相关论文: Gauss sums, superoscillations and the Talbot carpe…
We study random exponential sums of the form $\sum_{k=1}^nX_k\times\ex p\{i(\lambda_k^{(1)}t_1+...+\lambda_k^{(s)}t_s)\}$, where $\{X_n\}$ is a sequence of random variables and $\{\lambda_n^{(i)}:1\leq i\leq s\}$ are sequences of real…
The present paper is devoted to the semiclassical analysis of linear Schr\"odinger equations from a Gabor frame perspective. We consider (time-dependent) smooth Hamiltonians with at most quadratic growth. Then we construct higher order…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry.…
We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower order term $q(t,x)$, we can recover the X-ray transform of…
We eliminate by KAM methods the time dependence in a class of linear differential equations in $\ell^2$ subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator $…
In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system which can be interpreted as a one-parameter deformation of the…
We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…
We develop a non-linear distributional renormalisation algebra for Gaussian Quantum Foam, built from sequences of scaled Gaussians on spacelike hypersurfaces of homotopic, globally hyperbolic spacetimes and their distributional limits. The…
We analytically derive novel explicit integral representations for the solution of nonhomogeneous initial-boundary-value problems for a large category of evolution partial differential equations of Sobolev-Galpern type with generic…
We show that the Collins-Soper-Sterman resummation approach to the derivation of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is gauge invariant. The special gauge-dependent parton distribution function employed in the…
We consider the kinetic derivative nonlinear Schr\"odinger equation, which is a one-dimensional nonlinear Schr\"odinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. In our previous work, we proved…
The purpose of this article is to construct global solutions, in a probabilistic sense, for the nonlinear Schr{\"o}dinger equation posed on $\mathbb{R}^d$, in a supercritical regime. Firstly, we establish Bourgain type bilinear estimates…
There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One…
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational methods, such as the classical circulant embedding technique…
The stationary Schroedinger equation of the harmonic oscillator is deformed by a Darboux transformation to construct time-dependent potentials with the oscillator profile. The Darboux (supersymmetric or factorization) method is usually…
In this paper a class of oscillatory integrals is interpreted as a limit of Lebesgue integrals with Gaussian regularizers. The convergence of the regularized integrals is shown with an improved version of iterative integration by parts that…
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral…
This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.…
Using the Carleman linearization technique the continuous iteration of a mapping is studied. Based on the detailed analysis of the Carleman embedding matrix the precise mathematical meaning is given to such notion. The ordinary differential…