Related papers: Distributional Borel Summability of Odd Anharmonic…
We study the Schr\"odinger equation on $\R$ with a polynomial potential behaving as $x^{2l}$ at infinity, $1\leq l\in\N$ and with a small time quasiperiodic perturbation. We prove that if the symbol of the perturbation grows at most like…
For many nonlinear physical systems, approximate solutions are pursued by conventional perturbation theory in powers of the non-linear terms. Unfortunately, this often produces divergent asymptotic series, collectively dismissed by Abel as…
In anisotropic crystals, Maxwell's equations permit only birefringence for the propagation of light. Notwithstanding, multirefringent systems comprising more than two propagating modes exist, such as in electron optics and photonic…
We study random vectors of the form $(\operatorname {Tr}(A^{(1)}V),...,\operatorname {Tr}(A^{(r)}V))$, where $V$ is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the $A^{(\nu)}$ are…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…
In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact…
The Rayleigh quotient, which provides the classical variational characterization of the spectral radius of Hermitian matrices, can be extended to nonsymmetric nonnegative irreducible matrices, ${\bf A}$, by the inclusion of a diagonal…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
Numerical simulations show that a massive real scalar field in a nonlinear theory can form long-lived oscillating localized states. For a self-interacting scalar on a fixed background these objects are named oscillons, while for the…
We study oscillations in the eigenfunctions for a fractional Schr\"odinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane and provides a…
We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
We present an analytical study of a nonlinear oscillator subject to an additive Ornstein-Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or…
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D.…
Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator…
Methods of determining, from small-variable asymptotic expansions, the characteristic exponents for variables tending to infinity are analyzed. The following methods are considered: diff-log Pad\'e summation, self-similar factor…
The N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden…