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Quantum Boltzmann Equations

Yves Pomeau A, Minh-Binh Tran

Lecture notes in physicsJan 1, 20190 citations

Some Considerations on the Derivation of the Nonlinear Quantum Boltzmann Equation

Dario Benedetto, François Castella, R. Esposito +1 more

arXiv:math-ph/0301025Journal of Statistical PhysicsAug 1, 200466 citations

Quantum Boltzmann equations for binary interactions between identical particles

Pagiotis Vasilopoulos, Carolyn M. Van Vliet

Physica A Statistical Mechanics and its ApplicationsSep 1, 19837 citations

Quantum Boltzmann Transport Equation in the Presence of Interactions; Application to the 2D Hall Effect

C. M. Van Vliet, Th. Samson

Abstract The quantum Boltzmann equation (QBE), derived in previous papers, is extended to systems with strong interparticle interactions. In particular, the non‐diagonal hierarchy of kinetic equations for [ℒ︁hin]N c cζ, N = 0, 1,…, ∞, where ℒ︁in is the interaction Liouvillian, is solved by iteration in order to obtain a generalized non‐diagonal QBE. The application to the 2D quantum Hall effect, integral and fractional, is discussed.

physica status solidi (b)Oct 1, 19940 citations

Quantum Boltzmann equation of composite fermions interacting with a gauge field

Yong Baek Kim, Patrick A. Lee, Xiao-Gang Wen

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the \ensuremath{\nu}=1/2 state using the nonequilibrium Green's-function technique. The lowest-order perturbative correction to the self-energy due to the strong gauge-field fluctuations suggests that there is no well-defined Landau quasiparticle. Therefore, we cannot assume the existence of the Landau quasiparticles a priori in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi-surface displacement which corresponds to the local variation of the chemical potential in momentum space. From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at \ensuremath{\nu}=1/2 (in the long-wavelength and the low-frequency limits) and the singular behavior of the energy gap obtained from the finite-temperature activation behavior of the compressibility near \ensuremath{\nu}=1/2. Implications of these results for recent experiments are also discussed.We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the \ensuremath{\nu}=1/2 state using the nonequilibrium Green's-function technique. The lowest-order perturbative correction to the self-energy due to the strong gauge-field fluctuations suggests that there is no well-defined Landau quasiparticle. Therefore, we cannot assume the existence of the Landau quasiparticles a priori in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi-surface displacement which corresponds to the local variation of the chemical potential in momentum space. From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at \ensuremath{\nu}=1/2 (in the long-wavelength and the low-frequency limits) and the singular behavior of the energy gap obtained from the finite-temperature activation behavior of the compressibility near \ensuremath{\nu}=1/2. Implications of these results for recent experiments are also discussed.

arXiv:cond-mat/9504063Physical review. B, Condensed matterDec 15, 199585 citations

Quantum linear Boltzmann equation

Bassano Vacchini, Klaus Hornberger

arXiv:0904.3911Physics ReportsJun 12, 2009133 citations

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