Quantum Kinetic Theory of Plasmas

TL;DR

This paper reviews the extension of classical plasma kinetic theory to quantum regimes, incorporating effects like spin, exchange, Landau quantization, and relativistic phenomena, including pair creation at extreme fields.

Contribution

It provides a comprehensive overview of quantum kinetic models for plasmas, covering non-relativistic, relativistic, and fully quantum relativistic theories with applications.

Findings

Extension of Vlasov to Wigner-Moyal equation for quantum plasmas

Inclusion of spin, exchange, and Landau quantization effects

Analysis of relativistic and quantum relativistic regimes, including pair creation

Abstract

As is well-known, for plasmas of high density and modest temperature, the classical kinetic theory needs to be extended. Such extensions can be based on the Schr\"odinger Hamiltonian, applying a Wigner transform of the density matrix, in which case the Vlasov equation is replaced by the celebrated Wigner-Moyal equation. Extending the treatment to more complicated models, we investigate aspects such as spin dynamics (based on the Pauli Hamiltonian), exchange effects (using the Hartree-Fock approximation), Landau quantization, and quantum relativistic theory. In the relativistic theory we first study cases where the field strength is well beyond Schwingers critical field. Both weakly relativistic theory (gamma factors close to unity) and strongly relativistic theory are investigated, using assumptions that allow for a separation of electron and positron states. Finally, we study the Dirac-Heisenberg-Wigner (DHW) formalism, which is a fully quantum relativistic theory, allowing for field strengths of the order of the Schwinger critical field or even larger. As a result, the quantum kinetic theory is extended to cover phenomena such as Zitterbewegung and electron-positron pair creation. While the focus of this review is on the quantum kinetic models, we illustrate the theories with various applications throughout the manuscript.