Ch.J. Calkoen

Crossover from dissipative to conservative behaviour in period-doubling systems

We investigate the crossover properties, between the conservative and dissipative limit, for period-doubling bifurcations in two-dimentional iterative maps; as a generic example we use the standard form of the Henon map. The approximants to the Feigenbaum constant δ lie on a universal crossover curve, which turns out to be non-monotonic. A similar curve is found for the scaling factor α. More generally, we discuss the crossover of the trajectory scaling function 1/ σ, and its properties in the conservative limit.

Crossover from dissipative to conservative systems

We investigate the crossover properties of period-doubling bifurcations for the standard form of the Henon map. The approximants to the Feigenbaum constant δ lie on a universal curve which, as a function of the jacobian B, shows a dip. The scaling function 1/σ(t, B), which is generalization of the corresponding Feigenbaum function for B = 0, tends to very large values at t = 14 for B → 1; Mackays scaling factor β is recovered from a different scaling function.

The volume viscosity of a massive neutrino gas

Abstract The volume viscosity of a gas of neutrinos with mass m is found to be equal to 2 −6 3 −2 π −1 G −2 ◑ 2 c 3 (kT) −5 (mc 2 ) 4 × log ( kT mc 2 ) for the case kT ⪢ mc 2 . Here G is the weak interaction constant.

Collision brackets in quantum kinetic theory: I. Energy-momentum-transfer reduction method

Abstract A new effective method for reducing collision brackets, i.e. matrix elements of the linearized collision operator, to a fivefold integral is presented. Collisional energy and momentum transfer are used as basic dynamical variables. The method covers classical and quantum statistics, and is applicable to non-relativistic as well as relativistic multicomponent systems.

Volume viscosity of lepton systems, including massive neutrinos

From relativistic kinetic theory, using the weak interaction Lagrangian, the volume viscosity is calculated for a gas consisting of leptons, including massive (anti-)neutrinos as a function of the temperature and the particle masses.

Collision brackets in quantum kinetic theory: II. Landau, degenerate Fermi, and Lorentz limits

Abstract The method for reducing collision brackets, developed in a previous paper, is applied to a hot classical plasma, a highly degenerate plasma, and a neutrino-nucleus system as a particular example of a Lorentz model. Various known results are rederived from a unified point of view, and generalized relativistically. In particular the quantum-mechanical Balescu-Guernsey-Lenard (BGL) bracket is studied and reduced to a twofold collision integral. With regards to degenerate systems, the method is shown to be superior to the standard phase-space decomposition (PSD) approximation to the extent that the first finite-temperature contribution, which may be substantial, is furnished correctly. For a statistically screened interaction this is corroborated by numerical calculation of the exact fourfold integral expression for the collision bracket, which appears to be well suited for integration by the Monte Carlo routine VEGAS.

The volume viscosity of a degenerate massive neutrino system

From the week interaction and the relativistic generalization of the quantum transport equation the volume viscosity of a degenerate massive neutrino gas is derived as a function of the density and the neutrino mass.

Volume viscosity of a massive neutrino gas

From the weak interaction Lagrangian and the principles of relativistic kinetic theory, the volume viscosity of a massive neutrino gas is calculated as a function of the temperature T and the neutrino mass m.

Collision brackets in quantum kinetic theory

It is shown that the collision bracket of the linearized quasiparticle Boltzmann equation can be reduced to a five-fold integral expression. It generalizes earlier work in so far that it accomodates an energy dependent effective mass and allows the calculation of transport coefficients for quasiparticle systems at finite temperature. As an example, the thermal conductivity of liquid 3He is calculated for a simple one-Landau parameter model for various pressures. The result, parametrized by a single reduced temperature, compares favourably with Greywalls experimental data.

Thermal conductivity of normal liquid3He at finite temperatures

Greywalls experimental data for the thermal conductivity of normal liquid3He are reanalyzed. The temperature dependence at various pressures seems consistent with a law of corresponding states in the sense that it can be described by a universal function of a reduced temperature. It is suggested that the appreciable dynamical screening of the scattering amplitude for the quasiparticles in3He is responsible for this behavior. For illustration the thermal conductivity is calculated at finite temperature for a class of screened interaction models to leading order in the screening parameter. Good agreement is found with experiment by fitting the single Landau parameterAa0.