Exotic light dynamics around an exceptional point of order four associated with three connecting second-order exceptional points

2021 ◽  
Vol 38 (4) ◽  
pp. 1297
Author(s):  
Sibnath Dey ◽  
Arnab Laha ◽  
Somnath Ghosh
Keyword(s):  
Second Order ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Order Four

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

All possible second-order four-impedance two-stage Colpitts oscillators

2011 ◽  
Vol 5 (3) ◽  
pp. 196 ◽  
Author(s):  
A.S. Elwakil ◽  
M.A. Al-Radhawi
Keyword(s):  
Second Order ◽  
Two Stage ◽  
Order Four

Bandwidth-enhanced lumped-element absorptive bandstop filter topology and its application to LTCC bandstop filter design

2014 ◽  
Vol 7 (6) ◽  
pp. 691-698 ◽  
Author(s):  
Juseop Lee ◽  
Byungguk Kim ◽  
Kangho Lee ◽  
William J. Chappell
Keyword(s):  
Low Temperature ◽  
Filter Design ◽  
Second Order ◽  
Center Frequency ◽  
Q Factor ◽  
First Order ◽  
Lumped Element ◽  
Bandstop Filter ◽  
Analytic Design ◽  
Order Four

In this paper, we show a second-order (four-resonator) absorptive bandstop filter circuit topology which gives a larger bandwidth compared to a first-order topology. Due to the absorptive characteristic, it creates a large attenuation at the center frequency using low-Q resonators. Since low-Q resonators can be used in generating a large attenuation, small-size resonators can be employed in bandstop filter design. Analytic design equations are provided so that a higher-order absorptive bandstop filter can be designed analytically. It is also shown that the second-order filter topology exhibits a better frequency selectivity having a same bandwidth. The proposed filter topology has been applied to a design of a miniaturized low-temperature co-fired ceramic bandstop filter with low-Q resonators. The Q-factor of the lumped-element resonators has been chosen to be 5 for demonstration.

The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis

2020 ◽  
Author(s):  
Felicitas Schäfer ◽  
Shuai Guo ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Large Sets ◽  
Training Samples ◽  
Numerical Stability Analysis ◽  
Increased Sensitivity ◽  
Positive Growth Rate ◽  
Input Uncertainties ◽  
The Impact

Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.

Sign in / Sign up

Export Citation Format

Share Document