We deduce the effects of quantum interference on the conductance of chaotic cavities by using a statistical ansatz for the S matrix. Assuming that the circular ensembles describe the S matrix of a chaotic cavity, we find that the conductance fluctuation and weak-localization magnitudes are universal: they are independent of the size and shape of the cavity if the number of incoming modes, N , is large. The limit of small N is more relevant experimentally; here we calculate the full distribution of the conductance and find striking differences as N changes or a magnetic field is applied.The effect of quantum interference on transport through microstructures has been intensively investigated and is one of the main subjects of mesoscopic physics [1]. For diffusive transport in disordered structures, both microscopic perturbative and macroscopic random matrix theories give a good account of the phenomena. In the latter case [2], one assumes that the transfer matrix for an ensemble of such disordered microstructures can be chosen from a simple statistical ensemble with only symmetry constraints applied. The success of this theory is perhaps the best theoretical demonstration of the ubiquity of mesoscopic interference effects.More recently, interest has focused on quantum transport in ballistic microstructures-structures in which impurity scattering can be neglected so that only scattering from the boundaries of the conducting region is important [1]. Quantum interference effects in such structures depend on the nature of the classical dynamics [3][4][5][6][7][8], in particular whether it is regular or chaotic [9]. Recent experiments have studied transport in such ballistic structures [10-13] and have detected a difference between nominally regular and chaotic structures [10].The theoretical work on this subject [3-7] has concentrated on either numerical quantum calculations or semiclassical theory. On the other hand, it has been proposed [8] that chaotic scattering in the quantum regime [14] should be described by a random matrix theory for the S-matrix. The emphasis in both that work and very recent work on the S-matrix of disordered structures [15] is on the properties of the eigenphases of S. The eigenphases, however, are not directly connected to the transport properties because they involve both reflection and transmission. In contrast, in this paper we derive the implications of such a random S-matrix theory for the quantum transport properties and provide numerical evidence that this theory applies to the class of ballistic microstructures investigated experimentally. In this way we obtain experimentally accessible predictions for the quantum transport properties of chaotic billiards.A quantum scattering problem is described by its Smatrix. For scattering involving two leads (see Fig. 1) each with N channels and width W , we havewhere r, t are the N × N reflection and transmission matrices for particles from the left and r ′ , t ′ for those from the right. In terms of S, the conductance is [16]Because of curren...

We demonstrate the existence of resistance fluctuations in experimentally realizable ballistic conductors due to scattering from geometric features. The magnetic-field and energy correlation functions are calculated both semiclassically and exactly numerically, and are found to have a scale determined by the underlying chaotic classical scattering. These systems provide a test of the "random" quantum behavior of classically chaotic systems.

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