Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
نویسنده
چکیده
The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.
منابع مشابه
Coupling of eigenvalues of complex matrices at diabolic and exceptional points
The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossin...
متن کاملCoalescence of Two Exceptional Points in the Anti-hermitian 3-level Pairing Model
An essential part of the motion of short-lived nucleonic matter is in classically forbidden regions and, hence, its properties are effected by both the continuum and many-body correlations 1,2. The effect of resonances and the non-resonant scattering states can be considered in the OQS extension of the shell model (SM), the so-called continuum shell model (CSM) 1. Two realizations of the CSM ha...
متن کاملLocal Analysis near a Folded Saddle-Node Singularity
Folded saddle-nodes occur generically in one parameter families of singularly perturbed systems with two slow variables. We show that these folded singularities are the organizing centers for two main delay phenomena in singular perturbation problems: canards and delayed Hopf bifurcations. We combine techniques from geometric singular perturbation theory – the blow-up technique – and from delay...
متن کاملEigenvalue calculator for Islanded Inverter-Based Microgrids
The stability analysis of islanded inverter-based microgrids (IBMGs) is increasingly an important and challenging topic due to the nonlinearity of IBMGs. In this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. Using the linear model makes it easy to analyze the eigenvalues and stability of IBMGs due to the fact that it derive...
متن کاملA non-Hermitian PT −symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
We study a non-Hermitian PT −symmetric generalization of an Nparticle, two-mode Bose-Hubbard system, modeling for example a Bose-Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analyzed ...
متن کامل