Boundary condition at the junction

M. Harmer, B. Pavlov, A. Yafyasov


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 $.

Quantum Graph, boundary condition at the junction

Math Review Classification
Primary Mathematical Physics ; Secondary Scattering Theory

Last Updated
22 may 2006

5 p

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