590 research outputs found
Algebraic entropy for algebraic maps
We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Backlund transformations
Thermal transport measurements of individual multiwalled nanotubes
The thermal conductivity and thermoelectric power of a single carbon nanotube
were measured using a microfabricated suspended device. The observed thermal
conductivity is more than 3000 W/K m at room temperature, which is two orders
of magnitude higher than the estimation from previous experiments that used
macroscopic mat samples. The temperature dependence of the thermal conductivity
of nanotubes exhibits a peak at 320 K due to the onset of Umklapp phonon
scattering. The measured thermoelectric power shows linear temperature
dependence with a value of 80 V/K at room temperature.Comment: 4 pages, figures include
Backlund transformations for many-body systems related to KdV
We present Backlund transformations (BTs) with parameter for certain
classical integrable n-body systems, namely the many-body generalised
Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the
fact that all these systems may be obtained as particular reductions
(stationary or restricted flows) of the KdV hierarchy; alternatively they may
be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide
exact time-discretizations of the original (continuous) systems, preserving the
Lax matrix and hence all integrals of motion, and satisfy the spectrality
property with respect to the Backlund parameter.Comment: LaTeX2e, 8 page
Discrete Painlevé equations from Y-systems
We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients.
A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlev\'e equations can arise from this construction
A lattice model of hydrophobic interactions
Hydrogen bonding is modeled in terms of virtual exchange of protons between
water molecules. A simple lattice model is analyzed, using ideas and techniques
from the theory of correlated electrons in metals. Reasonable parameters
reproduce observed magnitudes and temperature dependence of the hydrophobic
interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter
Bridge Hopping on Conducting Polymers in Solution
Configurational fluctuations of conducting polymers in solution can bring
into proximity monomers which are distant from each other along the backbone.
Electrons can hop between these monomers across the "bridges" so formed. We
show how this can lead to (i) a collapse transition for metallic polymers, and
(ii) to the observed dramatic efficiency of acceptor molecules for quenching
fluorescence in semiconducting polymers.Comment: RevTeX 12 pages + 2 Postscript figure
Two-component generalizations of the Camassa-Holm equation
A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa-Holm equation is carried out via the perturbative symmetry approach. Independently, a classification of compatible pairs of Hamiltonian operators is carried out, which leads to bi-Hamiltonian structures for the same systems of equations. Some exact solutions and Lax pairs are also constructed for the systems considered
A family of integrable maps associated with the Volterra lattice
Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in
four dimensions admitting two invariants (first integrals) with a particular
degree structure, by considering recurrences of fourth order with a certain
symmetry. The last three of the maps so obtained were shown to be Liouville
integrable, in the sense of admitting a non-degenerate Poisson bracket with two
first integrals in involution. Here we show how the first of these three
Liouville integrable maps corresponds to genus 2 solutions of the infinite
Volterra lattice, being the case of a family of maps associated with the
Stieltjes continued fraction expansion of a certain function on a hyperelliptic
curve of genus . The continued fraction method provides explicit
Hankel determinant formulae for tau functions of the solutions, together with
an algebro-geometric description via a Lax representation for each member of
the family, associating it with an algebraic completely integrable system. In
particular, in the elliptic case (), as a byproduct we obtain Hankel
determinant expressions for the solutions of the Somos-5 recurrence, but
different to those previously derived by Chang, Hu and Xin. By applying
contraction to the Stieltjes fraction, we recover integrable maps associated
with Jacobi continued fractions on hyperelliptic curves, that one of us
considered previously, as well as the Miura-type transformation between the
Volterra and Toda lattices
Partial Wave Analysis of Scattering with Nonlocal Aharonov-Bohm Effect and Anomalous Cross Section induced by Quantum Interference
Partial wave theory of a three dmensional scattering problem for an arbitray
short range potential and a nonlocal Aharonov-Bohm magnetic flux is
established. The scattering process of a ``hard shere'' like potential and the
magnetic flux is examined. An anomalous total cross section is revealed at the
specific quantized magnetic flux at low energy which helps explain the
composite fermion and boson model in the fractional quantum Hall effect. Since
the nonlocal quantum interference of magnetic flux on the charged particles is
universal, the nonlocal effect is expected to appear in quite general potential
system and will be useful in understanding some other phenomena in mesoscopic
phyiscs.Comment: 6 figure
Ac Stark Effects and Harmonic Generation in Periodic Potentials
The ac Stark effect can shift initially nonresonant minibands in
semiconductor superlattices into multiphoton resonances. This effect can result
in strongly enhanced generation of a particular desired harmonic of the driving
laser frequency, at isolated values of the amplitude.Comment: RevTeX, 10 pages (4 figures available on request), Preprint
UCSBTH-93-2
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