https://xkcd.com/356/

https://xkcd.com/356/

Welcome to my pages

I am doing some research on quantum materials, which is probably the best opportunity to study a wide range of quantum mechanical phenomena, integrating many distinct concepts from different areas of theoretical physics. Be it compound-nuclear reactions or cosmology, quantum electrodynamics or classical physics, the underlying theoretical tools have found their way to the description of quantum materials, sometimes in an unexpected manner.

The fascination of many-body quantum theory lives from a few key ingredients. Most important: Identical particles, in particular many of them. Due to their non-distinguishability, they behave completely different, unexepected, and often counter-intuitive. This has surfaced already in the 19th century, most prominently in the form of the so-called mixing entropy, an increase in entropy when mixing two homogeneous, single-phase materials which is absent when these materials are identical. This absence is a purely quantum-mechanical phenomenon, also known as the Gibbs paradoxon, named after Josiah Willard Gibbs (1839–1903).

Also any form of magnetism emerges from quantum mechanics and cannot be understood classically. The Bohr-van-Leeuwen theorem tells us that if we require that electrodynamic processes in nature are invariant with respect to local U(1) gauge transformations (like Maxwell’s equations are), magnetism cannot exist within the framework of classical statistical mechanics. This applies to the longest-known form of magnetism, a ferromagnet, as well as to its modern cousins.

Frustrated magnetism: route to new exotic phases

We concentrate our research on frustrated magnetism, that is magnetic systems «not knowing what to do», given the highly (quasi-)degenerate ground state manifold and low-energy excitations inherent to these. An assembly of interacting spin S = 1/2 objects is prototypical, having the advantage of the possibility to explore these systems numerically on today’s computers. This is absolutely necessary, because traditional theoretical methods simply fail to give a decent physical understanding and at best can only simulate certain properties. We advance the numerical methods to describe frustrated magnets in a systematic way, nonetheless we use a variety of analytical tools to complement the numerical results in order to get a complete picture.

We work closely together with experimental physicists. Our goal is to advance the accurate numerical description of in particular magnetic and magnetocaloric measurements to give insight into these and to guide the experiments towards the discovery of new quantum phases. Over the last years we have implemented code to achieve this which is world-leading in the approximation-free evaluation of the corresponding partition functions and cumulants we use to express thermodynamic and magnetocaloric properties.

Excursion: hydrodynamic description of electron transport

Essentially unrelated to magnetism, we had a look at how we can contribute to the understanding of unusual transport properties in some ultrapure, layered metallic materials.

Conventionally, electronic transport is regarded as a dissipative process where electrons lose their phase coherence via momentum relaxing collisions when travelling through a conducting sample. The corresponding theoretical descriptions of electronic resistance are based on this assumption, typically regarding momentum conserving processes as well as boundary effects as unimportant. However Boltzmann’s fundamental transport equation does not exclude these momentum conserving processes at all, leaving room for a hydrodynamic theory of electronic resistance.

High-purity samples and the focused-ion beam technology make it possible to study such hydrodynamic effects experimentally. We support the experiments with a semiclassical theory of the electronic transport which can successfully describe the behavior of the resistance, in particular its dependence on the sample geometry. And we do this with materials having a lot of electrons, not with low-density conductors having just a few charge carriers like the obvious candidate graphene.