average collision time which takes effectively into account the two-body effects. The functional dependencies of particle-phonon interaction and average collision time on the temperature and magnetic field are phenomenologically treated. The galvano-magnetic and thermo-magnetic effects in the quantum system appear as the result of the transitional processes at low temperatures.

Quantum Hall and Shubnikov-de Haas Effects in Graphene within Non-Markovian Langevin Approach

“…was formulated in ref. [46]. The term H c is the Hamiltonian of the collective subsystem embedded in the external uniform magnetic and electric fields.…”

“…In our model, the one-body, two-body, and non-Markovian effects are taken into consideration. Note, that the quantum Langevin approach was widely used to describe various macroscopic phenomena [36][37][38][39][40][41][42][43][44][45][46].…”

Open quantum system in external magnetic field within non-Markovian quantum Langevin approach

“…Let us consider a two-dimensional motion of a charged quantum particle in the presence of heat bath and external constant magnetic field B = (0, 0, B). The total Hamiltonian of this system is [23,29]…”

“…where α ν and β ν are the real coupling constants. Equation ( 4) is already used in literature [20,23,25,28,29]. The first term of H cb in Eq.…”

“…For a charged particle moving in a two-dimensional harmonic oscillator and an uniform magnetic field, the time-dependent friction and diffusion coefficients have been analytically derived and numerically studied within the non-Markovian quantum Langevin formalism in Ref. [28,29]. A charged particle moving in a static external magnetic field (without a confined potential) and linearly coupled to a heat bath has been only treated in Refs.…”