Joint moments of proper delay times

Martínez-Argüello, A. M.; Martínez-Mares, M.; García, J. C.

doi:10.1063/1.4890559

Cited by 16 publications

(15 citation statements)

References 47 publications

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“…However, traces of Q and its powers are insensitive to such a symmetrization, giving the identity Equations (15) and (16) therefore readily yield the variance of the Wigner time delay in the form of (4). Likewise, we can arrive at the same result by using the variance [32] and covariance [33] of the proper time-delays. For later use we quote the relevant expression for the second moment [31,32]…”

Section: Resonance Scattering Approachmentioning

confidence: 78%

“…the proper time-delays, turned out to be determined by the Laguerre ensemble from RMT [28]. This provided a route to apply orthogonal polynomials to compute marginal distributions [30] and various moments [31][32][33][34] or use a Coulomb gas method to study the total density [35]. Very recently, Mezzadri and Simm [36] applied the integrable theory of certain matrix integrals to the problem and developed an efficient method for computing cumulants of arbitrary order.…”

Section: W Hmentioning

confidence: 99%

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Efficient semiclassical approach for time delays

2014

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The Wigner time delay, defined by the energy derivative of the total scattering phase shift, is an important spectral measure of an open quantum system characterizing the duration of the scattering event. It is proportional to the trace of the Wigner-Smith matrix Q that also encodes other time-delay characteristics. For chaotic cavities, these quantities exhibit universal fluctuations that are commonly described within random matrix theory. Here, we develop a new semiclassical approach to the time-delay matrix which is formulated in terms of the classical trajectories that connect the exterior and interior regions of the system. This approach is superior to previous treatments because it avoids the energy derivative. We demonstrate the methodʼs efficiency by going beyond previous work in establishing the universality of time-delay statistics for chaotic cavities with perfectly connected leads. In particular, the moment generating function of the proper time-delays (eigenvalues of Q) is found semiclassically for the first five orders in the inverse number of scattering channels for systems with and without time-reversal symmetry. We also show the equivalence of random matrix and semiclassical results for the second moments and for the variance of the Wigner time delay at any channel number. 123018 J Kuipers et al eff 1 that describes the propagation in the open system 6 New J. Phys. 16 (2014) 123018 J Kuipers et al 7 New J. Phys. 16 (2014) 123018 J Kuipers et al 8 New J. Phys. 16 (2014) 123018 J Kuipers et al W 0 9 New J. Phys. 16 (2014) 123018 J Kuipers et al New J. Phys. 16 (2014) 123018 J Kuipers et al

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Section: Resonance Scattering Approachmentioning

confidence: 78%

Section: W Hmentioning

confidence: 99%

Efficient semiclassical approach for time delays

2014

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“…A few other polynomial functions have also been computed 29,30 . A recent review, also considering extension to non-ideal openings and other symmetry classes, can be found in 31 .…”

Section: Introductionmentioning

confidence: 99%

Statistics of time delay and scattering correlation functions in chaotic systems. I. Random matrix theory

Novaes

2015

Journal of Mathematical Physics

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We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = −i ̵ hS † dS dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to Smatrix correlation functions, from which the statistics of Q can also be derived.Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.

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“…This was done by extracting the essence that comes from the level repulsion in the joint distribution of proper delay times, that transcends to the kth moment of a proper delay time. 34 We test our formula by random matrix theory simulations for all symmetry classes and for several number of channels.…”

Section: Introductionmentioning

confidence: 99%

Delay times in chaotic quantum systems

Martínez-Argüello¹,

Fernández-Marín²,

Martínez-Mares³

2017

Eur. Phys. J. Spec. Top.

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By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an arbitrary number of channels and any symmetry. This distribution was not completely known for all symmetry classes. Our theoretical distribution is verified by random matrix theory simulations of ballistic chaotic cavities.

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Joint moments of proper delay times

Cited by 16 publications

References 47 publications

Efficient semiclassical approach for time delays

Efficient semiclassical approach for time delays

Statistics of time delay and scattering correlation functions in chaotic systems. I. Random matrix theory

Delay times in chaotic quantum systems

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