TY - JOUR
T1 - Generalization of Wigner time delay to subunitary scattering systems
AU - Chen, Lei
AU - Anlage, Steven M.
AU - Fyodorov, Yan V.
N1 - Funding Information:
Acknowledgments. We acknowledge Jen-Hao Yeh for early experimental work on complex time delays. This work was supported by AFOSR COE Grant No. FA9550-15-1-0171, NSF Grant No. DMR2004386, and ONR Grant No. N000141912481.
Publisher Copyright:
© 2021 American Physical Society.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/5
Y1 - 2021/5
N2 - We introduce a complex generalization of the Wigner time delay τ for subunitary scattering systems. Theoretical expressions for complex time delays as a function of excitation energy, uniform and nonuniform loss, and coupling are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-loss element. We find that the time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in Re[τ] and Im[τ] serves as a reliable indicator of the condition for coherent perfect absorption (CPA). By reinforcing the concept of time delays in lossy systems this work provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable an approach to achieving CPA at an arbitrary frequency in complex scattering systems.
AB - We introduce a complex generalization of the Wigner time delay τ for subunitary scattering systems. Theoretical expressions for complex time delays as a function of excitation energy, uniform and nonuniform loss, and coupling are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-loss element. We find that the time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in Re[τ] and Im[τ] serves as a reliable indicator of the condition for coherent perfect absorption (CPA). By reinforcing the concept of time delays in lossy systems this work provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable an approach to achieving CPA at an arbitrary frequency in complex scattering systems.
UR - http://www.scopus.com/inward/record.url?scp=85107265135&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.103.L050203
DO - 10.1103/PhysRevE.103.L050203
M3 - Article
AN - SCOPUS:85107265135
VL - 103
JO - Physical review. E
JF - Physical review. E
SN - 2470-0045
IS - 5
M1 - L050203
ER -
TY - JOUR
T1 - Nonlinearity-generated resilience in large complex systems
AU - Belga Fedeli, Sirio
AU - Fyodorov, Yan
AU - Ipsen, J R
N1 - Funding Information:
We acknowledge support by the Engineering and Physical Sciences Research Council Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems through Grant No. EP/L015854/1 (S.B.F.) and by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (J.R.I.).
Publisher Copyright:
© 2021 American Physical Society.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/2/1
Y1 - 2021/2/1
N2 - We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as long as the origin remains stable, it is surrounded by a “resilience gap”: there are no other fixed points within a radius r∗>0 and the system is therefore expected to be resilient to a typical initial displacement small in comparison to r∗. The radius r∗ is shown to vanish at the same threshold where the origin loses local stability, revealing a mechanism by which systems close to the tipping point become less resilient. We also find that beyond the resilience radius the number of fixed points in a ball surrounding the original point of equilibrium grows exponentially with N, making systems dynamics highly sensitive to far enough displacements from the origin.
AB - We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as long as the origin remains stable, it is surrounded by a “resilience gap”: there are no other fixed points within a radius r∗>0 and the system is therefore expected to be resilient to a typical initial displacement small in comparison to r∗. The radius r∗ is shown to vanish at the same threshold where the origin loses local stability, revealing a mechanism by which systems close to the tipping point become less resilient. We also find that beyond the resilience radius the number of fixed points in a ball surrounding the original point of equilibrium grows exponentially with N, making systems dynamics highly sensitive to far enough displacements from the origin.
UR - http://www.scopus.com/inward/record.url?scp=85101286743&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.103.022201
DO - 10.1103/PhysRevE.103.022201
M3 - Article
VL - 103
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 2
M1 - 022201
ER -