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When time-reversal symmetry is broken, the average conductance through a chaotic cavity, from an entrance lead with N 1 open channels to an exit lead with N 2 open channels, is given by N 1 N 2/ M, where M = N 1 + N 2. We show that, when tunnel barriers of reflectivity Îł are placed on the leads, two correction terms appear in the average conductance, and that one of them is proportional to Îł M . Since M ∼ â„Ź âˆ'1, this correction is exponentially small in the semiclassical limit. We derive this term from a semiclassical approximation, generally expected to give only leading orders in powers of â„Ź. Even though the theory is built perturbatively both in Îł and in 1/ M, the final result is exact. [ABSTRACT FROM AUTHOR]

We consider the problem of electronic quantum transport through ballistic mesoscopic systems with chaotic dynamics, connected to a three-terminal architecture in which one of the terminals has a tunnel barrier. Using a semiclassical approximation based on matrix integrals, we calculate several transport statistics, such as average and variance of conductance, average shot-noise power, among others, that give access to the extreme quantum regime (small channel numbers in the terminal) for broken and intact time-reversal symmetry, which the traditional random matrix approach does not access. As an application, we treat the dephasing regime. [ABSTRACT FROM AUTHOR]

In this article I present an introduction to the problem of quantum chaos, i.e. the characterization and treatment of quantum systems whose classical analogue has chaotic dynamics. Two of the main approaches to this problem are discussed: one is statistical, making use of random matrices, while the other is based on the semiclassical approximation. Results obtained by these approaches are mentioned for closed systems (spectral correlation functions), transport (moments like conductance and shot noise) and resonances (fractal Weyl law and fractal wave functions). [ABSTRACT FROM AUTHOR]

We present a semiclassical calculation, based on classical action correlations implemented by means of a matrix integral, of all moments of the Wigner–Smith time delay matrix, Q , in the context of quantum scattering through systems with chaotic dynamics. Our results are valid for broken time reversal symmetry and depend only on the classical dwell time and the number of open channels, M , which is arbitrary. Agreement with corresponding random matrix theory reduces to an identity involving some combinatorial concepts, which can be proved in special cases. • Implements an efficient semiclassical approach in terms of a matrix integral. • Computes general statistics of time delay in quantum chaotic systems. • Advances a new conjecture in the theory of symmetric polynomials. [ABSTRACT FROM AUTHOR]

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory. [ABSTRACT FROM AUTHOR]

We investigate the transition from integrability to chaos in a system built of usp(4) elements, both in the quantum case and in its classical limit, obtained using coherent states. This algebraic Hamiltonian consists in an integrable term plus a nonlinear perturbation, and we see that the level spacing distribution for the quantum system is well approximated by the Berry–Robnik–Brody distribution, and accordingly the classical limit displays mixed dynamics. [Copyright &y& Elsevier]

We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and therefore provide constructive interference. We calculate explicitly the first correlation functions, to leading orders in their energy arguments, for both unitary and orthogonal symmetry classes. The results agree with corresponding predictions from random matrix theory, thereby giving solid support to the conjecture of universality. [ABSTRACT FROM AUTHOR]