Related papers: Distributional Borel Summability of Odd Anharmonic…
We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the…
Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh-Schrodinger power series. This power series is proved to be…
The axial propagation of circularly polarized light in an optically active structurally chiral medium is exactly solved via full electromagnetic analysis. Some symmetries of the system's characteristic matrix reveal new insights, which are…
Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying…
Undular bores, or dispersive shock waves, are non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude with distance travelled. We…
Darboux transformations of the singular harmonic oscillator are considered. Analytical expressions for the propagators are obtained, using the image method applied to formal singular propagators. Two-well and three-well families of…
We consider stochastic differential equations driven by Gaussian white noise on $\R^d$. % We provide applications to models for financial %markets. Particular attention is given to the kernel $p_t,\,t\geq 0$ of the transition semigroup…
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…
The spectral problem for O(D) symmetric polynomial potentials allows for a partial algebraic solution after analytical continuation to negative even dimensions D. This fact is closely related to the disappearance of the factorial growth of…
In this note we consider the Hausdorff dimension of self-affine sets with random perturbations. We extend previous work in this area by allowing the random perturbation to be distributed according to distributions with unbounded support as…
We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg--de Vries, equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave…
After reviewing basic facts about large-order behaviour of perturbation expansions in various fields of physics, I consider several alternatives to the Borel summation method and discuss their relevance to different physical situations.…
We obtain rge Erd\" os-R\' enyi type law of large numbers for "nonconventional" sums of the form $S_n=\sum^n_{m=1}F(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of i.i.d. random variables and $F$ is a bounded Borel…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…
The symmetrized Slater determinants of orthogonal polynomials with respect to a non-negative Borel measure are shown to be represented by constant multiple of Hankel determinants of two other families of polynomials, and they can also be…
We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular…
A novel superconducting state under the broken time-reversal symmetry is studied in conventional phonon-mediated superconductors. By solving the Eliashberg equation self-consistently with the mass renormalization effect, it is found that…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…