arXiv subjects

David Müller

Publications and source records attributed to David Müller.

39 records · Page 3Linked to original sources

arXiv2016

Simulating collisions of thick nuclei in the color glass condensate framework

We present our work on the simulation of the early stages of heavy-ion collisions with finite longitudinal thickness in the laboratory frame in 3+1 dimensions. In particular we study the effects of nuclear thickness on the production of a glasma state in the McLerran-Venugopalan model within the color glass condensate framework. A finite thickness enables us to describe nuclei at lower energies, but forces us to abandon boost-invariance. As a consequence, random classical color sources within the nuclei have to be included in the simulation, which is achieved by using the colored particle-in-cell (CPIC) method. We show that the description in the laboratory frame agrees with boost-invariant approaches as a limiting case. Furthermore we investigate collisions beyond boost-invariance, in particular the pressure anisotropy in the glasma.

hep-ph↗

arXiv2016

Minimax principles, Hardy-Dirac inequalities and operator cores for two and three dimensional Coulomb-Dirac operators

For $n\in\{2,3\}$ we prove minimax characterisations of eigenvalues in the gap of the $n$ dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value $1/(4-n)$. This result implies a so-called Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on $\mathsf{C}_{0}^{\infty}(\mathbb{R}^n\setminus\{0\};\mathbb{C}^{2(n-1)})$, as long as the coupling constant does not exceed $1/(4-n)$. We also find an explicit description of an operator core of this operator.

math-ph↗

arXiv2014

On the minimax principle for Coulomb-Dirac operators

Let q and v be symmetric sesquilinear forms such that v is a form perturbation of q. Then we can associate a unique self-adjoint operator B to q+ v. Assuming that B has a gap (a, b) in the essential spectrum, we prove a minimax principle for the eigenvalues of B in (a, b) using a suitable orthogonal decomposition of the domain of q. This allows us to justify two minimax characterisations of eigenvalues in the gap of three-dimensional Dirac operators with electrostatic potentials having strong Coulomb singularities.

math-ph↗