| Kirchhoff's rule for quantum wires (1998) | |||||||||||
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| Kirchho Rule for Quantum Wires Kostrykin Lehrstuhl fur Lasertechnik Rheinisch Westfalische Technische Hochschule Aachen Steinbachstr Aachen Germany and Schradery Institut fur Theoretische Physik Freie Universitat Berlin Arnimallee Berlin Germany June this article formulate and discuss one particle quantum scattering theory arbitrary nite graph with open ends and where the Hamiltonian minus the Laplace operator with general boundary conditions the vertices This results scattering theory with channels The corresponding shell matrix formed the ection and transmission amplitudes for incoming plane waves energy explicitly given terms the boundary conditions and the lengths the internal lines shown unitary which may viewed the quantum version Kirchho law exhibit covariance and symmetry properties symmetric the boundary conditions are real Also there duality transformation the set boundary conditions and the lengths the internal lines such that the low energy behaviour one theory gives the high energy behaviour the transformed theory Finally provide composition rule which the shell matrix graph factorizable terms the matrices its subgraphs All proofs only use known facts from the theory self adjoint extensions standard linear algebra complex function theory and elementary arguments from the theory Hermitean symplectic forms Abstract und Quantenphysik mail schrader physik berlin Supported part DFG SFB erentialgeometrie mail kostrykin online kostrykin ilt fhg Introduction present meso | |||||||||||
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