2 7 A ug 1 99 7 Semi - classical spectrum of integrable systems in a magnetic field

2 7 A ug 1 99 7 Heat kernel of integrable billiards in a magnetic field

Heat kernel of integrable billiards in a magnetic field. Abstract We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered one involving the large energy asymptotic expansion of the resolvent (Stewartson-Waechter method) is a...

ar X iv : h ep - t h / 99 05 22 4 v 2 2 7 A ug 1 99 9 Whitham Deformations and Tau Functions in N = 2 Supersymmetric Gauge Theories ∗

We review new aspects of integrable systems discovered recently in N = 2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten curves for classical gauge groups, (ii) its application to contact terms in the u-plane integral of topologically twisted theories, and (iii) a connection be...

0 v 1 1 2 A ug 1 99 7 PRIMORDIAL MAGNETIC FIELDS AND THEIR DEVELOPMENT ( APPLIED FIELD THEORY )

A ug 1 99 9 Semiclassical density of degeneracies in quantum regular systems

The spectrum of eigenenergies of a quantum integrable system whose hamil-tonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits. We compare the resu...

A ug 1 99 6 Exact Solutions of 1 + 1 Dimensional Dilaton Gravity Coupled to Matter

A class of integrable models of 1+1 dimensional dilaton gravity coupled to scalar and electromagnetic fields is obtained and explicitly solved. More general models are reduced to 0+1 dimensional Hamiltonian systems, for which two integrable classes (called s-integrable) are found and explicitly solved. As a special case, static spherical solutions of the Einstein gravity coupled to electromagne...