The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A semiclassical extension of this approach to quantum many-body systems was suggested by Uehling and Uhlenbeck in 1933 for both Fermi and Bose statistics, and many further generalization of this approach are known as the Boltzmann-Uehling-Uhlenbeck (BUU) equations. Here I suggest a pure quantum version of the BUU type of equations, which is mathematically equivalent to a generalized Time-Dependent Density Functional Theory extended to superfluid systems.
The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A semiclassical extension of this approach to quantum many-body systems was suggested by Uehling and Uhlenbeck in 1933 for both Fermi and Bose statistics, and many further developments of this approach are known as the Boltzmann-Uehling-Uhlenbeck (BUU) equations. Here I introduce a pure quantum version of the BUU type of equations, which is mathematically equivalent to a generalized time-dependent density functional theory extended to superfluid systems. As expected, during nonequilibrium processes the quantum Boltzmann one-body entropy increases during evolution.
Abstract Ladder summation techniques are applied to the recently developed c‐number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T‐matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell‐Boltzmann statistics), the T‐matrix introduced coincides with the usual T‐matrix of conventional two‐body scattering theory in free space. In low‐temperature Fermi systems, the T‐matrix differs from the reaction matrix of the Brueckner‐Goldstone theory because the “healing” property of the two‐body wave function does not obtain.