Universal Braess paradox in open quantum dots

Abstract

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 ...

Anomalous transport of light at the phase transition to localization: strong dependence with incident angle

“…We demonstrate that the transport of light in the low concentration sample behaves insensitive with respect to the incidence angle (internal reflection), as expected at diffusive regime, while the high concentration sample shows a decrease of optical conductance and an increase of absorption near the input border. We remark that this anomalous behavior of transport of light near the mobility edge with the internal reflection has been theoretically predicted by Ramos and co-workers in disordered electronic system [42] but never shown in optics. These results could open new avenues for the design and manufacture of more efficient photonic devices based on strongly disordered optical media.…”

“…The increase of localization with incidence angle near the input border could be also interpreted as that photons from superficial localized states that would be emitted by nonlinear effects (non-equilibrium) [43,55] can be again trapped in another superficial localized state, due to the increase of internal reflection. This latter implies in that the density and residence time (Q factor) of superficial localized states would increase as internal reflection (incidence angle) increases, which can be inferred from the theoretical predictions of Mirlin [39,40] and Ramos and co-workers [42] in disordered electronic media. Notice that an increase of the internal reflection with incidence angle would be remarkable, mainly for the coherently backscattered photons (previously localized), due to the enhanced refractive index that these photons would feel.…”

“…An increase of the FAP value is observed as the incidence angle is increased (figure S3g supplementary material), reveling an increase of leO and absorption near the input border as the incidence angle is increased. The latter can be understood as that, an increase in the incidence angle provokes an increase in the density of superficial localized states by the increase of the internal reflection [42]. In turn, an increase in the density of superficial localized states leads to an increase of the light-matter interaction [1,6], which would result in an increase of absorption ((lIn0) − ) and refractive index (neff0) near the input border.…”

Braess Paradox in a quantum network

“…In [20] it was shown that while sending classical information over a network, the efcets of Braess paradox can be mitigated with access to quantum resources. In [21] Braess paradox was shown to occur in chaotic quantum dots.…”

Time-reversal symmetry breaking and decoherence in chaotic Dirac billiards

“…The theoretical works covering this topic include universal fingerprints as the probability distributions of transmission eigenvalues and conductance [24][25][26][27][28], interference effects [29][30][31][32][33][34], entanglement [8,27,35,36], time-reversal symmetry breaking [25,28,[37][38][39] and phase coherence breaking or decoherence [40][41][42][43][44], which produce a large number of experimental fundamental consequences [5][6][7][8]. However, the analytical results are usually obtained in very specific regimes [5,6], motivating numerical studies of regimes beyond such analytical limitations and giving a deep understanding of electronic transport properties [26,28,36,38,45].…”