Quantum Kinetic Theory and Applications

M. Bönitz

Jens Zamanian, M. Marklund, Gert Brodin

Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from being a formulation of principal interest, such scalar quantum kinetic equation makes the comparison to classical kinetic theory straightforward, and lends itself naturally to currently available numerical Vlasov and Boltzmann schemes. Moreover, while the quasi-distribution is a Wigner function in regular phase space, it is given by a Q-function in spin space. As such, nonlinear and dynamical quantum plasma problems are readily handled. Moreover, the issue of gauge invariance is treated. Applications (e.g. ultra-dense laser compressed targets and their diagnostics), possible extensions, and future improvements of the presented quantum statistical model are discussed.

Shile Chen, Shuzhe Shi, Pengfei Zhuang

In this work, we construct one-dimensional interacting lattice spinor theories with discretization in momentum space. We focus on strongly interacting Schwinger and Nambu--Jona-Lasinio models and perform ab-initio calculation of their single-particle and two-particle momentum distribution functions at finite temperature. We observe, at low temperature, high-momentum tail in single-particle and two particle distribution which reveals relative momentum in fermion-antifermion boundstates, as well as quasi-free spinor gases behavior at high temperature. The non-vanishing connected four-momentum function reveals the quantum coherence in momentum space under thermal equilibrium of the system and indicate the single particle correlation would remember more microscopic details within a thermal system. Overall, for a high-enough temperature at which the thermal kinetic energy comparable with the interaction, we observe that the two-particle correlation is subdominant compared to the single particle distributions, which indicates the applicability of kinetic theory.

A. N. Temchin

Sergiy F. Lyagushyn, Alexander I. Sokolovsky, Volodymyr V. Yarlik +1 more

Kinetics of a quantum system immersed in an equilibrium medium and completely described by its statistical operator is investigated. The case of a separable interaction is considered in details. A concept of the effective Hamilton operator of the system is discussed. The kinetic equation for a point particle in a spatially uniform external field placed in a medium of point particles is obtained in terms of the Wigner distribution function of a particle. The kinetic equation is applicable for strong spatially inhomogeneous (localized) states of the particle and strong external field. The elaborated theory is used also for a system of two-level emitters and photons interacting with an equilibrium phonon medium. The kinetic equation for the statistical operator of the system of the emitters and photons that describes the effect of emitter motion on the super radiance phenomenon is obtained.