In this work we use a diagrammatic method for integration over the unitary group to obtain a quantum correction to the average shot-noise power of a chaotic cavity with non-ideal contacts. We present maximally crossed diagrams representing the physical modes of the system responsible for the dominant quantum correction. We demonstrate with explicit calculations that the suppression-amplification effect reported in Ramos et al (2008 Phys. Rev. B 78 235305) occurs both for systems in the presence of time-reversal (TR) and spin-rotation (SR) symmetries and for systems with broken SR symmetry but in the presence of TR symmetry.

We present analytical results for the leading ͑weak-localization͒ quantum interference correction to the shot-noise power in a ballistic chaotic cavity coupled nonideally to two electron reservoirs via leads with an arbitrary number of open scattering channels. The calculations were performed using two independent methods: S-matrix diagrammatic perturbation theory and quantum circuit theory. We obtained an unexpected amplification-suppression transition as a function of both the number of open channels and the barriers' transparencies. The effect results from a subtle combination of temporal and spatial quantum coherence in the electron propagation through the system.

We present analytical and numerical results that demonstrate the presence of the Braess paradox in chaotic quantum dots. The paradox that we identify, originally perceived in classical networks, shows that the addition of more capacity to the network can suppress the current flow in the universal regime. We investigate the weak localization term, showing that it presents the paradox encoded in a saturation minimum of the conductance, provided the existence of hyper-flow in the external leads. In addition, we demonstrate that the weak localization suffers a transition signal depending on the over-capacity lead, and presents an echo on the magnetic crossover, before going to zero due to the full time reversal symmetry breaking. We also show that the quantum interference contribution can dominate the Ohm term in the presence of constrictions, and that the corresponding Fano factor engenders an anomalous behavior. Introduction. -The Braess paradox asserts that the addition of a new road to the paths between two locations can counterintuitively increase the travel time of a vehicle [1]. The associated flux density depletion was also perceived in scenarios such as electrical networks [2], wave packet propagation through a circular ring [3], mechanical devices, scanning gate microscopy among others [4]. Generically, we can say that the addition of extra capacity to a network can paradoxically lead to a depletion in its overall performance, under certain circunstances.The classic arguments for the Braess paradox include the Nash equilibrium condition [5] about the competition between extra roads and the incentives to change the vehicle routes. In the electronic transport through a parallel network, Ohm's law imposes a conductance amplification according to the increasing of the number of parallel leads, i.e., the absence of Braess paradox in classical electronic circuits. On the other hand, the dynamics suggested by quantum mechanics impose, as in Nash dynamics, a peculiar complex competition between the subjacent wave phenomena on multi-terminal nanostructures [6]. The Braess paradox has also been identified at the quantum level, both experimentally and numerically in an electrical network in [2], and numerically in a circular quantum ring with the propagation of the wave packet calculated using the split-operator technique [3]. The main conclusion is that the transport inefficiency also occurs at the nonometric scale, strongly influenced by quantum scattering and interference.Such factual evidences motivate an investigation of quantum dots (QDs) coupled thought leads and performing appropriate networks. The more general investigation occurs in the universal regime, achieved when the chaos, due to the confinement of several resonances within each QD, generate statistical phenomena involving only fundamental symmetries of nature [7,8]. The symmetries significantly affect both the interference, manifest in the quantum sector of the conductance (the weak localization term), and the corpuscular electronic nature, manifest ...

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We investigate the propagation of electronic waves described by the Dirac equation subject to a Lévy-type disorder distribution. Our numerical calculations, based on the transfer matrix method, in a system with a distribution of potential barriers show that it presents a phase transition from anomalous to standard to anomalous localization as the incidence energy increases. In contrast, electronic waves described by the Schrödinger equation do not present such transitions. Moreover, we obtain the phase diagram delimiting anomalous and standard localization regimes, in the form of an incidence angle versus incidence energy diagram, and argue that transitions can also be characterized by the behavior of the dispersion of the transmission. We attribute this transition to an abrupt reduction in the transmittance of the system when the incidence angle is higher than a critical value which induces a decrease in the transmission fluctuations.