Wigner time delay and Wigner-Smith matrix in disordered 1D models

Scattering by a random potential: Distribution of the Wigner time delay

The Wigner time delay is a concept of scattering theory. Consider for example the scattering of a particle on some potential localised in space: the time delay is defined as the derivatives of scattering phase shifts with resspect with the energy. In a semiclassical picture, it measures the delay in time caused by the presence of the potential (note that the notion may be formulated in classical scattering theory, cf. S.-K. Ma, Statistical mechanics, World Scientific, chapter 14). The Wigner time delay can be related to the variation of the density of states due to the introduction of the scattering potential, through the Krein-Friedel sum rule. Therefore the time delay provides a measure of the density of states in a scattering situation.

  • Alain Comtet and Christophe Texier,
    On the distribution of the Wigner time delay in one-dimensional disordered systems
    J. Phys. A: Math. Gen. 30, 8017-8025 (1997).
    cond-mat/9707046.
  • Christophe Texier and Alain Comtet,
    Universality of the Wigner time delay distribution for one-dimensional random potentials
    Phys. Rev. Lett. 82(21), 4220-4223 (1999).
    cond-mat/9812196.
  • Christophe Texier and Alain Comtet,
    Wigner time delay distribution for one-dimensional random potentials
    in « Quantum physics at mesoscopic scale », ed. by C.Glattli, M.Sanquer and J.Trân Thanh Vân, EDP Sciences, 2000, p. 475, Proceedings of the XXXIVth Moriond conference, 23-30 january 1999.
    ps file.

A poster : Wigner time delay distribution for one-dimensional random potentials.
ps (1.3MB), pdf (0.5MB).

Also, cf. the review article:

  • Christophe Texier
    Wigner time delay and related concepts — Application to transport in coherent conductors
    Physica E 82, 16-33 (2016), contribution to a special issue “Frontiers in quantum electronic transport – in memory of Markus Büttiker
    cond-mat arXiv:1507.00075 (arXiv version updated after publication in Physica E)

 

Wigner-Smith time delay matrix and Wigner time delay for semi-infinite multichannel disordered wires

(within the multichannel Schrödinger equation)

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