The statistical distribution of theS-matrix in the one-channel case

López, Gustavo V.; Mello, Pier A.; Seligman, T. H.

doi:10.1007/bf01414267

Cited by 38 publications

(30 citation statements)

References 9 publications

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“…In fact, it turns out that the sums involved in computing the K-matrix in a one channel system are exactly of the type we are interested in and their distribution can be found exactly under the assumption that the ensemble is ergodic and analytic in the energy. For details see [22] and [23]. Before turning to the more difficult case of problems where transport limitations play a role in the tunneling mechanism, let us come back to a couple of points not treated in the above discussion.…”

Section: The Case Without Barriersmentioning

confidence: 99%

The level splitting distribution in chaos-assisted tunnelling

Leyvraz

Ullmo²

1996

J. Phys. A: Math. Gen.

109

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A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain two-dimensional systems. This mechanism is known as chaos-assisted tunneling. We study its consequences for the distribution of the level splittings and obtain a general analytical form for this distribution under the assumption that chaos assisted tunneling is the only operative mechanism. We have checked that the analytical form we obtain agrees with splitting distributions calculated numerically for a model system in which chaos-assisted tunneling is known to be the dominant mechanism. The distribution depends on two parameters: The first gives the scale of the splittings and is related to the magnitude of the classically forbidden processes, the second gives a measure of the efficiency of possible barriers to classical transport which may exist in the chaotic region. If these are weak, this latter parameter is irrelevant; otherwise it sets an energy scale at which the splitting distribution crosses over from one type of behavior to another. The detailed form of the crossover is also obtained and found to be in good agreement with numerical results for models for chaos-assisted tunneling.

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Section: The Case Without Barriersmentioning

confidence: 99%

The level splitting distribution in chaos-assisted tunnelling

Leyvraz

Ullmo²

1996

J. Phys. A: Math. Gen.

109

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“…In this section we will restrict to a system coupled only via a single channel to the environment and rely on the references [20,21]. The statistical distributions of the S-matrix elements with imperfect coupling have been addressed by several authors [32][33][34][35][36][37][38]. Experimentally not only the direct processes have to be taken into account but also losses or absorption.…”

Section: Poisson Kernel and Width Distributionmentioning

confidence: 99%

Microwave experiments using open chaotic cavities in the realm of the effective Hamiltonian formalism

Kuhl

Legrand

Mortessagne

2012

Fortschritte der Physik

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The description of open quantum system successfully uses the concept of the effective Hamiltonian, which takes into account the coupling to the environment. The concept can be extended to classical waves. Experimentally, classical waves are very convenient as they allow to control boundaries, coupling and absorption. We combine here recent works with microwaves investigating properties of open systems which can be described by an effective Hamiltonian. This ranges from spectral properties like modifications to level dynamics, width distribution and coupling fidelity to spatial properties like intensity distributions and complexness parameter which describes the non‐orthogonality of eigenfunctions.

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“…After pioneering work of López et al [28] came theoretical studies of the properties of statistical distributions of the S matrix with direct processes and imperfect coupling [29][30][31]. In a recent experiment work [32] the distribution of the S matrix for chaotic microwave cavities with absorption was investigated.…”

Section: Theorymentioning

confidence: 99%