Editorial: The pre-history of Chaos—An Interdisciplinary Journal of Nonlinear Science

Published versio

Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling α exceeds a critical value α_c. Using sum rules, we show that the phonon spectral function has divergent (for N→∞) weight extending to zero frequency for α<α_c. The phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0<α<α_c and the q=π phonon does not soften (to zero frequency) at α=α_c.First author draf

Behavior and Breakdown of Higher-Order Fermi-Pasta-Ulam-Tsingou Recurrences

We investigate numerically the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the alpha and beta Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. Interestingly, these singularities depend very sensitively on the initial energy and the respective nonlinear parameters. Furthermore, we compare the mechanisms by which the super-recurrences in the two model's breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of super-recurrences in the beta-FPUT lattice is associated with the destruction of the so-called metastable state and hence is associated with relaxation towards equilibrium. For the alpha-FPUT lattice, we find this is not the case and show that the super-recurrences break down while the lattice is still metastable. We close with comments on the generality of our results for different lattice sizes

Chaos at Fifty

In 1963 Edward Lorenz revealed deterministic predictability to be an illusion and gave birth to a field that still thrives. This Feature Article discusses Lorenz's discovery and developments that followed from it.Comment: For an animated visualization of the Lorenz attractor, click here http://www.youtube.com/watch?v=iu4RdmBVdp

Critical Entanglement for the Half-Filled Extended Hubbard Model

We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied with careful pinning.Comment: 10 pages, 12 figure

Highly Deformable Graphene Kirigami

Graphene's exceptional mechanical properties, including its highest-known stiffness (1 TPa) and strength (100 GPa) have been exploited for various structural applications. However, graphene is also known to be quite brittle, with experimentally-measured tensile fracture strains that do not exceed a few percent. In this work, we introduce the notion of graphene kirigami, where concepts that have been used almost exclusively for macroscale structures are applied to dramatically enhance the stretchability of both zigzag and armchair graphene. Specifically, we show using classical molecular dynamics simulations that the yield and fracture strains of graphene can be enhanced by about a factor of three using kirigami as compared to standard monolayer graphene. This enhanced ductility in graphene should open up interesting opportunities not only mechanically, but also in coupling to graphene's electronic behavior.Comment: 5 pages, 7 figure

The mesoscopic magnetron as an open quantum system

Motivated by the emergence of materials with mean free paths on the order of microns, we propose a novel class of solid state radiation sources based on reimplementing classical vacuum tube designs in semiconductors. Using materials with small effective masses, these devices should be able to access the terahertz range. We analyze the DC and AC operation of the simplest such device, the cylindrical diode magnetron, using effective quantum models. By treating the magnetron as an open quantum system, we show that it continues to operate as a radiation source even if its diameter is only a few tens of magnetic lengths.Comment: 11 pages, 7 figures; submitted to Physical Review Applie

Norman Julius Zabusky OBITUARY

Norman Julius Zabusky, who laid the foundations for several critical advancements in nonlinear science and experimental mathematics, died of idiopathic pulmonary fibrosis on 5 February 2018 in Beersheba, Israel. He also made fundamental contributions to computational fluid dynamics and advocated the importance of visualization in science.Published versio