Algebraic Fermi curves
Alternative method for determining the Feynman propagator of a non-relativistic quantum mechanical problem.
An analysis of the effect of ghost force oscillation on quasicontinuum error
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic...
An electrostatic inequality with applications to the constitution of matter
An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics
This paper gives an error analysis of the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the high-dimensional linear Schrödinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main result of this...
An infinite level atom coupled to a heat bath.
An upper and lower solution approach for a generalized Thomas-Fermi theory of neutral atoms.
Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential.
In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potentialVTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of⎧ y''(x) = x-1/2y3/2(x),⎨ y(0) = 1,⎩ y(∞) = 0.
Atomistic to Continuum limits for computational materials science
The present article is an overview of some mathematical results, which provide elements of rigorous basis for some multiscale computations in materials science. The emphasis is laid upon atomistic to continuum limits for crystalline materials. Various mathematical approaches are addressed. The setting is stationary. The relation to existing techniques used in the engineering literature is investigated.
Auger spectra and different ionic charges following and sub-shells photoionization of Kr atoms.
Axiomatic approach to perturbative quantum field theory
Best N-term approximation in electronic structure calculations. II. Jastrow factors
We present a novel application of best N-term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best N-term approximation spaces , we prove...
Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix
We discuss best N-term approximation spaces for one-electron wavefunctions and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted spaces of wavelet coefficients to proof that both and ρ are in for all with . Our proof is based on the...
Born-Infeld electrodynamics: Clifford number and spinor representations.
Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations
One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and analyzing the...
Bounds on the excess charge and the ionization energy for the Hellmann-Weizsacker model
-cross products and a generalized quantum mechanical -body problem.
Charged fields, Higgs phenomenon and confinement. Lesson from soluble models
Charged particles with short range interactions
Charges in gauge theories.