Vorträge in der Woche 12.12.2022 bis 18.12.2022

Donnerstag, 15.12.2022: Maximizing the electromagnetic chirality for metallic nanowires in the visible spectrum

Marvin Knöller (KIT - Karlsruhe Institute of Technology)

Electromagnetic chirality describes differences in the interaction of scattering objects with electromagnetic fields of different helicity. If the scattering behavior of an object with respect to incident waves of one helicity cannot be reproduced with incident fields of the opposite helicity, then the object is said to be electromagnetically chiral (em-chiral), otherwise it is called em-achiral. Em-chirality can be quantified by chirality measures that attain the value 0 for an em-achiral object and the value 1 for a maximally em-chiral object. We study a shape optimization problem, where the goal is to construct thin metallic nanowires that exhibit large measures of em-chirality at a given frequency. We present a gradient based optimization method, based on an asymptotic representation formula for approximating scattered fields due to thin metallic scattering objects. In the visible range, the metallic nanowires obtained by our optimization scheme, exceed the chirality values attained by traditional metallic helices.

Donnerstag, 15.12.2022: Decay of waves in gravitational solitons

Sharmila Gunasekaran (Fields Institute)

Gravitational solitons are globally stationary, horizonless asymptotically flat spacetimes with positive energy. I will address the stability of a particular family of solitons at the simplest level by investigating solutions to the linear wave equation. I will describe a methodology to prove that massless scalar waves in this family of soliton spacetimes cannot decay faster than inverse logarithmically in time. This slow decay can be attributed to the stable trapping of null geodesics and is suggestive of instability at the nonlinear level. This is joint work with Hari Kunduri.

Donnerstag, 15.12.2022: Weak Hopf algebras, matrix product operators and the classification of quantum phases of matter

Alberto Ruiz de Alarcon (Complutense University of Madrid)

Understanding the entanglement structure of quantum many-body systems is one of the driving forces in theoretical physics in recent decades. In particular, this has led to the use of tensor networks, the central objects of this talk, which are models described in terms of local tensors contracted along an underlying graph structure. We will first establish how representations of well-known algebraic structures, such as weak Hopf algebras, give rise to one-dimensional tensor networks exhibiting exotic properties. In addition, we will provide a dictionary between the algebraic properties and those of the corresponding tensors, which allows very interesting results to be transferred between these two configurations. As applications, we will classify a wide variety of quantum mixed states via shallow circuits of quantum channels. Also, we will demonstrate the power of our framework by constructing a large class of topological states and by providing promising tools for the study of topological phases.

Donnerstag, 15.12.2022: A spectral gap in the t<1, spin-1 Motzkin chain

Radu Andrei (ETH Zürich)

In recent years, the weighted Motzkin spin chain has gained popularity due to its ground-state entanglement entropy properties, when its area weight is t>1. In the complementary regime t<1, it has been conjectured to have a finite spectral gap in the thermodynamic limit, which is a necessary condition for topological properties that have been suggested by previous studies. In this talk, I will give a brief overview of the model, as well as the special properties that motivated its introduction. Next, I will outline a proof of the gap conjecture in the case of spin-1 and t<1. After introducing the finite-size criterion formulated for this problem, I will describe its application to the Motzkin Hamiltonian, through a two-part ground-state approximation scheme. Finally, I will discuss further research directions for the spin-1 model, as well as possible approaches to the higher spin question.

Freitag, 16.12.2022: Krichevers erzeugende Funktion der Witham-Gleichung

Jonas Ziefle (Uni Tübingen)