相关论文: Sharp regularity results for many-electron wave fu…
We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.
We shall give a priori conditions on the illuminations $\phi_i$ such that the solutions to the Helmholtz equation $-div(a \nabla u^i)-k q u^i=0$ in \Omega, $u^i=\phi_i$ on $\partial\Omega$, and their gradients satisfy certain non-zero and…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
The evolution of the centre-of-mass wave-function for a mesoscopic particle according to the Schr\"odinger-Newton equation can be approximated by a harmonic potential, if the wave-function is narrow compared to the size of the particle. It…
The similarity of the electronic structures of NaFeAs and other Fe pnictides has been demonstrated on the basis of first-principle calculations. The global double-degeneracy of electronic bands along X-M and R-A direction indicates the…
Potential energy surfaces of electron dynamics (ePES) are constructed from a model of localized electron wave packets (eWP) with non-orthogonal valence-bond (VB) spin coupling and applied to quantum dynamics simulations of high harmonic…
In this paper, we prove a sharp local well-posedness result for spherically symmetric solutions to quasilinear wave equations with rough initial data, when the spatial dimension is three or higher. Our approach is based on Morawetz type…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problem \begin{equation}\label{ab eqn} \begin{cases} \partial_t u(t,x)=\psi(t,-i\nabla)u(t,x)+f(t,x),\quad &(t,x)\in(0,T)\times\mathbb{R}^d,\\…
We establish local regularity results for minimizers of autonomous vectorial integrals of Calculus of Variations, assuming $\psi$-growth conditions and imposing $\varphi$-quasiconvexity only in an asymptotic sense, both in the sub-quadratic…
A stochastic minimization method for a real-space wavefunction, $\Psi({\bf r}_{1},{\bf r}_{2}\ldots{\bf r}_{n})$, constrained to a chosen density, $\rho({\bf r})$, is developed. It enables the explicit calculation of the Levy constrained…
We present an example of an electronic wavefunction with maximally entangled MPS representation, in the sense that the bond dimension is maximal and cannot be lowered by any re-ordering of the underlying one-body basis. Our construction…
Let $G$ be a simple linear algebraic group defined over an algebraically closed field of characteristic $p\geq 0$ and let $\phi$ be a $p$-restricted irreducible representation of $G$. Let $T$ be a maximal torus of $G$ and $s\in T$. We say…
This paper is devoted to the study of the expected-integral multifunctions given in the form \begin{equation*} \operatorname{E}_\Phi(x):=\int_T\Phi_t(x)d\mu, \end{equation*} where $\Phi\colon T\times\mathbb{R}^n \rightrightarrows…
Recent neural networks demonstrated impressively accurate approximations of electronic ground-state wave functions. Such neural networks typically consist of a permutation-equivariant neural network followed by a permutation-antisymmetric…
In this paper we study the existence of solutions of a one-dimensional eigenvalue problem $-\left(|\phi_x|^{p-2}\phi_x\right)_x=\lambda \left(|\phi|^{q-2}\phi-f(\phi)\right)$ such that $\phi(0)=\phi(1)=0$, where $p,q>1$, $\lambda$ is a…
A previous article showed that alternative expressions for calculating oblate spheroidal radial functions of both kinds can provide accurate values over very large parameter ranges using double precision arithmetic, even where the…
The shape function f(k_+) describes Fermi motion effects in inclusive semi-leptonic decays such as B -> X_u+e+nu near the end-point of the lepton spectrum. We compute the leading one-loop corrections to the shape function f(k_+) in the…
We investigate fractional regularity estimates up to the boundary for solutions to fully nonlinear elliptic equations with measurable ingredients. Specifically, under the assumption of uniform ellipticity of the operator, we demonstrate…
A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring…