Jens Bolte and Jonathan Harrison 2003 J. Phys. A: Math. Gen. 36 2747 doi:10.1088/0305-4470/36/11/307
Jens Bolte and Jonathan Harrison
Show affiliationsWe determine conditions for the quantization of graphs using the Dirac operator for both two- and four-component spinors. According to the Bohigas–Giannoni–Schmit conjecture for such systems with time-reversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantization condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation.
Issue 11 (21 March 2003)
Received 23 October 2002, in final form 29 January 2003
Published 6 March 2003
Jens Bolte and Jonathan Harrison 2003 J. Phys. A: Math. Gen. 36 2747
Raffaele Rani et al 2003 Class. Quantum Grav. 20 1929
E. L. Wright et al. 2009 ApJS 180 283
E Minguzzi 2003 Class. Quantum Grav. 20 2443
Markus J Buehler et al 2004 Modelling Simul. Mater. Sci. Eng. 12 S391
J. Dunkley et al. 2009 ApJS 180 306
B. Gold et al. 2009 ApJS 180 265
Brian G Spratt 2002 J. Radiol. Prot. 22 125
Alfonso García-Parrado and José M M Senovilla 2003 Class. Quantum Grav. 20 L139
Alfonso García-Parrado and José M M Senovilla 2003 Class. Quantum Grav. 20 625