Аннотация: We consider a system that consists of two single-quantum billiards (QBs) coupled by a waveguide and study the transmission through this system as a function of length and width of the waveguide. To interpret the numerical results for the transmission, we explore a simple model with a small number of states which allows us to consider the problem analytically. The transmission is described in the S-matrix formalism by using the non-Hermitian effective Hamilton operator for the open system. The coupling of the single QBs to the internal waveguide characterizes the 'internal' coupling strength u of the states of the system while that of the system as a whole to the attached leads determines the 'external' coupling strength v of the resonance states via the continuum (waves in the leads). The transmission is resonant for all values of v/u in relation to the effective Hamiltonian. It depends strongly on the ratio u/u via the eigenvalues and eigenfunctions of the effective Hamiltonian. The results obtained are compared qualitatively with those from simulation calculations for larger systems. Most interesting is the existence of resonance states with vanishing widths that may appear at all values of v/u. They cause zeros in the transmission through the double QB due to trapping of the particle in the waveguide.
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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
ИФ СО РАН
Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, S-581 83 Linkoping, Sweden
Max-Planck-Institut fur Physik Komplexer Systeme, D-01187 Dresden, Germany
Доп.точки доступа:
Bulgakov, E. N.; Булгаков, Евгений Николаевич; Rotter, I.; Садреев, Алмаз Фаттахович