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We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the so-called diagonal approximation, i.e. by incorporating classical action correlations. In this context we review and explain the two main trajectory-based methods developed for calculating quantum corrections: the configuration space approach and the phase space approach that can be regarded as less illustrative but more general than the first one.

Classical Correlations and Quantum Interference in Ballistic Conductors