Statistics of Complex Wigner Time Delays as a Counter of S -Matrix Poles: Theory and Experiment

TY - JOUR

T1 - Statistics of Complex Wigner Time Delays as a Counter of S -Matrix Poles

T2 - Theory and Experiment

AU - Chen, Lei

AU - Anlage, Steven M.

AU - Fyodorov, Yan V.

N1 - Publisher Copyright: © 2021 American Physical Society.

PY - 2021/11/12

Y1 - 2021/11/12

N2 - We study the statistical properties of the complex generalization of Wigner time delay τW for subunitary wave-chaotic scattering systems. We first demonstrate theoretically that the mean value of the Re[τW] distribution function for a system with uniform absorption strength η is equal to the fraction of scattering matrix poles with imaginary parts exceeding η. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave-chaotic scattering system in the short-wavelength limit, including quantum wires and dots, acoustic and electromagnetic resonators, and quantum graphs.

AB - We study the statistical properties of the complex generalization of Wigner time delay τW for subunitary wave-chaotic scattering systems. We first demonstrate theoretically that the mean value of the Re[τW] distribution function for a system with uniform absorption strength η is equal to the fraction of scattering matrix poles with imaginary parts exceeding η. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave-chaotic scattering system in the short-wavelength limit, including quantum wires and dots, acoustic and electromagnetic resonators, and quantum graphs.

UR - http://www.scopus.com/inward/record.url?scp=85119215037&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.127.204101

DO - 10.1103/PhysRevLett.127.204101

M3 - Article

AN - SCOPUS:85119215037

SN - 0031-9007

VL - 127

JO - Physical Review Letters

JF - Physical Review Letters

IS - 20

M1 - 204101

ER -