2015/01/16 by Dmitrii N. Maksimov, Almas F. Sadreev, Maksimov, Dmitrii N. +5 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.48550/arxiv.1501.04653
arxiv created 2015/04/11 · arxiv updated 2015/04/14
We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems. In higher than one dimensions the method represents acoustic coupled mode theory in which the scattering solution within an open resonator is found in the form of expansion over the eigenmodes of the closed resonator decoupled from the waveguides. The problem of finding the transmission spectra is reduced to solving a set of linear equations with a non-Hermitian matrix whose anti-Hermitian term accounts for coupling between the resonator eigenmodes and the scattering channels of the waveguides. Numerical applications to acoustic two-, and three-dimensional resonator-waveguide problems are considered.