8,206 research outputs found
Magnetic excitation in a new spin gap compound CuScGeO: Comparison to CuFeGeO
The compound \CuScGeO is presented as a new member of the family of weakly
coupled spin chain and dimer compounds \CuMGeO. Magnetic susceptibility, heat
capacity, and neutron inelastic scattering measurements reveal that the
compound has the same spin dimer component as \CuFeGeO. The observed narrow
band excitation in bulk measurements is consistent with spin gap behavior. The
energy scale of the weakly coupled dimers in the Sc compound is perfectly
coincident with that in the Fe compound.Comment: 5 page
Reentrant Spin-Peierls Transition in Mg-Doped CuGeO_3
We report a synchrotron x-ray scattering study of the diluted spin-Peierls
(SP) material Cu_{1-x}Mg_xGeO_3. In a recent paper we have shown that the SP
dimerization attains long-range order only for x < x_c = 0.022(0.001). Here we
report that the SP transition is reentrant in the vicinity of the critical
concentration x_c. This is manifested by broadening of the SP dimerization
superlattice peaks below the reentrance temperature, T_r, which may mean either
the complete loss of the long-range SP order or the development of a
short-range ordered component within the long-range ordered SP state. Marked
hysteresis and very large relaxation times are found in the samples with Mg
concentrations in the vicinity of x_c. The reentrant transition is likely
related to the competing Neel transition which occurs at a temperature similar
to T_r. We argue that impurity-induced competing interchain interactions play
an essential role in these phenomena.Comment: 5 pages, 4 embedded eps figure
Collective fluctuations in networks of noisy components
Collective dynamics result from interactions among noisy dynamical
components. Examples include heartbeats, circadian rhythms, and various pattern
formations. Because of noise in each component, collective dynamics inevitably
involve fluctuations, which may crucially affect functioning of the system.
However, the relation between the fluctuations in isolated individual
components and those in collective dynamics is unclear. Here we study a linear
dynamical system of networked components subjected to independent Gaussian
noise and analytically show that the connectivity of networks determines the
intensity of fluctuations in the collective dynamics. Remarkably, in general
directed networks including scale-free networks, the fluctuations decrease more
slowly with the system size than the standard law stated by the central limit
theorem. They even remain finite for a large system size when global
directionality of the network exists. Moreover, such nontrivial behavior
appears even in undirected networks when nonlinear dynamical systems are
considered. We demonstrate it with a coupled oscillator system.Comment: 5 figure
Analysis of relative influence of nodes in directed networks
Many complex networks are described by directed links; in such networks, a
link represents, for example, the control of one node over the other node or
unidirectional information flows. Some centrality measures are used to
determine the relative importance of nodes specifically in directed networks.
We analyze such a centrality measure called the influence. The influence
represents the importance of nodes in various dynamics such as synchronization,
evolutionary dynamics, random walk, and social dynamics. We analytically
calculate the influence in various networks, including directed multipartite
networks and a directed version of the Watts-Strogatz small-world network. The
global properties of networks such as hierarchy and position of shortcuts,
rather than local properties of the nodes, such as the degree, are shown to be
the chief determinants of the influence of nodes in many cases. The developed
method is also applicable to the calculation of the PageRank. We also
numerically show that in a coupled oscillator system, the threshold for
entrainment by a pacemaker is low when the pacemaker is placed on influential
nodes. For a type of random network, the analytically derived threshold is
approximately equal to the inverse of the influence. We numerically show that
this relationship also holds true in a random scale-free network and a neural
network.Comment: 9 figure
Models of q-algebra representations: Matrix elements of the q-oscillator algebra
This article continues a study of function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. Here a q analog of the oscillator algebra (not a quantum algebra) is considered. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. This ``local'' approach applies to more general families of special functions, e.g., with complex arguments and parameters, than does the quantum group approach. It is shown that the matrix elements themselves transform irreducibly under the action of the algebra. q analogs of a formula are found for the product of two hypergeometric functions 1F1 and the product of a 1F1 and a Bessel function. They are interpreted here as expansions of the matrix elements of a ``group operator'' (via the exponential mapping) in a tensor product basis (for the tensor product of two irreducible oscillator algebra representations) in terms of the matrix elements in a reduced basis. As a by-product of this analysis an interesting new orthonormal basis was found for a q analog of the BargmannâSegal Hilbert space of entire functions
Macroscopic and Local Magnetic Moments in Si-doped CuGeO with Neutron and SR Studies
The temperature-concentration phase diagram of the Si-doped spin-Peierls
compound CuGeO is investigated by means of neutron scattering and muon
spin rotation spectroscopy in order to determine the microscopic distribution
of the magnetic and lattice dimerised regions as a function of doping. The
analysis of the zero-field muon spectra has confirmed the spatial inhomogeneity
of the staggered magnetisation that characterises the antiferromagnetic
superlattice peaks observed with neutrons. In addition, the variation of the
macroscopic order parameter with doping can be understood by considering the
evolution of the local magnetic moment as well as of the various regions
contributing to the muon signal
New connection formulae for some q-orthogonal polynomials in q-Askey scheme
New nonlinear connection formulae of the q-orthogonal polynomials, such
continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and
q-Gegenbauer polynomials, in terms of their respective classical analogues are
obtained using a special realization of the q-exponential function as infinite
multiplicative series of ordinary exponential function
59Co-NQR study on superconducting NaxCoO2.yH2O
Layered Co oxide NaxCoO2.yH2O with a superconducting transition temperature
Tc =4.5 K has been studied by 59Co NQR. The nuclear spin relaxation rate 1/59T1
is nearly proportional to temperature T in the normal state. In the
superconducting state, it exhibits the coherence peak and decreases with
decreasing T below ~0.8Tc. Detailed comparison of the 1/T1T values and the
magnetic susceptibilities between NaxCoO2.yH2O and NaxCoO2 implies that the
metallic state of the former system is closer to a ferromagnetic phase than
that of the latter. These experimental results impose a restriction on the
mechanism of the superconductivity.Comment: 7 pages, 5 figures. to be published in J. Phys. Soc. Jpn. 72 (2003)
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