Effective coupling for open billiards

Pichugin, K. N.; Schanz, Holger; Šeba, P.

doi:10.1103/physreve.64.056227

Cited by 66 publications

(95 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Some Properties of the Resonant State in Quantum Mechanics and Its Computation

Hatano¹,

Sasada²,

Nakamura³

et al. 2008

Progress of Theoretical Physics

160

View full text Add to dashboard Cite

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.

show abstract

Section: A Effective Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some Properties of the Resonant State in Quantum Mechanics and Its Computation

Hatano¹,

Sasada²,

Nakamura³

et al. 2008

Progress of Theoretical Physics

160

View full text Add to dashboard Cite

show abstract

“…[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%

Conductance of open quantum billiards and classical trajectories

et al. 2002

View full text Add to dashboard Cite

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.

show abstract

“…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%