Related papers: Distributional Borel Summability of Odd Anharmonic…
We present a new prescription for the resummation of contributions due to soft gluon emission to the trasverse momentum distribution of processes such as Drell-Yan production in hadronic collisions. We show that familiar difficulties in…
We obtain existence and uniqueness for odd second order oscillators in the space of odd functions without topological assumptions on the nonlinear part.
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…
This work investigates the multiplicity and differentiability of eigenfrequencies in structures with various symmetries. In particular, the study explores how the geometric and design variable symmetries affect the distribution of…
We study discrete spectral quantities associated to Schr\"odinger operators of the form $-\Delta_{\mathbb{R}^d}+V_N$, $d$ odd. The potential $V_N$ models a highly disordered crystal; it varies randomly at scale $N^{-1} \ll 1$. We use…
The Schr\"odinger equation for the four-dimensional double singular oscillator is separable in Eulerian, doble polar and spheroidal coordinates in ${\rm I R}^4$. It is shown that the coefficients for the expansion of double polar basis in…
Spectral asymptotics of the Sturm-Liouville problem with a singular self-conformal weight measure is considered. A stronger version of the bounded distortion property is assumed for the conformal iterated function system corresponding to…
The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of…
We study the eigenvalues of a Laplace-Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. By assigning partitions with the restricted uniform measure,…
The factorization method of Infeld and Hull is applied to the radial Schr\"{o}dinger equation for $d$-dimensional isotropic harmonic oscillator and various ladder operators are defined. The radial energy eigenstates are expressed in terms…
We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized…
Alternating the signs of the frequencies for Fourier components with even and odd (normalized) wavenumbers in the nonlinear-wave, such as the Korteweg-de Vries, equations maintains a constantly drifting dispersive shock with similar…
We discuss the method of conformal mappings applied to perturbative QCD. The approach is based on the Borel-Laplace integral regulated with the principal value prescription and the expansion of the Borel transform in powers of the variable…
We present here a formulation for the calculation of the configuration-averaged optical conductivity in random alloys. Our formulation is based on the augmented-space theorem introduced by one of us [A. Mookerjee, J. Phys. C: Solid State…
Starting from the divergence pattern of perturbation expansions in Quantum Field Theory and the (assumed) asymptotic character of the series, we address the problem of ambiguity of a function determined by the perturbation expansion. We…
We study a complex perturbation of a self-adjoint infinite band Schrodinger operator (defined in the form sense), and obtain the Lieb--Thirring type inequalities for the rate of convergence of the discrete spectrum of the perturbed operator…
Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon…
We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these…
Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade…
We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the…