Vacuum energy and repulsive Casimir forces in quantum star graphs
Abstract
Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive, but we present several counterexamples, notably a simple type of quantum graph in which the sign of the force depends upon the number of edges. We also show that Casimir forces in quantum graphs can be reliably computed by summing over the classical orbits, and study the rate of convergence of the periodic orbit expansion. In generic situations where no analytic expression is available, the sign and approximate magnitude of Casimir forces can often be obtained using only the shortest classical orbits.
 Publication:

Physical Review A
 Pub Date:
 July 2007
 DOI:
 10.1103/PhysRevA.76.012118
 arXiv:
 arXiv:quantph/0608122
 Bibcode:
 2007PhRvA..76a2118F
 Keywords:

 03.65.Sq;
 03.70.+k;
 11.10.Kk;
 42.25.Gy;
 Semiclassical theories and applications;
 Theory of quantized fields;
 Field theories in dimensions other than four;
 Edge and boundary effects;
 reflection and refraction;
 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 4 pages, 2 figures