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S-matrix formalism of transmission through two quantum billiards coupled by a waveguide
Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation.
Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
2005 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 38, no 49, 10647-10661 p.Article in journal (Refereed) Published
Abstract [en]

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 v/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. © 2005 IOP Publishing Ltd.

Place, publisher, year, edition, pages
2005. Vol. 38, no 49, 10647-10661 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-50341DOI: 10.1088/0305-4470/38/49/012OAI: diva2:271237
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-12

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Sadreev, Almas
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The Institute of TechnologyDepartment of Physics, Chemistry and Biology
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