Exact scattering matrix of graphs in magnetic field and quantum noise
arXiv:1401.4967 · doi:10.1063/1.4893354
Abstract
We consider arbitrary quantum wire networks modelled by finite, noncompact, connected quantum graphs in the presence of an external magnetic field. We find a general formula for the total scattering matrix of the network in terms of its local scattering properties and its metric structure. This is applied to a quantum ring with external edges. Connecting the external edges of the ring to heat reservoirs, we study the quantum transport on the graph in ambient magnetic field. We consider two types of dynamics on the ring: the free Schrödinger and the free massless Dirac equations. For each case, a detailed study of the thermal noise is performed analytically. Interestingly enough, in presence of a magnetic field, the standard linear Johnson-Nyquist law for the low temperature behaviour of the thermal noise becomes nonlinear. The precise regime of validity of this effect is discussed and a typical signature of the underlying dynamics is observed.
27 pages
References in corpus (7)
- Impurity and correlation effects on transport in one-dimensional quantum wires
- Quantum wires with magnetic fluxes
- Junctions of anyonic Luttinger wires
- Quantum Fields on Star Graphs
- Duality between normal and superconducting junctions of multiple quantum wires
- Renormalization group study of transport through a superconducting junction of multiple one-dimensional quantum wires
- Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances