Related papers: Spectra of absolute instruments from the WKB appro…
A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…
The results of the development of an approximate approach, which can be considered as an analogue of the WKB method, are presented. This approach gives possibility to divide the electromagnetic field in structured waveguides into forward…
We draw attention on the fact that the Riccati-Pad\'e method developed some time ago enables the accurate calculation of bound-state eigenvalues as well as of resonances embedded either in the continuum or in the discrete spectrum. We apply…
The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and…
We present a new method to compute resonance Raman spectra based on ab initio level calculations using the frequency-dependent Placzek approximation. We illustrate the efficiency of our hybrid quantum-classical method by calculating the…
We perform a systematic WKB expansion to all orders for a one--dimensional system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the series to the exact energy spectrum. Then we show that any finite order WKB approximation…
Precise spectroscopy of oscillating fields plays significant roles in many fields. Here, we propose an experimentally feasible scheme to measure the frequency of a fast-oscillating field using a single-qubit sensor. By invoking a stable…
We analyze the problem of calculating the solutions and the spectrum of a string with arbitrary density and fixed ends. We build a perturbative scheme which uses a basis of WKB-type functions and obtain explicit expressions for the…
Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly…
We describe a possible new technique for precise wavelength calibration of high-resolution astronomical spectrographs using femtosecond-pulsed mode-locked lasers controlled by stable oscillators such as atomic clocks. Such `frequency combs'…
Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and…
Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be…
This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with the complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This is a…
We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this…
We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in…
An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.
We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions…
Certain quantum mechanical systems with a discrete spectrum, whose observables are given by a transseries in $\hbar$, were shown to admit $\hbar_0$-deformations with Borel resummable expansions which reproduce the original model at…
After a brief introduction to quasinormal modes in dissipative systems, we review the WKB formalism in the context of the analytical calculation of quasinormal frequencies. We apply these results to the calculation of quasinormal…
We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the…