相关论文: Network Models in Class C on Arbitrary Graphs

We investigate a randomly evolving process of subgraphs in an underlying host graph using the spectral theory of semigroups related to the Tsetlin library and hyperplane arrangements. Starting with some initial subgraph, at each iteration,…

The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…

Electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices. We solve the problem of its calculation using a quantum network model. The proposed scheme consists of three…

The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…

The question of perfect state transfer existence in quantum spin networks based on weighted graphs has been recently presented by many authors. We give a simple condition for characterizing weighted circulant graphs allowing perfect state…

Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…

We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…

We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalised tensor networks. This class specifically includes spin networks, the kinematic…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

Advances in recent years have made it possible to explore quantum dots as a viable technology for scalable quantum information processing. Charge qubits for example can be realized in the lowest bound states of coupled quantum dots and the…

We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…

The theoretical description of transport in a wide class of novel materials is based upon quantum percolation and related random resistor network (RRN) models. We examine the localization properties of electronic states of diverse…

Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges,…

We study the propagation of wave packets for a one-dimensional system of two coupled Schr\"odinger equations with a cubic nonlinearity, in the semi-classical limit. Couplings are induced by the nonlinearity and by the potential, whose…

A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-{\em dynamical} models, which then…

Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…

We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…