Related papers: Semiclassical Lp estimates
In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lam\'e and the Laplacian…
Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…
We present and empirically evaluate an efficient algorithm that learns to aggregate the predictions of an ensemble of binary classifiers. The algorithm uses the structure of the ensemble predictions on unlabeled data to yield significant…
In Semi-Supervised Semi-Private (SP) learning, the learner has access to both public unlabelled and private labelled data. We propose a computationally efficient algorithm that, under mild assumptions on the data, provably achieves…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
The interaction of a weakly bound Rydberg electron with an electromagnetic half-cycle pulse (HCP) is described with the help of a multidimensional semiclassical treatment. This approach relates the quantum evolution of the electron to its…
A method for computing lower bounds to eigenvalues of sums of lower semibounded self-adjoint operators is presented. We apply the method to one-electron Hamiltonians. To improve the lower bounds we consider symmetry of molecules and use…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
There are three upper limits (2, 2.sqrt{2}, 2.sqrt{3}) of the Bell operator corresponding to different physical concepts: classical, hidden-variable and quantum-mechanical. Only the classical concept corresponding to the lowest limit has…
In the first section of the present work, we introduce the concept of pseudocomplementation for semirings and show semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some…
We study the semiclassical behaviour of a two--dimensional nonintegrable system. In particular we analyze the question of quantum corrections to the semiclassical quantization obtaining up to the second order of perturbation theory an…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this letter, we show that the Semiclassical Einstein's Field Equation can be recovered using the generalized entropy $S_{gen}$. This approach is reminiscent of non-equilibrium thermodynamics. Furthermore, contrary to the entanglement…
This paper is concerned with nonlinear elliptic equations in nondivergence form where the operator has a first order drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative…
We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the $p$-Laplace equation. We investigate the maximum extent for the…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole $\eps_2$, octupole $\eps_3$, and hexadecapole $\eps_4$) deformations of simple metal clusters with $90 \le N \le 550$ atoms in their…
In this note we examine the a priori and a posteriori analysis of discontinuous Galerkin finite element discretisations of semilinear elliptic PDEs with polynomial nonlinearity. We show that optimal a priori error bounds in the energy norm…
The chemical potiential for the ground states of the atomic elements have been calculated within the semiclassical approximation The present work closely follows Schwinger and Englert's semiclassical treatment of atomic structure.
It has been suggested in arXiv:1010.1415 that certain derivatively coupled non-renormalizable scalar field theories might restore the perturbative unitarity of high energy hard scatterings by classicalization, i.e. formation of…