Difference Boltzmann Equation
  Difference Boltzmann Equation is derived 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 Boltzmann Equation transforms into the classical Boltzmann Equation in the limit, where distribution function varies little in and 
Alexandr A. Klyukanov
math-ph math.MP quant-ph