Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation

Abstract

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 BoltzmannUehling-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 non-equilibrium processes the quantum Boltzmann one body entropy increases during evolution.

7 pages, 1 figure, Title changed, text has significant new material, new citations, published version

References in corpus (8)

• Momentum sharing in imbalanced Fermi systems
• Overview of Neutron-Proton Pairing
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Collision dynamics of two ${}^{238}$U atomic nuclei
• Mixed-Spin Pairing Condensates in Heavy Nuclei
• The time-dependent generator coordinate method in nuclear physics
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• New developments in fission studies within the time-dependent density functional theory framework
• Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization
• Non-Markovian character and irreversibility of real-time quantum many-body dynamics
• Examining the justification for the introduction of a fermion localization function
• A critical assessment of the current implementations of the Generator Coordinate Method
• Local Quantum Cooling for Large Fermi Systems with Pairing