We have measured the probability density jc͑r͒j 2 in the semiclassical limit of a classically chaotic square well potential with and without time reversal symmetry, and compared our findings with theoretical predictions. We find that wave functions with time-reversal symmetry have larger fluctuations than those without time-reversal symmetry. To quantify the degree of these fluctuations, eigenmodes both with and without time-reversal symmetry are statistically analyzed and the two-point spatial correlation function and the probability density distribution function of the eigenmodes are found to agree with theoretical predictions. [S0031-9007(98)07259-7] PACS numbers: 05.45. + b, 03.65.Ge, 85.70.Ge The quantum mechanical behavior of nonintegrable systems has been a very intriguing subject for many decades and is still one of active research [1]. This is not only because of the interesting fundamental physics of "quantum chaos" but also because of the strong analogy between the quantum mechanical behavior of mesoscopic systems and the wave chaotic behavior of nonintegrable systems [2]. Hence the subject can pave the way to understanding the statistical properties of electronic eigenstates and eigenfunctions of mesoscopic systems, such as quantum dots and quantum wires, which will be increasingly important for future technological applications.Theories and numerical simulations suggest that for integrable (nonchaotic) systems a large degree of degeneracy is allowed in the eigenvalues of the system; therefore the spacing between neighboring eigenvalues obeys Poisson statistics. For nonintegrable systems the existence of classical chaos breaks the degeneracies, and therefore the eigenvalue spacing statistics are clearly no longer Poisson. Theories propose that the statistics of the eigenvalue spacing are governed not only by the integrability but also by the time-reversal symmetry of the system. One expects the spectral properties of a chaotic system with time-reversal symmetry to follow the statistics of a Gaussian orthogonal ensemble (GOE) of random matrices, while a chaotic system with broken time-reversal symmetry is expected to follow the statistics of a Gaussian unitary ensemble (GUE) of random matrices. In recent years several experiments similar to those described here have demonstrated that these theoretical predictions are indeed correct [3][4][5].An even more intriguing subject is the investigation of the eigenfunctions of wave chaotic systems. Although some of the interesting behavior of eigenfunctions in systems with GOE symmetry has been explored by several groups [6][7][8], there has been no experimental examination of the time-reversal symmetry dependence of the eigenfunction behavior [9]. Investigating the detailed behavior of both time-reversal symmetric (TRS) and time-reversal symmetry broken (TRSB) wave functions is also imperative as it will give insights into the behavior of electronic wave functions of nanoscale structures that have these symmetries.In this paper we report our experimental re...

We have developed a method to measure the electric field standing wave distributions in a microwave resonator using a scanned perturbation technique.Fast and reliable solutions to the Helmholtz equation (and to the Schrödinger equation for two dimensional systems) with arbitrarily-shaped boundaries are obtained. We use a pin perturbation to image primarily the microwave electric field amplitude, and we demonstrate the ability to image broken time-reversal symmetry standing wave patterns produced with a magnetized ferrite in the cavity. The whole cavity, including areas very close to the walls, can be imaged using this technique with high spatial resolution over a broad range of frequencies.

In recent years, many DHT-based P2P systems have been proposed, analyzed, and certain deployments have reached a global scale with nearly one million nodes. One is thus faced with the question of which particular DHT system to choose, and whether some are inherently more robust and scalable. Toward developing such a comparative framework, we present the reachable component method (RCM) for analyzing the performance of different DHT routing systems subject to random failures. We apply RCM to five DHT systems and obtain analytical expressions that characterize their routability as a continuous function of system size and node failure probability. An important consequence is that in the large-network limit, the routability of certain DHT systems go to zero for any non-zero probability of node failure. These DHT routing algorithms are therefore unscalable, while some others, including Kademlia, which powers the popular eDonkey P2P system, are found to be scalable.

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a two-dimensional microwave resonator are analyzed as a function of an experimentally determined time-reversal symmetry-breaking parameter. We test four theories of one-point eigenfunction statistics and introduce a new theory relating the one-point and two-point statistical properties in the crossover regime. We also find a universal correlation between the one-point and two-point statistical parameters for the crossover eigenfunctions.

Abstract-We present a novel framework, called balanced overlay networks (BON), that provides scalable, decentralized load balancing for distributed computing using large-scale pools of heterogeneous computers. Fundamentally, BON encodes the information about each node's available computational resources in the structure of the links connecting the nodes in the network. This distributed encoding is self-organized, with each node managing its in-degree and local connectivity via randomwalk sampling. Assignment of incoming jobs to nodes with the most free resources is also accomplished by sampling the nodes via short random walks. Extensive simulations show that the resulting highly dynamic and self-organized graph structure can efficiently balance computational load throughout large-scale networks. These simulations cover a wide spectrum of cases, including significant heterogeneity in available computing resources and high burstiness in incoming load. We provide analytical results that prove BON's scalability for truly large-scale networks: in particular we show that under certain ideal conditions, the network structure converges to Erdös-Rényi (ER) random graphs; our simulation results, however, show that the algorithm does much better, and the structures seem to approach the ideal case of d-regular random graphs. We also make a connection between highly-loaded BONs and the well-known ball-bin randomized load balancing framework.