arXiv subjects

Richard Dengler

Publications and source records attributed to Richard Dengler.

5 recordsLinked to original sources

arXiv2026

The electromagnetic stress tensor in cubic crystals and amorphous solids

The electromagnetic vacuum stress tensor in a system consisting of classical point-like atoms on a cubic lattice is derived directly from the electric field and, alternatively, using the known more phenomenological formula involving the (usually unknown) derivative of the dielectric tensor. The results agree. The stress tensor contains a nontrivial constant and therefore cannot be obtained from macroscopic electrodynamics alone. A system consisting of a mosaic of randomly oriented grains of a cubic crystal is used as a model of an amorphous solid. The electromagnetic stress tensor in this system is deduced by averaging the corresponding quantity in a cubic crystal over all orientations. Two components remain: the component in the direction of the electric field and the component perpendicular to it. The transverse component agrees with the analogous quantity for liquids derived by Peierls in an entirely different way.

cond-mat.mtrl-sci↗

arXiv2026

The continuum limit of the Poland-Scheraga DNA denaturation model

Using a field theory equivalent to a lattice version of the Poland-Scheraga model, the phase diagram for a long DNA molecule is derived in closed form. For the generalized model with excluded-volume interactions a one-loop renormalization group calculation shows that there are two stable fixed points. At both fixed points, the excluded-volume effect plays a role. At the fixed point reached when the original excluded-volume effect is weak, the phase transition is continuous. At the other fixed point, the phase transition is first order.

cond-mat.soft↗

arXiv2025

A solvable microscopic model for the propagation of light in a dielectric medium

Maxwell's equations resemble Schrödinger's equation in that an exact solution for a well-defined model delivers all physically relevant details. Solvable microscopic electrodynamic models, however, are rare. An exception is the discrete dipole approximation (DDA), which models a medium as a lattice of point dipoles. We use a regularized DDA variant to examine mechanical and electromagnetic momentum of light signals in such a medium in detail. The results agree in essential parts with that of the theory of R. Peierls from 1976.

physics.class-ph↗

arXiv2022

A universality class for RNA-like polymers and double polymers

We examine the statistics of conformations of a linear polymer in a solvent. The polymer is allowed to form double polymers. We closely follow a classical technique to derive a field theory for the problem from an $O\left(n\right)$ symmetric spin model. The field theory is a model for RNA or DNA with constant binding energy per monomer. It is shown that there is a stable renormalization group fixed point, at which the double polymer decouples from the single-strand polymer and becomes a branched polymer of the conventional type with a three-point interaction. To reach this fixed point, at least one parameter must be adjusted. The critical dimension is eight. Fisher-renormalization, equation of state and critical exponents are reproduced in this limit. The single-strand polymer depends on the double-strand polymer and disappears at the critical point, but has its own critical exponents.

cond-mat.soft↗

arXiv2022

The ABC of scale invariance at the level of action integrals, and the software tool Kanon

A central and common aspect of renormalizable field theories is scale invariance of the action integral. This note introduces the software tool \emph{Kanon}, which allows to assemble arbitrary action integrals interactively, and to determine their critical dimension and scale invariance. The tool contains more than 60 well-known models with comments and references to the literature.

cond-mat.soft↗