Related papers: The operator approach to the truncated multidimens…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particle methods through a matching with a set of…
Let $\mathsf{A}=\{a_1,\dots,a_m\}$, $m\in\mathbb{N}$, be measurable functions on a measurable space $(\mathcal{X},\mathfrak{A})$. If $\mu$ is a positive measure on $(\mathcal{X},\mathfrak{A})$ such that $\int a_i d\mu<\infty$ for all $i$,…
We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
The dominant method for defining multivariate operator means is to express them as fix-points under a contraction with respect to the Thompson metric. Although this method is powerful, it crucially depends on monotonicity. We are developing…
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defined in such a way that the wealth of techniques developed…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be…
A time operator is a Hermitian operator that is canonically conjugate to a given Hamiltonian. For a particle in 1-dimension, a Hamiltonian conjugate operator in position representation can be obtained by solving a hyperbolic second-order…
We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space…
An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system…
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…
We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The…
In this article we study the bivariate truncated moment problem (TMP) of degree $2k$ on the union of parallel lines. First we present an alternative proof of Fialkow's solution \cite{Fia15} to the TMP on the union of two parallel lines…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning…
This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation…
Time operator can be introduced by three different approaches: by pertaining it to dynamical variables; by quantizing the classical expression of time; taken as the restriction of energy shift generator to the Hilbert space of a physical…