A two-dimensional junction is modelled by a quantum graph with a resonance hode. The boundary condition at the node is calculated from the frirst principles . In low temperators limit for simplest T-junction it coincides with the the boundary condition suggested by Datta. The free parameter contained in Datta's condition is interpreted in spectral terms of an intermediate Hamiltonian. The derived boundary condition is applicable for any junction of straight semi-infinite quantum wires attached to the quantum dot, if the junction is thin : the ratio r of the diameter of the quantum dot to the width of the wires is sufficintly large $r approx 4 - 10 $. |
Keywords
Quantum Graph, boundary condition at the junction
Math Review Classification
Primary Mathematical Physics
; Secondary Scattering Theory
Last Updated
22 may 2006
Length
5 p
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