Related papers: On the effective secular equation
The usual implement procedure for the reconstruction of secular equation for an effective Hamiltonian has been discussed and improved. A relative characteristic polynomial has been introduced for the effective Hamiltonian, to obtain a…
We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is greatly facilitated by the application of the discriminant to…
Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville…
We demonstrate with soluble models how to employ the effective Hamiltonian approach of Lee and Suzuki to obtain all the exact eigenvalues of the full Hamiltonian. We propose a new iteration scheme to obtain the effective Hamiltonian and…
We prove that integral points can be effectively determined on all but finitely many modular curves, and on all but one modular curve of prime power level.
We show that a method proposed recently, based on the characteristic polynomial of an effective Hamiltonian, had been developed several years earlier by other authors in a clearer and more general way. We outline both implementations of the…
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions…
We develop a more accurate secular form for the Redfield non-secular master equation, which is insensitive to the choice of the basis. This completely solves the ambiguity on which basis should be used when the secular approximation of the…
This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for the Benjamin equation.
We study the Floquet solutions of the Mathieu equation. In order to find an explicit relation between the characteristic exponents and their corresponding eigenvalues of the Mathieu operator, we consider the Whittaker-Hill formula. This…
Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
We prove here an energy estimate for the Cauchy problem for hyperbolic equations with double characteristics which contains both effectively hyperbolic and non effectively hyperbolic points.
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several…
The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring…
The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been…
In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we prove Liouville theorems for ancient solutions satisfying the…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the…
I compute the derivative expansion of an effective action at finite temperature using the imaginary time approach. I show that it is a well behaved expansion giving a unique seriers contrary to previous results. This disparity is shown to…