4,588 research outputs found
Toda Lattice and Tomimatsu-Sato Solutions
We discuss an analytic proof of a conjecture (Nakamura) that solutions of
Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato
solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl
solutions completely and for generic cases partially.Comment: LaTeX 8 page
A Characterization of Discrete Time Soliton Equations
We propose a method to characterize discrete time evolution equations, which
generalize discrete time soliton equations, including the -difference
Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.Comment: 13 page
Novel in-gap spin state in Zn-doped La_1.85Sr_0.15CuO_4
Low-energy spin excitations of La1.85Sr0.15Cu1-yZnyO4 were studied by neutron
scattering. In y=0.004, the incommensurate magnetic peaks show a well defined
``spin gap'' below Tc. The magnetic signals at omega=3 meV decrease below Tc=27
K for y=0.008, also suggesting the gap opening. At lower temperatures, however,
the signal increases again, implying a novel in-gap spin state. In y=0.017, the
spin gap vanishes and elastic magnetic peaks appear. These results clarify that
doped Zn impurities induce the novel in-gap state, which becomes larger and
more static with increasing Zn.Comment: 4 pages, 4 figure
L1521E: A Starless Core in the Early Evolutionary Stage ?
We have studied the physical and chemical properties of a quiescent starless
core L1521E with various molecular lines. It is found that there exists a
compact dense core traced by the H^13CO^+, HN^13C, CCS, and HC_3N lines; their
distributions have a single peak at the same position. The core radius is as
small as 0.031 pc, whereas the H_2 density at the peak position is as high as
(1.3-5.6)times10^5 cm^-3. Although the density is high enough to excite the
inversion transitions of NH_3, these lines are found to be very faint in
L1521E. The distributions of NH_3 and CCS seem to be different from those of
well-studied starless cores, L1498 and L1544, where the distribution of CCS
shows a shell-like structure while that of NH_3 is concentrated at the center
of the core. Abundances of carbon-chain molecules are higher in L1521E than the
other dark cloud cores, and especially those of sulfur-bearing molecules C_nS
are comparable to the cyanopolyyne peak of TMC-1. Our results suggest that
L1521E would be in a very early stage of physical and chemical evolution.Comment: 10 pages, 3 EPS figures, uses aaspp4.sty and epsf.sty, AAS LaTeX
macros v4.0, The Astrophysical Journal, in pres
Analytical three-dimensional bright solitons and soliton-pairs in Bose-Einstein condensates with time-space modulation
We provide analytical three-dimensional bright multi-soliton solutions to the
(3+1)-dimensional Gross-Pitaevskii (GP) equation with time and space-dependent
potential, time-dependent nonlinearity, and gain/loss. The zigzag propagation
trace and the breathing behavior of solitons are observed. Different shapes of
bright solitons and fascinating interactions between two solitons can be
achieved with different parameters. The obtained results may raise the
possibility of relative experiments and potential applications.Comment: 5 pages, 4 figure
Hypothesis of two-dimensional stripe arrangement and its implications for the superconductivity in high-Tc cuprates
The hypothesis that holes doped into high-Tc cuprate superconductors organize
themselves in two-dimensional (2D) array of diagonal stripes is discussed, and,
on the basis of this hypothesis, a new microscopic model of superconductivity
is proposed and solved. The model describes two kinds of hole states localized
either inside the stripes or in the antiferromagnetic domains between the
stripes. The characteristic energy difference between these two kinds of states
is identified with the pseudogap. The superconducting (SC) order parameter
predicted by the model has two components, whose phases exhibit a complex
dependence on the the center-of-mass coordinate. The model predictions for the
tunneling characteristics and for the dependence of the critical temperature on
the superfluid density show good quantitative agreement with a number of
experiments. The model, in particular, predicts that the SC peaks in the
tunneling spectra are asymmetric, only when the ratio of the SC gap to the
critical temperature is greater than 4. It is also proposed that, at least in
some high-Tc cuprates, there exist two different superconducting states
corresponding to the same doping concentration and the same critical
temperature. Finally, the checkerboard pattern in the local density of states
observed by scanning tunneling microscopy in Bi-2212 is interpreted as coming
from the states localized around the centers of stripe elements forming the 2D
superstructure.Comment: Text close to the published version. This version is 10 per cent
shorter than the previous one. All revisions are mino
Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method
The renormalization group (RG) method is extended for global asymptotic
analysis of discrete systems. We show that the RG equation in the discretized
form leads to difference equations corresponding to the Stuart-Landau or
Ginzburg-Landau equations. We propose a discretization scheme which leads to a
faithful discretization of the reduced dynamics of the original differential
equations.Comment: LaTEX. 12pages. 1 figure include
Complex Analysis of a Piece of Toda Lattice
We study a small piece of two dimensional Toda lattice as a complex dynamical
system. In particular the Julia set, which appears when the piece is deformed,
is shown analytically how it disappears as the system approaches to the
integrable limit.Comment: 17 pages, LaTe
On a discrete Davey-Stewartson system
We propose a differential difference equation in and study it by
Hirota's bilinear method. This equation has a singular continuum limit into a
system which admits the reduction to the Davey-Stewartson equation. The
solutions of this discrete DS system are characterized by Casorati and Grammian
determinants. Based on the bilinear form of this discrete DS system, we
construct the bilinear B\"{a}cklund transformation which enables us to obtain
its Lax pair.Comment: 12 pages, 2 figure
Neutron Scattering Study of Temperature-Concentration Phase Diagram of (Cu1-xMgx)GeO3
In doped CuGeO3 systems, such as (Cu1-xZnx)GeO3 and Cu(Ge1-xSix)O3, the
spin-Peierls (SP) ordering (T<Tsp) coexists with the antiferromagnetic (AF)
phase (T<TN<Tsp). Tsp decreases while TN increases with increasing x in low
doping region. For higher x, however, the SP state disappears and only the AF
state remains. These features are common for all the doped CuGeO3 systems so
far studied, indicating the existence of universal T-x phase diagram. Recently,
Masuda et al. carried out comprehensive magnetic susceptibility (chi)
measurements of (Cu1-xMgx)GeO3, in which doping concentration can be controlled
significantly better than the Zn doped systems. They found that TN suddenly
jumps from 3.43 to 3.98K at the critical concentration xc sim 0.023 and that a
drop in chi corresponding to the SP ordering also disappears at x>xc. They thus
concluded that there is a compositional phase boundary between two distinct
magnetic phases. To clarify the nature of two phases, we performed
neutron-scattering measurements on (Cu1-xMgx)GeO3 single crystals with various
x. Analysis of the data at fixed temperature points as a function of doping
concentration has revealed sudden changes of order parameters at the critical
concentration xc=0.027 +- 0.001. At finite temperatures below TN, the drastic
increase of the AF moment takes place at xc. The spin-Peierls order parameter
delta associated with lattice dimerization shows a precipitous decrease at all
temperature below Tsp. However, it goes to zero above xc only at the low
temperature limit.Comment: 9 pages, 9 figure
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