Related papers: Strichartz estimates for quadratic repulsive poten…

We examine the dynamic spreading of a dense overdamped suspension of particles under power law repulsive potentials, often called Riesz gases. That is, potentials that decay with distance as 1/r^k where k\in (-2,\infty]. Depending on the…

We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian,$H(\beta)=-d^2/dx^2+x^2+i\sqrt{\beta}x^3$,for $\beta$ in the cut plane $\C_c:=\C\backslash (-\infty, 0)$. Moreover, we prove that the spectrum…

The aim of this work is to provide asymptotic estimates for the splitting of separatrices in a perturbed 3-degree-of-freedom Hamiltonian system, associated to a 2-dimensional whiskered torus (invariant hyperbolic torus) whose frequency…

In this paper, we consider the dispersive estimates for Schr\"odinger operators with Coulomb-like decaying potentials, such as $V(x)=-c|x|^{-\mu}$ for $|x|\gg 1$ with $0<\mu<2$, in one dimension. As an application, we establish both the…

We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced…

We consider a family of non-autonomous reaction-diffusion equations with almost periodic, rapidly oscillating principal part and nonlinear interactions. As the frequency of the oscillations tends to infinity, we prove that the solutions of…

We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically we consider the effect of…

We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic…

This is the last in a series of four papers on Poisson formalism for the cubic nonlinear Schrodinger equation with repulsive nonlinearity. In this paper we consider scattering potentials.

We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. We deal with…

The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original…

We prove Strichartz estimates for the Schroedinger equation with an electromagnetic potential, in dimension $n\geq3$. The decay and regularity assumptions on the potentials are almost critical, i.e., close to the Coulomb case. In addition,…

This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the…

The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…

We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…

For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements…

The potential of a static quark-antiquark pair is studied in the range 0.05 fm $<$ r $<$ 0.8 fm, employing a sequence of lattices up to 64^4. The continuum quantities are evaluated by extrapolation of the data at finite lattice spacing. The…

We consider radial solutions to the Cauchy problem for the linear wave equation with a small short-range electromagnetic potential (the "square version" of the massless Dirac equation with a potential) and zero initial data. We prove two a…

Asymptotic stability in economic receding horizon control can be obtained under a strict dissipativity assumption, related to positive-definiteness of a so-called rotated cost, and through the use of suitable terminal cost and constraints.…

In this note we discuss the question of homogeneous $ L^2 L^{\infty} $ Strichartz estimates for the Wave equation in dimensions $ n \geq 4 $ raised by Fang and Wang and recently shown to fail by Guo, Li, Nakanishi and Yan using probability…