Majorana zero modes are central to the pursuit of fault-tolerant topological quantum computation. Our work focuses on a particularly promising system: a chiral ferromagnet hosting a magnetic skyrmion coupled to a superconducting film containing a superconducting vortex. Such skyrmion-vortex pairs have recently been realized experimentally and are theorized to harbor localized Majorana states. We present a comprehensive theoretical analysis of the low-energy quasiparticle bound states in these heterostructures. Extending previous studies, we develop an analytical framework for the Majorana wavefunctions as well as the wavefunctions and spectrum of other lowlying states within a Bogoliubov-de Gennes approach. The derived analytical results show excellent agreement with numerical simulations. The report is based on the work arXiv:2605.06828.

In a 2009 paper "Turbulence in Integrable Systems", Zakharov discussed weakly integrable systems which have an infinite, but not sufficient for the full integrability, number of invariants. An example is KP1 for which Zakharov wrote a kinetic equation describing wave turbulence, and which has an infinite number of invariants and thermodynamic equilibria. In the present talk, I will report on numerical simulations of this kinetic equation, in particular, a kinetic instability of a wavepacket, and relaxation to equilibrium characterised by a condensation into low-frequency waves.

Nonlocal phase-coherent transport via Majorana bound states, so-called teleportation, requires Coulomb blockade to suppress local Andreev reflection. We show that dissipation can replace the need for Coulomb blockade. We study a Kitaev chain coupled to a Markovian bath and identify a regime where the magnitude of nonlocal conductance contribution reach the local one. In this regime, the lowest-energy subspace is maximally mixed, reminiscent of a directly grounded nontrivial topological superconductor. Phase coherence is confirmed by Aharonov-Bohm oscillations. Our results establish dissipation as a tool for controlling quantum teleportation in Majorana systems.