Related papers: Bound State Energies using Phase Integral Analysis
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…
We consider the asymptotic behaviour of the second discrete Painlev\'{e} equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region…
In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties…
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…
In this work we study integral equations defined on the whole real line. Using a suitable Banach space, we look for solutions which satisfy some certain kind of asymptotic behavior. We will consider spectral theory in order to find fixed…
This article's subject matter is the study of the asymptotic analysis of the optimal control problem (OCP) constrained by the stationary Stokes equations in a periodically perforated domain. We subject the interior region of it with…
We present excitation energy spectra of few-electron vertically coupled quantum dots for strong and intermediate inter-dot coupling. By applying a magnetic field, we induce ground state transitions and identify the corresponding quantum…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing \cite{invent} and \cite{ode1}, to analyze singular behavior of nonlinear ODEs in a neighborhood of infinity and provide global…
In this study, we consider the asymptotic behaviour of the first discrete Painlev\{e} equation in the limit as the independent variable becomes large. Using an asymptotic series expansion, we identify two types of solutions which are…
In the framework of instantaneous approximations to the Bethe-Salpeter formalism for the description of bound states within quantum field theories, depending on the Lorentz structure of the Bethe-Salpeter interaction kernel the solutions of…
This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding…
Entanglement is a fundamental feature of quantum physics and a key resource for quantum communication, computing and sensing. Entangled states are fragile and maintaining coherence is a central challenge in quantum information processing.…
In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain energy function. We aim to construct the asymptotic solutions based on an axisymmetrical…
In these lectures, we provide an introduction to the complex WKB method, using as a guiding example a class of anharmonic oscillators that appears in the ODE/IM correspondence. In the first three lectures, we introduce the main objects of…
Salpeter equations with potential functions rising to infinity in configuration space do not automatically predict stable bound states. For this to happen, also the Lorentz behaviour of the involved Bethe-Salpeter kernels is crucial. At…
The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…