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Nonlinear Anti-(Parity-Time) Symmetric Dimer
In the present work we propose a nonlinear anti- P T -symmetric dimer, that at the linear level has been experimentally created in the realm of electric circuit resonators. We find four families of solutions, the so-called upper and lower branches, both in a symmetric and in an asymmetric (symmetry-broken) form. We unveil analytically and confirm numerically the critical thresholds for the existence of such branches and explore the bifurcations (such as saddle-node ones) that delimit their existence, as well as transcritical ones that lead to their potential exchange of stability. We find that out of the four relevant branches, only one, the upper symmetric branch, corresponds to a spectrally and dynamically robust solution. We subsequently leverage detailed direct numerical computations in order to explore the dynamics of the different states, corroborating our spectral analysis results.
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Publication Date:
NSF-PAR ID:
10345508
Journal Name:
Frontiers in Physics
Volume:
10
ISSN:
2296-424X
5. A bstract We derive explicit formulae to compute the a and c central charges of four dimensional $$\mathcal{N}$$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$\mathcal{N}$$ N = 2 SCFTs which culminate with our $$\mathcal{N}$$ N = 2 UV-IR simple flavor condition . This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$\mathcal{N}$$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper. This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.