Semiclassical Theory of Short Periodic Orbits in Quantum Chaos

We have developed a semiclassical theory of short periodic orbits to obtain all quantum information of a bounded chaotic Hamiltonian system. If T_1 is the period of the shortest periodic orbit, T_2 the period of the next one and so on, the number N_p.o. of periodic orbits required in the calculation is such that T_1+...+T_N_{p.o} is approximately T_H, with T_H the Heisenberg time. As a result N_p.o \simeq h T_{H}/\ln (h T_{H}), where h is the topological entropy. For methods related to the trace formula N_{p.o} \simeq \exp(h T_{H})/ (h T_{H}).