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The non-relativistic bosonic ground state is studied for quantum N -body systems with Coulomb interactions, modeling atoms or ions made of N “bosonic point electrons” bound to an atomic point nucleus of Z absolute “electron” charges, treated in Born–Oppenheimer approximation (the...
For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h , for Re h≠0 . A survey of models known to have the...
We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.
We consider a large neutral molecule with total nuclear charge Z in a model with self-generated classical magnetic field and where the kinetic energy of the electrons is treated relativistically. To ensure stability, we assume that Z α < 2/π, where α denotes the fine structure constant. We are...
We start from the geometrical observation that a finite set of pure states correspond to some points on a sphere and their convex span cannot be the whole set of states. If we call the left over entangled we can pursue this picture from the simplest case of a two dimensional Hilbert space to the...
Given a two-dimensional no-pair Weyl operator W Z with a point nucleus of charge Z , we show that a homogeneous magnetic field does not lower the critical charge beyond which it collapses.
Brownian motions on a metric graph are defined. Their generators are characterized as Laplace operators subject to Wentzell boundary at every vertex. Conversely, given a set of Wentzell boundary conditions at the vertices of a metric graph, a Brownian motion is constructed pathwise on this graph...
In this work we reexamine the many-fermion problem in arbitrary dimensions. It is shown that in two dimensions or higher, the Hamiltonian of interacting fermions can be separated into individual nonintersecting sectors labeled by the wave-vector q⃗ . Within each sector the Hamiltonian maps onto...
In this paper we provide a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms.
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