Difference Kinetic Equations in Many-Particle Physics
  Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors is used as the second quantization basis allowing introducing the positively definite distribution function. It is obtained that inhomogeneous system is described by numbers of particles at quantized positions with quantized momenta. Difference Kinetic Equation for distribution function transforms into the classical Boltzmann Equation in the limit, where expectation value of particles number varies little. 
Alexandr A. Klyukanov
quant-ph cond-mat.stat-mech