56,609 research outputs found
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
Magnetic Excitations of Stripes Near a Quantum Critical Point
We calculate the dynamical spin structure factor of spin waves for weakly
coupled stripes. At low energy, the spin wave cone intensity is strongly peaked
on the inner branches. As energy is increased, there is a saddlepoint followed
by a square-shaped continuum rotated 45 degree from the low energy peaks. This
is reminiscent of recent high energy neutron scattering data on the cuprates.
The similarity at high energy between this semiclassical treatment and quantum
fluctuations in spin ladders may be attributed to the proximity of a quantum
critical point with a small critical exponent .Comment: 4+ pages, 5 figures, published versio
Magnetic Excitations of Stripes and Checkerboards in the Cuprates
We discuss the magnetic excitations of well-ordered stripe and checkerboard
phases, including the high energy magnetic excitations of recent interest and
possible connections to the "resonance peak" in cuprate superconductors. Using
a suitably parametrized Heisenberg model and spin wave theory, we study a
variety of magnetically ordered configurations, including vertical and diagonal
site- and bond-centered stripes and simple checkerboards. We calculate the
expected neutron scattering intensities as a function of energy and momentum.
At zero frequency, the satellite peaks of even square-wave stripes are
suppressed by as much as a factor of 34 below the intensity of the main
incommensurate peaks. We further find that at low energy, spin wave cones may
not always be resolvable experimentally. Rather, the intensity as a function of
position around the cone depends strongly on the coupling across the stripe
domain walls. At intermediate energy, we find a saddlepoint at for
a range of couplings, and discuss its possible connection to the "resonance
peak" observed in neutron scattering experiments on cuprate superconductors. At
high energy, various structures are possible as a function of coupling strength
and configuration, including a high energy square-shaped continuum originally
attributed to the quantum excitations of spin ladders. On the other hand, we
find that simple checkerboard patterns are inconsistent with experimental
results from neutron scattering.Comment: 11 pages, 13 figures, for high-res figs, see
http://physics.bu.edu/~yaodx/spinwave2/spinw2.htm
Intermittent many-body dynamics at equilibrium
The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q-breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.We thank P. Jeszinszki and I. Vakulchyk for helpful discussions on computational aspects. The authors acknowledge financial support from IBS (Project Code No. IBS-R024-D1). (IBS-R024-D1 - IBS)Published versio
Transfer of BECs through discrete breathers in an optical lattice
We study the stability of a stationary discrete breather (DB) on a nonlinear
trimer in the framework of the discrete nonlinear Schr\"odinger equation
(DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein
condensates in leaking optical lattices, collisions between a DB and a lattice
excitation, e.g. a moving breather (MB) or phonon, were studied. These
collisions lead to the transmission of a fraction of the incident (atomic) norm
of the MB through the DB, while the DB can be shifted in the direction of the
incident lattice excitation. Here we show that there exists a total energy
threshold of the trimer, above which the lattice excitation can trigger the
destabilization of the DB and that this is the mechanism leading to the
movement of the DB. Furthermore, we give an analytic estimate of upper bound to
the norm that is transmitted through the DB. Our analysis explains the results
of the earlier numerical studies and may help to clarify functional operations
with BECs in optical lattices such as blocking and filtering coherent (atomic)
beams.Comment: 8 pages, 5 figure
The ubiquitous 1100 charge ordering in organic charge-transfer solids
Charge and spin-orderings in the 1/4-filled organic CT solids are of strong
interest, especially in view of their possible relations to organic
superconductivity. We show that the charge order (CO) in both 1D and 2D CT
solids is of the ...1100... type, in contradiction to mean field prediction of
>...1010... CO. We present detailed computations for metal-insulator and
magnetic insulator-insulator transitions in the theta-ET materials. Complete
agreement with experiments in several theta systems is found. Similar
comparisons between theory and experiments in TCNQ, TMTTF, TMTSF, and ET
materials prove the ubiquity of this phenomenon.Comment: 3 pages, 4 eps figures; ICSM 200
Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
We studied the kink-antikink collision process for the "double sine-Gordon"
(DSG) equation in 1+1 dimensions at different values of the potential parameter
. For small values of we discuss the problem of resonance frequencies.
We give qualitative explanation of the frequency shift in comparison with the
frequency of the discrete level in the potential well of isolated kink. We show
that in this region of the parameter the effective long-range interaction
between kink and antikink takes place.Comment: 9 pages, LaTeX, 4 figures (eps
- …