Jeremiah Birrell

Compact ultradense matter impactors.

We study interactions of meteorlike compact ultradense objects (CUDO), having nuclear or greater density, with Earth and other rocky bodies in the Solar System as a possible source of information about novel forms of matter. We study the energy loss in CUDO puncture of the body and discuss differences between regular matter and CUDO impacts.

Relic neutrino freeze-out: Dependence on natural constants

Analysis of cosmic microwave background radiation fluctuations favors an effective number of neutrinos, Nν > 3. This motivates a reinvestigation of the neutrino freeze-out process. Here we characterize the dependence of Nν on the Standard Model (SM) parameters that govern neutrino freeze-out. We show that Nν depends on a combination η of several natural constants characterizing the relative strength of weak interaction processes in the early Universe and on the Weinberg angle sin 2 θW. We determine numerically the dependence Nν(η,sin 2 θW) and discuss these results. The extensive numerical computations are made possible by two novel numerical procedures: a spectral method Boltzmann equation solver adapted to allow for strong reheating and emergent chemical non-equilibrium, and a method to evaluate Boltzmann equation collision integrals that generates a smooth integrand.

The transition from ergodic to explosive behavior in a family of stochastic differential equations

We study a family of quadratic, possibly degenerate, stochastic differential equations in the plane, motivated by applications to turbulent transport of heavy particles. Using Lyapunov functions, Hormander’s hypoellipticity theorem, and geometric control theory, we find a critical parameter value α1=α2 such that when α2>α1 the system is ergodic and when α2<α1 solutions are not defined for all times.

Small Mass Limit of a Langevin Equation on a Manifold

We study damped geodesic motion of a particle of mass m on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as

Boltzmann equation solver adapted to emergent chemical non-equilibrium

{m \to 0}

Fugacity and Reheating of Primordial Neutrinos

m→0, its solutions converge to solutions of a limiting equation which includes a noise-induced drift term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.

Phase Space Homogenization of Noisy Hamiltonian Systems

Abstract The effective number of neutrinos, N eff , obtained from CMB fluctuations accounts for all effectively massless degrees of freedom present in the Universe, including but not limited to the three known neutrinos. Using a lattice-QCD derived QGP equation of state, we constrain the observed range of N eff in terms of the freeze-out of unknown degrees of freedom near to quark–gluon hadronization. We explore limits on the coupling of these particles, applying methods of kinetic theory, and discuss the implications of a connection between N eff and the QGP transformation for laboratory studies of QGP.

Proposal for resonant detection of relic massive neutrinos

We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T ( t ) and phase space occupation factor ? ( t ) . In this first paper we address (effectively) massless fermions and derive dynamical equations for T ( t ) and ? ( t ) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component ( e ? -annihilation).