Vertex routing models

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.Comment: 12 pages, 6 figure

Interaction induced Fermi-surface renormalization in the t1−t2t_1{-}t_2 Hubbard model close to the Mott-Hubbard transition

We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating state, with a first-order reorganization when crossing into the conducting state.Comment: 6 pages and 7 figure

Statistics of the electromagnetic response of a chaotic reverberation chamber

This article presents a study of the electromagnetic response of a chaotic reverberation chamber (RC) in the presence of losses. By means of simulations and of experiments, the fluctuations in the maxima of the field obtained in a conventional mode-stirred RC are compared with those in a chaotic RC in the neighborhood of the Lowest Useable Frequency (LUF). The present work illustrates that the universal spectral and spatial statistical properties of chaotic RCs allow to meet more adequately the criteria required by the Standard IEC 61000-4-21 to perform tests of electromagnetic compatibility.Comment: 6 pages, 9 figure

Tunnelling matrix elements with antiferromagnetic Gutzwiller wave functions

We use a generalized Gutzwiller Approximation (GA) elaborated to evaluate matrix elements with partially projected wave functions and formerly applied to homogeneous systems. In the present paper we consider projected single-particle (hole) excitations for electronic systems with antiferromagnetic (AFM) order and obtain the corresponding tunnelling probabilities. The accuracy and the reliability of our analytical approximation is tested using the Variational Monte Carlo (VMC). Possible comparisons with experimental results are also discussed.Comment: 16 pages, 10 figure

Speech Notes for Eleanor Snell\u27s Testimonial Dinner, May 22, 1970

These are typed notes for speeches given at Eleanor Snell\u27s Testimonial Dinner.https://digitalcommons.ursinus.edu/snell_docs/1034/thumbnail.jp

A Variational Monte Carlo Study of the Current Carried by a Quasiparticle

With the use of Gutzwiller-projected variational states, we study the renormalization of the current carried by the quasiparticles in high-temperature superconductors and of the quasiparticle spectral weight. The renormalization coefficients are computed by the variational Monte Carlo technique, under the assumption that quasiparticle excitations may be described by Gutzwiller-projected BCS quasiparticles. We find that the current renormalization coefficient decreases with decreasing doping and tends to zero at zero doping. The quasiparticle spectral weight Z_+ for adding an electron shows an interesting structure in k space, which corresponds to a depression of the occupation number k just outside the Fermi surface. The perturbative corrections to those quantities in the Hubbard model are also discussed.Comment: 9 pages, 9 figure

Bosonic resonating valence bond wave function for doped Mott insulators

We propose a new class of ground states for doped Mott insulators in the electron second-quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the t-J model. At half filling, the ground state describes spin correlations of the S=1/2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi-liquid-like in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a d-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.Comment: 28 pages, 5 figures, final version to appear in Phys. Rev.