LETTER TO THE EDITOR The diagonal approximation for non-time-reversal-symmetric systems

Abstract. We present a simple, heuristic justification for the diagonal approximation in the periodic orbit theory of long-range spectral statistics for chaotic systems without time reversal symmetry. For ergodic systems, this extends the validity of the approximation beyond the log.1=h̄ / time, where it is supported by more elementary arguments, to times of the order of the Heisenberg time TH D 2h ̄ Nd. This is in agreement with eigenvalue correlations in the Gaussian unitary ensemble of random matrix theory. For diffusive systems, the same argument suggests that the diagonal approximation breaks down on a time scale consistent with that expected on the basis of the scaling theory of localization. Random matrix theory (RMT) models the universal behaviour of quantum systems that are chaotic in the classical limit [1–4]. Consider, for example, the form facto