The quantum chaos conjecture and generalized continued fractions

The proof of the quantum chaos conjecture for a broad class of quantum systems including the ‘kicked rotator’ model as a special case is given: the distribution of distances between adjacent energy levels is close to Poisson distribution and differ from it by a third order term of smallness. The proof essentially uses results on the distribution of distances between adjacent fractional parts of polynomial values. The estimate of the remainder term is based on the new theory of generalized continued fractions for vectors.