arXiv subjects

Dietmar Herdt

Publications and source records attributed to Dietmar Herdt.

2 recordsLinked to original sources

arXiv2024

HYPERTILING -- a high performance Python library for the generation and visualization of hyperbolic lattices

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincaré disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.

physics.comp-ph↗

arXiv2022

Breitenlohner-Freedman bound on hyperbolic tilings

We establish how the Breitenlohner-Freedman (BF) bound is realized on tilings of two-dimensional Euclidean Anti-de Sitter space. For the continuum, the BF bound states that on Anti-de Sitter spaces, fluctuation modes remain stable for small negative mass-squared $m^2$. This follows from a real and positive total energy of the gravitational system. For finite cutoff $\varepsilon$, we solve the Klein-Gordon equation numerically on regular hyperbolic tilings. When $\varepsilon\to0$, we find that the continuum BF bound is approached in a manner independent of the tiling. We confirm these results via simulations of a hyperbolic electric circuit. Moreover, we propose a novel circuit including active elements that allows to further scan values of $m^2$ above the BF bound.

hep-th↗