10,279 research outputs found
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 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
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