# Theoretical Physics

**13 November 2013**

**Time:**15:00 to 16:00

**Location:**EC Stoner SR 8.62

Emilio Cobanera (Leiden, Netherlands)

Anyons in second quantization and the fractional Josephson effect

We introduce and describe in second quantization a family of particle species with unconventional (p=2,3,...) exclusion and (theta=2 pi/p) exchange statistics. We call these anyons Fock parafermions. They are the particles naturally associated to clock models in various dimensions and low energy effective descriptions of mesoscopically manipulated arrays of fractional topological insulators and/or quantum Hall bilayers. Creation, annihilation, and number operators for Fock parafermions are derived from and characterized in terms of the simpler concept of a Fock algebra. As a consequence, normal-ordering remains a well-defined operation, opening the way for developing anyonic diagrammatic perturbation theories. We show how the parafermions sought for topological quantum information processing appear pinned down to defects in lattice models with BEC condensation of multiplets of Fock parafermions, and show how to model an ``anyonicÂ¨ Josephson junction of Fock parafermions displaying a fractional Josephson effect with period depending on the statistical angle.

Based on arXiv:1307.6214

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