Wigner time delay and related concepts: Application to transport in coherent conductors

Texier, Christophe

doi:10.1016/j.physe.2015.09.041

Cited by 82 publications

(92 citation statements)

References 203 publications

(512 reference statements)

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“…This important expression is valid at arbitrary degree of the resonance overlap, leading to an interpretation of the Wigner time delay (4) as the density of states in open systems, see [17,18,20] for further discussion. The spectral average of τ W over a narrow energy window is given by τ W = 2π/(N ∆), where ∆ is the mean level spacing (which carries a smooth ε-dependence in general).…”

Section: Introductionmentioning

confidence: 99%

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

Grabsch¹,

Savin²,

Texier³

2018

J. Phys. A: Math. Theor.

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We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix S. We develop a random matrix approach to study the statistical properties of the symmetrised Wigner-Smith time-delay matrix Q s = −i S −1/2 ∂ ε S S −1/2 , and obtain the joint distribution of S and Q s for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) 0 < T 1. We derive two representations of the distribution of Q s in terms of matrix integrals specified by the Dyson symmetry index β = 1, 2, 4 (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay τ W = (1/N ) tr Q s , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution P N,β (τ ) of the Wigner time delay in the weak coupling limit N T 1 and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour P N,β (τ ) ∼ τ −βN 2 /2−3/2 exp − βN T /(8τ ) for τ T .(ii) The distribution shows the universal τ −3/2 behaviour in some intermediate range T τ 1/(T N 2 ). (iii) It has a power law decay P N,β (τ ) ∼ T 2 N 3 (T N 2 τ ) −2−βN/2 for large τ 1/(T N 2 ).

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Section: Introductionmentioning

confidence: 99%

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

Grabsch¹,

Savin²,

Texier³

2018

J. Phys. A: Math. Theor.

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“…Since ρ is not an asymptotic state, the actual scattering matrix S is extracted from the (lower-right) N q × N q block ofŜ. In addition, we introduce an operator K, due to Krein, Friedal and Lloyd (KFL) [64,65], defined as the difference of the spectral functions…”

Section: The Lee Modelmentioning

confidence: 99%

Thermal contribution of unstable states

Giacosa

2019

Eur. Phys. J. C

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Within the framework of the Lee model, we analyze in detail the difference between the energy derivative of the phase shift and the standard spectral function of the unstable state. The fact that the model is exactly solvable allows us to demonstrate the construction of these observables from various exact Green functions. The connection to a formula due to Krein, Friedal, and Lloyd is also examined. We also directly demonstrate how the derivative of the phase shift correctly identifies the relevant interaction contributions for consistently including an unstable state in describing the thermodynamics.

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“…Statistics of Wigner time delays and related quantities in wave-chaotic scattering attracted a considerable interest for about three decades and is still an active research topic, see [53,54,55,56,57,58,59,60,61,62,63,64] and references therein. Interestingly, τ W (λ) naturally appears in characterization of systems with spatially-uniform absorption.…”

Section: Introductionmentioning

confidence: 99%