Relativistic Boltzmann-Vlasov Research Articles

Effects of magnetic field on the evolution of energy density fluctuations

We study the effects of a static and uniform magnetic field on the evolution of energy density fluctuations present in a medium. By numerically solving the relativistic Boltzmann-Vlasov equation within the relaxation time approximation, we explicitly show that magnetic fields can affect the characteristics of energy density fluctuations at the timescale the system achieves local thermodynamic equilibrium. A detailed momentum mode analysis of fluctuations reveals that a magnetic field increases the damping of mode oscillations, especially for the low momentum modes. This leads to a reduction in the ultraviolet (high momentum) cutoff of fluctuations and also slows down the dissipation of relatively low momentum fluctuation modes. We discuss the phenomenological implications of our study on various sources of fluctuations in relativistic heavy-ion collisions.

Modelling general-relativistic plasmas with collisionless moments and dissipative two-fluid magnetohydrodynamics

ABSTRACT Relativistic plasmas are central to the study of black hole accretion, jet physics, neutron star mergers, and compact object magnetospheres. Despite the need to accurately capture the dynamics of these plasmas and the implications for relativistic transients, their fluid modelling is typically done using a number of (overly) simplifying assumptions, which do not hold in general. This is especially true when the mean free path in the plasma is large compared to the system size, and kinetic effects start to become important. Going beyond common approaches used in the literature, we describe a fully relativistic covariant 14-moment based two-fluid system appropriate for the study of electron–ion or electron–positron plasmas. This generalized Israel-Stewart-like system of equations of motion is obtained directly from the relativistic Boltzmann–Vlasov equation. This new formulation can account for non-ideal effects, such as anisotropic pressures and heat fluxes, not present in previous formulations of two-fluid magnetohydrodynamics. We show that a relativistic two-fluid plasma can be recast as a single fluid coupled to electromagnetic fields with (potentially large) out-of-equilibrium corrections. We keep all electron degrees of freedom, which provide self-consistent evolution equations for electron temperature and momentum. The out-of-equilibrium corrections take the form of a collisional 14-moment closure previously described in the context of viscous single fluids. The equations outlined in this paper are able to capture the full two-fluid character of collisionless plasmas found in black hole accretion and flaring processes around compact objects, as well Braginskii-like two-fluid magnetohydrodynamics applicable to weakly collisional plasmas inside accretion discs.

Opinion formation with upper and lower bounds

We investigate the opinion formation with upper and lower bounds. We formulate the binary exchange of opinions between two individuals, and effects of the self-thinking and political party using the relativistic Boltzmann-Vlasov type equation with the randomly perturbed motion. The convergent form of the distribution function is determined by the balance between the cooling rate via the binary exchange of opinions between two individuals and the concentration of opinions by the political party, and heating rate via the self-thinking.

Damping of electromagnetic waves due to electron-positron pair production

The problem of the back reaction during the process of electron-positron pair production by a circularly polarized electromagnetic wave propagating in a plasma is investigated. A model based on the relativistic Boltzmann-Vlasov equation with a source term representing the Schwinger formula for the pair creation rate is used. The damping of the wave, the nonlinear up-shift of its frequency due to the plasma density increase, and the effect of the damping on the wave polarization and on the background plasma acceleration are investigated as a function of the wave amplitude.

Gauge-Invariant Relativistic Wigner Functions in External Electromagnetic Fields

On the basis of the Hamiltonian form of the Klein-Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gaugeinvariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off-diagonal elements correspond to cross-densities in phase-space. The system of coupled transport equations has been derived in case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the general relativistic quantum Boltzmann-Vlasov equation (RQBVE) is discussed. In the non-relativistic quantum Boltzmann-Vlasov equation (RQBVE) is discussed. In the non-relativistic limit (p/mc→0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged position and negaton densities. In the classical limit (þ→0) two relativistic Boltzmann-Vlasov equations result for the diagonal position and negaton densities. Even though the Planck constant þ is absent in the latter equations, the real part of the positon-negaton cross density does not vanish.

Gauge-invariant relativistic Wigner functions

On the basis of the Hamiltonian form of the Klein–Gordon equation for a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2 × 2W igner matrix has been constructed whose diagonal elements describe positive and negative charge densities and whose off-diagonal elements correspond to cross-densities in phase space. The system of coupled transport equations has been derived in the case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic an dt he classical limits of the relativistic quantum Boltzmann–Vlasov equation are discussed. In the nonrelativistic limit (p/mc → 0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities. In the classical limit (¯ → 0) two relativistic Boltzmann–Vlasov equations result for the diagonal positon and negaton

PAIR PRODUCTION IN A STRONG ELECTRIC FIELD: AN INITIAL VALUE PROBLEM IN QUANTUM FIELD THEORY

We review recent achievements in the solution of the initial-value problem for quantum backreaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining backreaction has to do with applications to theoretical models of production of the quark-gluon plasma though we here address practicable solutions for backreaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features like plasma oscillations and plateaus in the current appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.

Fermion pair production in a strong electric field.

The initial-value problem for the quantum back reaction in spinor QED is formulated and solved in the semiclassical mean-field approximation for a homogeneous but time-dependent electric field $E(t)$. We apply the method of adiabatic regularization to the Dirac equation in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. We solve this system in 1+1 dimensions numerically and compare the solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauliblocking factor. This model reproduces very well the time behavior of the electric field and the creation rate of ${e}^{+}{e}^{\ensuremath{-}}$ pairs of the semiclassical calculation.

Pair production in a strong electric field

We investigate the mechanism of pair creation in scalar QED from spatially homogeneous strong electric fields in 1+1 dimensions. Solution of the semiclassical field equations shows particle creation followed by plasma oscillations. We compare our results with a model based on a relativistic Boltzmann-Vlasov equation with a pair-creation source term related to the Schwinger mechanism. The time evolution of the electric field and the current obtained from the Boltzmann-Vlasov model is surprisingly similar to that found in the semiclassical calculation.

Dilepton production from a nonequilibrium quark-gluon plasma in ultrarelativistic nucleus-nucleus collisions.

Dilepton production from a nonequilibrium quark-gluon plasma produced in ultrarelativistic nucleus-nucleus collisions is studied, based on the flux-tube model which has been formulated in terms of a model relativistic Boltzmann-Vlasov equation with a boost-invariant particle source term. This model kinetic equation is solved with the collision term in the relaxation-time approximation. In the collisionless limit, the solution of the kinetic equation becomes oscillatory, indicating the spontaneous excitation of the plasma oscillation. We study how such a nonequilibrium evolution of the system is reflected in the dilepton spectrum. It is shown that the dileptons emitted during such a nonequilibrium stage of matter evolution does not necessarily lead to a spectrum which interpolates smoothly the spectrum from thermal emission and that from the Drell-Yan mechanism. Our results show, on the contrary, that the dilepton spectrum is softened significantly in the absence of thermalization. {ital M}{sub {ital T}} scaling, which is expected in scaling one-dimensional hydrodynamic evolution, is also broken due to the anisotropy in the phase-space distribution of quarks.

Transverse modes of a relativistic quantum plasma

The dispersion relation for long-wavelength transverse plasma weves propagating in a one-component relativistic quantum plasma is derived from the relativistic Boltzmann-Vlasov equation. The result is consistent with the one obtained from quantum electrodynamics by the method of dielectric response, but at variance with hydrodynamical calculations. The discrepancy is explained by making a distinction between collective and collision dominated plasmas.