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Exact scattering matrix of graphs in magnetic field and quantum noise

Caudrelier, V., Mintchev, M. & Ragoucy, E. (2014). Exact scattering matrix of graphs in magnetic field and quantum noise. Journal of Mathematical Physics, 55(8), article number 083524. doi: 10.1063/1.4893354


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 $N$ 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 Schr\"odinger 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.

Publication Type: Article
Additional Information: Copyright American Institute of Physics 2014
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
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