The Quantum Boltzmann Equation in Semiconductor Physics

Abstract

The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including models of excitons in bulk materials, electron-hole plasmas, and polariton gases.

14 pages, 8 figures. Dedicated to Manuel Cardona on the occasion of his 75th birthday celebration in Queretaro, Mexico

References in corpus (8)

• Observation of Half Quantum Vortices in an Exciton-Polariton Condensate
• Persistent currents and quantised vortices in a polariton superfluid
• Kinetics of Bose-Condensation
• Quantum Kinetic Theory I: A Quantum Kinetic Master Equation for Condensation of a weakly interacting Bose gas without a trapping potential
• Structure of completely positive quantum master equations with memory kernel
• Multi-mode description of an interacting Bose-Einstein condensate
• Theory of Bose-Einstein condensation and superfluidity of two-dimensional polaritons in an in-plane harmonic potential
• Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis

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• Steady state of interacting Floquet insulators
• Dynamics of Phase Coherence Onset in Bose Condensates of Photons by Incoherent Phonon Emission
• The Basis of the Second Law of Thermodynamics in Quantum Field Theory
• Numerical solver for the time-dependent far-from-equilibrium Boltzmann equation
• Theory of Non-equilibrium "Hot" Carriers in Direct Band-gap Semiconductors Under Continuous Illumination
• Octave-spanning 1 emission across the visible spectrum from single crystalline 1,3,5,7-tetrakis-($p$-methoxyphenyl)adamantane
• Numerical scheme for the far-out-of-equilibrium time-dependent Boltzmann collision operator: 1D second-degree momentum discretisation and adaptive time stepping
• Numerical Solver for the out-of-equilibrium time dependent Boltzmann Collision operator: Application to 2D materials
• Polaritonic linear dynamic in Keldysh formalism
• Entropy augmentation through subadditive excess: information theory in irreversible processes