2001
DOI: 10.1103/physreve.64.056227
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Effective coupling for open billiards

Abstract: We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard which is opened by attaching a waveguide. The Wigner time delay and the resonance positions resulting from the coupling constants are compared to an exact numerical calculation. Deviations can be attributed to evanescent modes in the waveguide and to the finite number of eigenstates taken into account. The influence of the shape of the billiard and of the boundary conditions at the mouth of the waveguide … Show more

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Cited by 66 publications
(95 citation statements)
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“…The effective potential was first introduced in nuclear physics half a century ago [24,25,26,27]. It is used in physics of mesoscopic systems from time to time in recent years [28,29,30,31,32,33,34,35].…”
Section: A Effective Potentialmentioning
confidence: 99%
See 1 more Smart Citation
“…The effective potential was first introduced in nuclear physics half a century ago [24,25,26,27]. It is used in physics of mesoscopic systems from time to time in recent years [28,29,30,31,32,33,34,35].…”
Section: A Effective Potentialmentioning
confidence: 99%
“…In the second part of the present paper, from Section V to Section VI, we introduce new numerical methods of treating the resonant state with the use of the effective potential [24,25,26,27,28,29,30,31,32,33,34,35]. A logical consequence of the arguments in Sections II and III is that the eigenfunction of the resonant state is diverging away from the scattering potential.…”
Section: Introductionmentioning
confidence: 99%
“…[15][16][17]. Due to the reordering processes the S matrix poles can not be approximated by using the E cc ′ as shown in a numerical study [25]. Instead, the poles of the S matrix are given by (5) where the interaction of the resonance states via the continuum is taken into account by diagonalizing the effective Hamiltonian in the subspace of discrete states embedded in the continuum.…”
Section: Basic Equations Of the Quantum Mechanical Descriptionmentioning
confidence: 99%
“…This is numerically not possible so the number of states must be truncated. For transmission calculations using an effective non-Hermitian Hamiltonian it has been shown that only the case with Neumann boundary condition is stable with a finite number of states (Pichugin, Schanz, & Seba, 2001). If the physical importance of the boundary conditions can be relaxed, effective non-Hermitian Hamiltonians could be used with Dirichlet boundary condition for…”
Section: Journal Of Young Investigatorsmentioning
confidence: 99%