Quantum quenches and thermalization on scale-free graphs

We show that after a quantum quench of the parameter controlling the number of particles in a Fermi-Hubbard model on scale free graphs, the distribution of energy modes follows a power law dependent on the quenched parameter and the connectivity of the graph. This paper contributes to the literature of quantum quenches on lattices, in which, for many integrable lattice models the distribution of modes after a quench thermalizes to a Generalized Gibbs Ensemble; this paper provides another example of distribution which can arise after relaxation. We argue that the main role is played by the symmetry of the underlying lattice which, in the case we study, is scale free, and to the distortion in the density of modes.Comment: 10 pages; 5 figures; accepted for publication in JTA

Asymptotic behavior of memristive circuits

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.Comment: 20 pages, 8 figures; proofs corrected, figures changed; results substantially unchanged; to appear in Entrop

Properties of Quantum Graphity at Low Temperature

We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms. Using mean field theory we find that an order parameter for the model is the average valence of the graph. We calculate the equilibrium distribution for the valence as an implicit function of the temperature. In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion. A discussion of the susceptibility function and a generalization of the model are given in the end.Comment: 21 pages, 5 figures; a plot added, corrections added; Accepted for publication in PR

Trajectories entropy in dynamical graphs with memory

In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.Comment: 15 pages one column, 10 figures; new analysis and memristor models added. Text improve

GEMs and amplitude bounds in the colored Boulatov model

In this paper we construct a methodology for separating the divergencies due to different topological manifolds dual to Feynman graphs in colored group field theory. After having introduced the amplitude bounds using propagator cuts, we show how Graph-Encoded-Manifolds (GEM) techniques can be used in order to factorize divergencies related to different parts of the dual topologies of the Feynman graphs in the general case. We show the potential of the formalism in the case of 3-dimensional solid torii in the colored Boulatov model.Comment: 20 pages; 20 Figures; Style changed, discussion improved and typos corrected, citations added; These GEMs are not related to "Global Embedding Minkowskian spacetimes

Correlations and Clustering in Wholesale Electricity Markets

We study the structure of locational marginal prices in day-ahead and real-time wholesale electricity markets. In particular, we consider the case of two North American markets and show that the price correlations contain information on the locational structure of the grid. We study various clustering methods and introduce a type of correlation function based on event synchronization for spiky time series, and another based on string correlations of location names provided by the markets. This allows us to reconstruct aspects of the locational structure of the grid.Comment: 30 pages, several picture

Comment on `Spinning loop black holes' [arXiv:1006.0232]

We review the derivations and conclusions made in Caravelli and Modesto (2010 \textit{Class. Quantum Grav.} \textbf{27} 245022, arXiv:1006.0232) and show that most of the analysis performed there is not valid.Comment: 2 pages, 1 figur

Memristors for the Curious Outsiders

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page