Semiclassics beyond the diagonal approximation [Elektronische Ressource] / vorgelegt von Marko Turek

Semiclassics beyond the diagonalapproximationDissertationzur Erlangung des Doktorgradesder Naturwissenschaften (Dr. rer. nat.)der naturwissenschaftlichen Fakult˜at II { Physikder Universit˜at Regensburgvorgelegt vonMarko Turekaus Halle (Saale)Februar 2004Promotionsgesuch eingereicht am 05. Februar 2004Promotionskolloquium am 21. April 2004Die Arbeit wurde von Prof. Dr. Klaus Richter angeleitet.Prufungsaussc˜ hu…:Vorsitzender: Prof. Dr. Christian Back1. Gutachter: Prof. Dr. Klaus Richter2. Gutachter: Prof. Dr. Matthias BrackWeiterer Prufer:˜ Prof. Dr. Tilo WettigAbstractThe statistical properties of the energy spectrum of classically chaotic closed quan-tumsystemsarethecentralsubjectofthisthesis. IthasbeenconjecturedbyO.Bo-higas, M.-J. Giannoni and C. Schmit that the spectral statistics of chaotic sys-tems is universal and can be described by random-matrix theory. This conjecturehas been conflrmed in many experiments and numerical studies but a formal proofis still lacking. In this thesis we present a semiclassical evaluation of the spectralform factor which goes beyond M.V. Berry’s diagonal approximation. To thisend we extend a method developed by M. Sieber and K. Richter for a speciflcsystem: the motion of a particle on a two-dimensional surface of constant negativecurvature.