We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin- particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 2 spin-density ('Wigner') matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the thermal (Fermi–Dirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin- particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 2 spin-density ('Wigner') matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the thermal (Fermi–Dirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.

arXiv:1411.2576Journal of Physics A Mathematical and TheoreticalFeb 10, 20152 citations

Kinetics of dense matter: Correlations and memory

V. G. Morozov

A link between correlation contributions to kinetic equations for dense quantum systems and the energy conservation is considered. In order that the energy be conserved by an approximate collision integral, the one-particle density matrix and the mean interaction energy are treated as independent state parameters. It is shown how the density operator method can be used to derive non-Markovian kinetic equations including the correlation effect associated with the energy conservation. A quantum generalization of the Enskog theory is discussed.A link between correlation contributions to kinetic equations for dense quantum systems and the energy conservation is considered. In order that the energy be conserved by an approximate collision integral, the one-particle density matrix and the mean interaction energy are treated as independent state parameters. It is shown how the density operator method can be used to derive non-Markovian kinetic equations including the correlation effect associated with the energy conservation. A quantum generalization of the Enskog theory is discussed.

Physics of Particles and NucleiNov 22, 20080 citations

Basic Quantum Kinetic Equations

Springer eBooksDec 9, 20070 citations

Quantum kinetic equations

William C. Schieve, Lawrence Paul Horwitz

Cambridge University Press eBooksApr 16, 20090 citations

Memory effects and conservation laws in the quantum kinetic evolution of a dilute Bose gas

Satyan Bhongale, R. Walser, Murray Holland

We derive a non-Markovian generalization to the quantum kinetic theory described by Walser et al. [Phys. Rev. A 59, 3878 (1999)] in the absence of a condensed fraction for temperatures above the Bose-Einstein condensation temperature i.e., $T>{T}_{c}.$ Within this framework, quasiparticle damping arises naturally due the finite duration of a binary collision and it leads to a systematic Markov approximation from the non-Markovian Born theory. Such a self-consistent theory conserves the total energy to second order in the interaction strength. By introducing an improved damping function, we demonstrate global energy conservation at the order of the perturbation theory. Finally, we apply this kinetic theory to a simple model of an inhomogeneous Bose gas that is confined in a spherical box. By studying numerically the real-time quantum evolution towards equilibrium, we obtain damping rates and frequencies of the collective modes and illustrate the emergence of differing time scales for correlation and relaxation.We derive a non-Markovian generalization to the quantum kinetic theory described by Walser et al. [Phys. Rev. A 59, 3878 (1999)] in the absence of a condensed fraction for temperatures above the Bose-Einstein condensation temperature i.e., $T>{T}_{c}.$ Within this framework, quasiparticle damping arises naturally due the finite duration of a binary collision and it leads to a systematic Markov approximation from the non-Markovian Born theory. Such a self-consistent theory conserves the total energy to second order in the interaction strength. By introducing an improved damping function, we demonstrate global energy conservation at the order of the perturbation theory. Finally, we apply this kinetic theory to a simple model of an inhomogeneous Bose gas that is confined in a spherical box. By studying numerically the real-time quantum evolution towards equilibrium, we obtain damping rates and frequencies of the collective modes and illustrate the emergence of differing time scales for correlation and relaxation.

arXiv:cond-mat/0203415Physical Review AOct 25, 200213 citations

T>{T}_{c}.

Within this framework, quasiparticle damping arises naturally due the finite duration of a binary collision and it leads to a systematic Markov approximation from the non-Markovian Born theory. Such a self-consistent theory conserves the total energy to second order in the interaction strength. By introducing an improved damping function, we demonstrate global energy conservation at the order of the perturbation theory. Finally, we apply this kinetic theory to a simple model of an inhomogeneous Bose gas that is confined in a spherical box. By studying numerically the real-time quantum evolution towards equilibrium, we obtain damping rates and frequencies of the collective modes and illustrate the emergence of differing time scales for correlation and relaxation.