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We study vacuum polarization due to strong fields, in the presence of an electron-positron plasma. For this purpose, we expand quantum kinetic equations using weak fields and slow temporal scales as expansion parameters. It is demonstrated that the evolution of the Dirac field can be described by classical-like distribution functions for electrons and positrons, which are weakly coupled through quantum interactions. Furthermore, we deduce that these coupling terms give rise to well-known expressions for vacuum polarization, in addition to quantum modifications proportional to the content of real particles. Depending on the initial plasma density, the dominant quantum corrections to classical evolution may arise from real particle couplings or from the vacuum polarization associated with virtual particles. The implications of our results are discussed.

For many purposes, classical plasma dynamics models can work surprisingly well, even for strong electromagnetic fields, approaching the Schwinger critical fields, and high frequencies, approaching the Compton frequency. However, the applicability of classical models tends to depend rather sensitively on the details of the problem. In the present paper, we study the specific case of plasma oscillations to draw a line between the classical and quantum relativistic regimes. Due to the field geometry of study, mechanisms like radiation reaction and Breit-Wheeler pair production, which tend to be important for electromagnetic fields, are rather effectively suppressed. Moreover, we find that the polarization current due to the electron spin is generally negligible for frequencies below the Compton frequency, compared with the free current, whose magnitude is well-approximated by the classical Vlasov theory. However, we show that pair creation due to the Schwinger mechanism can sometimes be important for surprisingly modest field strengths, of the order of 10% of the critical field or even smaller. A rough guideline for when the classical Vlasov theory can be applied is given.

The plasma physics community mourns the loss of Professor Fernando Haas, a distinguished Brazilian physicist, who passed away on December 2, 2024. For the last 25 years, Fernando was a highly active researcher in the field of theoretical quantum plasma physics, where he was recognized as an authority by his colleagues.

We study the transition from classical radiation reaction, described by the Landau-Lifshitz model, to the quantum mechanical regime. The plasma is subject to a circularly polarized field where the self-consistent plasma current is the source of the electromagnetic field through Ampere's law. The radiation reaction implies wave energy loss, frequency up-conversion, and a modified distribution function. Increasing the value of the quantum χ-parameter, the quantum results gradually differ from the classical ones. Moreover, the deviation between models also depends on the plasma parameters, including density and temperature. We discuss the implications of our findings.

We use a recently developed a kinetic model derived from the Dirac equation to study electromagnetic wave propagation in superstrong magnetic fields, such as in magnetars, where relativistic Landau quantization is prominent. The leading contribution to the conductivity tensor in such a plasma is calculated. It is found that the electron Hall current has an anomalous contribution, in the quantum relativistic regime, where the effective particle energy has a significant contribution from the diamagnetic and Zeeman energy. As a result, a new quantum resonance frequency appears, and the dispersion relation for the left- and right-hand polarized modes are strongly modified for long and moderate wavelengths. The implications for magnetar physics are discussed.

In this paper, a phase-space description of electron-positron pair-creation will be applied, based on a Wigner transformation of the Klein-Gordon equation. The resulting theory is similar in many respects to the equations from the Dirac-Heisenberg-Wigner formalism. However, in the former case, all physics related to particle spin is neglected. In the present paper we compare the pair-production rate in vacuum and plasmas, with and without spin effects, in order to evaluate the accuracy and applicability of the spinless approximation. It is found that for modest frequencies of the electromagnetic field, the pair production rate of the Klein-Gordon theory is a good approximation to the Dirac theory, provided the matter density is small enough for Pauli blocking to be neglected, and a factor of two related to the difference in the vacuum energy density is compensated for.  

Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as Schwinger pair creation are complemented by classical plasma nonlinearities. In this work we use the Dirac-Heisenberg-Wigner formalism to study the interplay between classical and quantum mechanical mechanisms in the regime of ultrastrong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined. Finally, comparisons with competing mechanisms such as radiation reaction and Breit-Wheeler pair production are made.

We study the contribution from the electron spin to the ponderomotive force, using a quantum kinetic model, including the spin-orbit correction. Specifically, we derive an analytical expression for the ponderomotive force, applicable for electrostatic waves propagating parallel to an external magnetic field. To evaluate the expression, we focus on the case of Langmuir waves and on the case of the spin resonance wave mode, where the classical and spin contributions to the ponderomotive force are compared. Somewhat surprisingly, depending on the parameter regime, we find that the spin contribution to the ponderomotive force may dominate for the Langmuir wave, whereas the classical contribution can dominate for the spin resonance mode.

We study the evolution of electrostatic plasma waves, using the relativistic Vlasov equation extended by the Landau-Lifshitz radiation reaction, accounting for the back-reaction due to the emission of single particle Larmor radiation. In particular, the Langmuir wave damping is calculated as a function of wave number, initial temperature, and initial electric field amplitude. Moreover, the background distribution function loses energy in the process, and we calculate the cooling rate as a function of initial temperature and initial wave amplitude. Finally, we investigate how the relative magnitude of wave damping and background cooling varies with the initial parameters. In particular, it is found that the relative contribution to the energy loss associated with background cooling decreases slowly with the initial wave amplitude.

We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac-Heisenberg-Wigner formalism. The vacuum contribution to the physical observables leads to ultraviolet divergences, which are removed by a charge renormalization. The remaining vacuum contribution is small and is in agreement with previously derived expressions for the time-dependent vacuum polarization. The main new feature of the theory is a damping mechanism similar to Landau damping, but where the plasmon energy gives rise to creation of electron-positron pairs. The dependence of the damping rate (pair-creation rate) on the wavenumber, temperature, and density is analyzed. Finally, the analytical results of linearized theory are compared with numerical solutions.