Quantum Vacuum Energy in Graphs and Billiards

The vacuum (Casimir) energy in quantum field theory is a problem relevant both to new nanotechnology devices and to dark energy in cosmology. The crucial question is the dependence of the energy on the system geometry under study. Despite much progress since the first prediction of the Casimir effect in 1948 and its subsequent experimental verification in simple geometries, even the sign of the force in nontrivial situations is still a matter of controversy. Mathematically, vacuum energy fits squarely into the spectral theory of second-order self-adjoint elliptic linear differential operators. Specifically, one promising approach is based on the small-t asymptotics of the cylinder kernel e^(-t sqrt(H)), where H is the self-adjoint operator under study. In contrast with the well-studied heat kernel e^(-tH), the cylinder kernel depends in a non-local way on the geometry of the problem. We discuss some results by the Louisiana-Oklahoma-Texas collaboration on vacuum energy in model systems, including quantum graphs and two-dimensional cavities. The results may shed light on general questions, including the relationship between vacuum energy and periodic or closed classical orbits, and the contribution to vacuum energy of boundaries, edges, and corners.Comment: 10 pages, 3 figure

Periodic orbit effects on conductance peak heights in a chaotic quantum dot

We study the effects of short-time classical dynamics on the distribution of Coulomb blockade peak heights in a chaotic quantum dot. The location of one or both leads relative to the short unstable orbits, as well as relative to the symmetry lines, can have large effects on the moments and on the head and tail of the conductance distribution. We study these effects analytically as a function of the stability exponent of the orbits involved, and also numerically using the stadium billiard as a model. The predicted behavior is robust, depending only on the short-time behavior of the many-body quantum system, and consequently insensitive to moderate-sized perturbations.Comment: 14 pages, including 6 figure

Gamma ray lines from TeV dark matter

We calculate, using unitarity, a lower bound on the branching ratio $\chi\chi\to \gamma\gamma$ and $\chi\chi\to \gamma Z$, where $\chi$ is any halo dark matter particle that has $W^+W^-$ as one of the major annihilation modes. Examples of such particles are supersymmetric particles with a dominant Higgsino component, or heavy triplet neutrinos. A substantial branching ratio is found for the $\gamma\gamma$ and $\gamma Z$ modes. We estimate the strength of the monoenergetic $\gamma$ ray lines that result from such annihilations in the Galactic or LMC halos. (Latex file; 2 compressed uuencoded postscript figures available by anonymous ftp from vanosf.physto.se in file pub/figures/lines.uu)Comment: 11 pages, USITP-94-03; PAR-LPTHE 94-0

A mesoscale numerical model and the development of a severe storm prediction system

The use of a mesoscale numerical model for predicting preferred zones of severe storm development is analyzed. A 60 consecutive day real-time test of the prediction system during the spring of 1978 proved useful in determining the problems and potentialities of such a system. A case study of severe storm development from this test period is described and compared to the model forecast fields