Related papers: Coupled Cavity Model: Correctness and Limitations
This paper presents the results of studies in elaboration of a mathematical model of the cavity-chain slow wave structures. Considered is the problem of coupling of an infinitely long cylindrical cavity chain coupled through centerholes in…
We present the short description of the methods for calculation of the coupling coefficients in the Coupling Cavity Model of arbitrary chain of resonators. In the first part the procedure that is based on the Mode Matching Method is given.…
We developed the general approach that gives possibility to calculate the coupling coefficients for arbitrary chain of resonators without using the great number of eigen functions. For understanding this method and having possibility to…
We present a quantized quasinormal approach to rigorously describe coupled lossy resonators, and quantify the quantum coupling parameters as a function of distance between the resonators. We also make a direct connection between classical…
The SWKB quantization condition is an exact quantization condition for the conventional shape-invariant potentials. On the other hand, this condition equation does not hold for other known solvable systems. The origin of the (non-)exactness…
This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…
Within the current uncertainties in the treatment of the coupling between pulsation and convection, limiting amplitude, nonlinear, convective models appear the only viable approach for providing theoretical predictions about the intrinsic…
We consider a nonlinear microcavity separating a waveguide channel into two parts so as the coupling between them is possible only due to the resonant properties of the microcavity. We provide a rigorous derivation of the equations used in…
We review the results of large scale simulations of noncompact quenched $QED$ which use spectrum and Equation of State calculations to determine the theory's phase diagram, critical indices, and continuum limit. The resulting anomalous…
We obtain the rigorous WKB expansion to all orders for the radial Kepler problem, using the residue calculus in evaluating the WKB quantization condition in terms of a complex contour integral in the complexified coordinate plane. The…
The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and…
In this work, we show that the eigenvalue continuation approach introduced recently in [Phys. Rev. Lett. {\bf 121}, 032501 (2018)], despite its many advantages, has some fundamental limitations which cannot be overcome when strongly…
Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by…
In this talk we review the limitations of including meson loops as perturbative corrections in a solvable quark model. We first discuss meson-meson scattering within a formalism which treats confined quark pairs and mesons on an equal…
For the formal verification and design of control systems, abstractions with quantified accuracy are crucial. This is especially the case when considering accurate deviation bounds between a stochastic continuous-state model and its finite…
Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that…
The characterization of an unknown quantum system requires the Hamiltonian identification. The full access to the system, however, is usually restricted, hindering the direct retrieval of relevant parameters, and a reliable indirect…
The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation…
For the semi-classical limit of the cubic, defocusing nonlinear Schrodinger equation with an external potential, we explain the notion of criticality before a caustic is formed. In the sub-critical and critical cases, we justify the WKB…
A new approach to the description of inhomogeneous disk-loaded waveguides (chains of coupled resonators) is proposed. New matrix difference equations based on the technique of coupled integral equations and the decomposition method are…