Exact scattering matrix of graphs in magnetic field and quantum noise
- Department of Mathematical Science, City University London, Northampton Square, London EC1V 0HB (United Kingdom)
- Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica dell’Università di Pisa, Largo Pontecorvo 3, 56127 Pisa (Italy)
- LAPTh, Laboratoire d’Annecy-le-Vieux de Physique Théorique, CNRS, Université de Savoie, BP 110, 74941 Annecy-le-Vieux Cedex (France)
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 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.
- OSTI ID:
- 22306030
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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