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Quantum Boltzmann Transport Equation in the Presence of Interactions; Application to the 2D Hall Effect
Author(s) -
van Vliet C. M.,
Samson Th.
Publication year - 1994
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221850215
Subject(s) - diagonal , boltzmann equation , boltzmann constant , quantum hall effect , hierarchy , kinetic energy , quantum , physics , fractional quantum hall effect , mathematical physics , mathematics , quantum mechanics , electron , quantum spin hall effect , geometry , economics , market economy
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 [ℒh in ] N c ζ † c ζ , N = 0, 1,…, ∞, where ℒ in 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.