S-matrix theory for transmission through billiards in tight-binding approach

Details S-matrix theory for transmission through billiards in tight-binding approach S-matrix theory for transmission through billiards in tight-binding approach

2003-04-23

arxiv.org/abs/quant-ph/0304147v1

Physics

Quantum Physics

29 pages, 9 figures, submitted to J. Phys. A: Math. and Gen

Scientific paper

10.1088/0305-4470/36/45/005

In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittes we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the energy restriction of the conductance band. The complex eigenvalues of the effective Hamiltonian define the poles of the scattering matrix. For some simple cases, we present exact values for the poles. We derive also the condition for the appearance of double poles.

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