# What becomes of vortices when they grow giant?

### APA

Penin, A. (2023). What becomes of vortices when they grow giant?. Perimeter Institute. https://pirsa.org/23110048

### MLA

Penin, Alexander. What becomes of vortices when they grow giant?. Perimeter Institute, Nov. 06, 2023, https://pirsa.org/23110048

### BibTex

@misc{ pirsa_PIRSA:23110048, doi = {10.48660/23110048}, url = {https://pirsa.org/23110048}, author = {Penin, Alexander}, keywords = {Particle Physics}, language = {en}, title = {What becomes of vortices when they grow giant?}, publisher = {Perimeter Institute}, year = {2023}, month = {nov}, note = {PIRSA:23110048 see, \url{https://pirsa.org}} }

Alexander Penin University of Alberta

## Abstract

Quantum vortices are two-dimensional solitons which carry a topological charge - the first Chern number n. They play a crucial role in many physical concepts from cosmic strings to mirror symmetry and dualities of supersymmetric models. When n grows the vortices become giant. The giant vortices are observed experimentally in a variety of quantum systems. Thus, it is quite appealing to identify their characteristic features and universal properties, which is quite a challenging mathematical problem. Though the nonlinear vortex equations may look deceptively simple, their analytic solution is not available. In this talk I demonstrate how by borrowing the asymptotic methods of fluid dynamics such a solution can be found in the large-n limit. I then construct a systematic expansion in inverse powers of the topological charge about this asymptotic solution which works amazingly well all the way down to the elementary vortex with n=1. I use this result to study the Majorana zero modes bound to giant vortices. The resulting local density of states has a number of features which give remarkable signatures for an experimental observation of the "Majorana fermions" in two dimensions.

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