On Discrete Models of the Quantum Boltzmann Equation

Localization of plane waves in low temperature regime

“…We shall also illustrate the non-Fermi liquid (NFL) behavior near possible QCPs by our discrete kinetic model which can deal with NFL by tuning a Pauli-blocking parameter (say, σ or B) (cf. Vedenyapin, et al [15]; Chu [11]). The effects of electron-electron interactions and disorder for the possible route to localization in 2D are clearly demonstrated here.…”

“…where (k, l) are admissible sets of collisions, i ∈ Λ ={1, · · · , p}, and the summation is taken over all j, k, l ∈ Λ, where A ij kl are nonnegative constants satisfying [11,[15][16] …”

“…Collisions which satisfy the conservation and reversibility conditions which have been stated above are defined admissible collisions. Now, with theÜhling-Uhlenbeck collision term [15] in equation (1),…”

“…Considering binary collision only, from equation (1), the model of (discrete) quantum Boltzmann equation for dilute atomic (Bose and Fermi) gases [15] is then a system of 2n semilinear partial differential equations of the hyperbolic type:…”

“…We must remind the readers that the derivation of present quantum kinetic approach was based on the binary encounter of a system of particles. Once the mean free path and the centre of mass coordinate system were introduced (especially when the effective, admissible collision and the microreversibility which neglects the history and the correlations when particles traverse in phase space [11,15] were presumed) the randomness and disorder might occur although they were illustrated implicitly.…”