arXiv subjects

Michael Loss

Publications and source records attributed to Michael Loss.

76 records · Page 5Linked to original sources

arXiv1999

Self-energy of electrons in non-perturbative QED

Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass renormalization. For $N$ fermions the bounds are proportional to $N$, but for bosons they are sublinear, which implies `binding', and hence that `free' bosons are never free. Both `relativistic' and non-relativistic kinematics are considered. Our bounds are non-perturbative and differ significantly from the predictions of perturbation theory.

math-ph↗

arXiv1999

Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature

This article is an expanded version of the plenary talk given by Evans Harrell at QMath98, a meeting in Prague, June 1998. We consider Laplace operators and Schrödinger operators with potentials containing curvature on certain regions of nontrivial topology, especially closed curves, annular domains, and shells. Dirichlet boundary conditions are imposed on any boundaries. Under suitable assumptions we prove that the fundamental eigenvalue is maximized when the geometry is round. We also comment on the use of coordinate transformations for these operators and mention some open problems.

math-ph↗

arXiv1995

Stability of Matter in Magnetic Fields

In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if $α$ or $Z$ is too large. Here we prove that matter {\it is stable\/} if $α<0.06$ and $Zα^2<0.04$.

cond-mat↗

arXiv1992

Fluxes, Laplacians and Kasteleyn's Theorem

The following problem, which stems from the ``flux phase'' problem in condensed matter physics, is analyzed and extended here: One is given a planar graph (or lattice) with prescribed vertices, edges and a weight $\vert t_{xy}\vert$ on each edge $(x,y)$. The flux phase problem (which we partially solve) is to find the real phase function on the edges, $θ(x,y)$, so that the matrix $T:=\{\vert t_{xy}\vert {\rm exp}[iθ(x,y)]\}$ minimizes the sum of the negative eigenvalues of $-T$. One extension of this problem which is also partially solved is the analogous question for the Falicov-Kimball model. There one replaces the matrix $-T$ by $-T+V$, where $V$ is a diagonal matrix representing a potential. Another extension of this problem, which we solve completely for planar, bipartite graphs, is to maximize $\vert {\rm det}\ T \vert$. Our analysis of this determinant problem is closely connected with Kasteleyn's 1961 theorem (for arbitrary planar graphs) and, indeed, yields an alternate, and we believe more transparent proof of it. {}.

cond-mat↗