Large-N expansion for the time-delay matrix of ballistic chaotic cavities

Fabio Cunden; Francesco Mezzadri; Nicholas Simm; Pierpaolo Vivo

doi:10.1063/1.4966642

Large-N expansion for the time-delay matrix of ballistic chaotic cavities

Fabio Cunden, Francesco Mezzadri, Nicholas Simm, Pierpaolo Vivo

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Abstract

We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β=1 and β=2) we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.

Original language	English
Article number	111901
Number of pages	16
Journal	Journal of Mathematical Physics
Volume	57
Issue number	11
Early online date	4 Nov 2016
DOIs	https://doi.org/10.1063/1.4966642
Publication status	Published - Nov 2016

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Wegner estimates and universality for non-Hermitian matrices
Mezzadri, F.
1/05/14 → 31/10/17
Project: Research
PHASE TRANSITIONS IN TWO DIMENSIONAL
Mezzadri, F.
1/09/06 → 1/03/09
Project: Research

Professor Francesco Mezzadri
- F.Mezzadribristol.acuk
- Probability, Analysis and Dynamics
- School of Mathematics - Professor of Mathematical Physics
- Applied Mathematics
- Mathematical Physics
Person: Academic , Member

Cite this

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title = "Large-N expansion for the time-delay matrix of ballistic chaotic cavities",

abstract = "We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β=1 and β=2) we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed. ",

author = "Fabio Cunden and Francesco Mezzadri and Nicholas Simm and Pierpaolo Vivo",

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doi = "10.1063/1.4966642",

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T1 - Large-N expansion for the time-delay matrix of ballistic chaotic cavities

AU - Cunden, Fabio

AU - Mezzadri, Francesco

AU - Simm, Nicholas

AU - Vivo, Pierpaolo

PY - 2016/11

Y1 - 2016/11

N2 - We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β=1 and β=2) we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.

AB - We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β=1 and β=2) we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.

U2 - 10.1063/1.4966642

DO - 10.1063/1.4966642

M3 - Article (Academic Journal)

SN - 0022-2488

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 11

M1 - 111901

ER -

Large-N expansion for the time-delay matrix of ballistic chaotic cavities

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Wegner estimates and universality for non-Hermitian matrices

PHASE TRANSITIONS IN TWO DIMENSIONAL

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Professor Francesco Mezzadri

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