Heat Transport and Majorana Fermions in a Superconducting Dot-Wire System: An Exact Solution

Abstract

We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of all crossovers that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating crossovers. The two Bogoliubov-de Gennes (BdG) symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system.

Modeling and Estimation of Thermal Flows Based on Transport and Balance Equations

“…Here, we will extend the use of QB for the purpose of estimation in the considered infinite dimensional context. It is worth noting that, in lieu of searching for exact solutions of the flow equations (see, e.g., [12,13]), here we deal with the construction of boundary-output observers with guaranteed stability properties on the estimation error.…”