Related papers: Prepotential approach to quasinormal modes
We propose a new method for constructing the quasi-exactly solvable (QES) potentials with two known eigenstates using supersymmetric quantum mechanics. General expression for QES potentials with explicitly known energy levels and wave…
The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
Optical phenomena associated with extremely localized field should be understood with considerations of nonlocal and quantum effects, which pose a hurdle to conceptualize the physics with a picture of eigenmodes. Here we first propose a…
In this paper, we undertake a comprehensive examination of quasinormal modes linked to Lee-Wick black holes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Such black holes can display a…
We propose a general method for constructing quasi-exactly solvable potentials with three analytic eigenstates. These potentials can be real or complex functions but the spectrum is real. A comparison with other methods is also performed.
We develop a new method for writing simple exact equations characterizing gravity solutions among which black holes and in particular the quasinormal modes. More precisely, we derive the full system of functional and Thermodynamic Bethe…
The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…
It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the…
We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schr\"odinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials.…
We give a systematic construction of new quasi-exactly solvable systems via Bethe ansatz and supersymmetric quantum mechanics (SUSYQM). Methods based on the intertwining of supercharges have been extensively used in the literature for…
We have extended the semianalytic technique of Iyer and Will for computing the complex quasinormal frequencies of black holes, $\omega,$ by constructing the Pad\'e approximants of the (formal) series for $\omega^{2}$. It is shown that for…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
Motivated by the substantial instability of the fundamental and high-overtone quasinormal modes, recent developments regarding the notion of black hole pseudospectrum call for numerical results with unprecedented precision. This work…
We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and…
We introduce the categories of quasi-measurable spaces, which are slight generalizations of the category of quasi-Borel spaces, where we now allow for general sample spaces and less restrictive random variables, spaces and maps. We show…
The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…
In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that quasi-integrable modules are not necessarily highest weight modules. We prove that each quasi-integrable module…
A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…