2,957 research outputs found
Determinant Representations for Correlation Functions of Spin-1/2 XXX and XXZ Heisenberg Magnets
We consider correlation functions of the spin-\half XXX and XXZ Heisenberg
chains in a magnetic field. Starting from the algebraic Bethe Ansatz we derive
representations for various correlation functions in terms of determinants of
Fredholm integral operators.Comment: 23 pages, TeX, BONN-TH-94-14, revised version: typos correcte
Correlations in the impenetrable electron gas
We consider non-relativistic electrons in one dimension with infinitely
strong repulsive delta function interaction. We calculate the long-time,
large-distance asymptotics of field-field correlators in the gas phase. The gas
phase at low temperatures is characterized by the ideal gas law. We calculate
the exponential decay, the power law corrections and the constant factor of the
asymptotics. Our results are valid at any temperature. They simplify at low
temperatures, where they are easily recognized as products of free fermionic
correlation functions with corrections arising due to the interaction.Comment: 17 pages, Late
Regularization of point vortices for the Euler equation in dimension two
In this paper, we construct stationary classical solutions of the
incompressible Euler equation approximating singular stationary solutions of
this equation.
This procedure is carried out by constructing solutions to the following
elliptic problem [ -\ep^2 \Delta
u=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p, \quad & x\in\Omega, u=0, \quad
& x\in\partial\Omega, ] where , is a bounded
domain, is a harmonic function.
We showed that if is simply-connected smooth domain, then for any
given non-degenerate critical point of Kirchhoff-Routh function
with the same strength , there is a
stationary classical solution approximating stationary points vortex
solution of incompressible Euler equations with vorticity .
Existence and asymptotic behavior of single point non-vanishing vortex
solutions were studied by D. Smets and J. Van Schaftingen (2010).Comment: 32page
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
In this paper we show how an infinite system of coupled Toda-type nonlinear
differential equations derived by one of us can be used efficiently to
calculate the time-dependent pair-correlations in the Ising chain in a
transverse field. The results are seen to match extremely well long large-time
asymptotic expansions newly derived here. For our initial conditions we use new
long asymptotic expansions for the equal-time pair correlation functions of the
transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising
model. Using this one can also study the equal-time wavevector-dependent
correlation function of the quantum chain, a.k.a. the q-dependent diagonal
susceptibility in the 2d Ising model, in great detail with very little
computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references
added and minor changes of style. vs3: Corrections made and reference adde
Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz
We prove that the solution to a pair of nonlinear integral equations arising
in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent
kernel of the linear integral operator with kernel
exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]Comment: 16 pages, LaTeX file, no figures. Revision has minor change
Coulomb Gaps in One-Dimensional Spin-Polarized Electron Systems
We investigate the density of states (DOS) near the Fermi energy of
one-dimensional spin-polarized electron systems in the quantum regime where the
localization length is comparable to or larger than the inter-particle
distance. The Wigner lattice gap of such a system, in the presence of weak
disorder, can occur precisely at the Fermi energy, coinciding with the Coulomb
gap in position. The interplay between the two is investigated by treating the
long-range Coulomb interaction and the random disorder potential in a
self-consistent Hartree-Fock approximation. The DOS near the Fermi energy is
found to be well described by a power law whose exponent decreases with
increasing disorder strength.Comment: 4 pages, revtex, 4 figures, to be published in Phys. Rev. B as a
Rapid Communicatio
Standard and Embedded Solitons in Nematic Optical Fibers
A model for a non-Kerr cylindrical nematic fiber is presented. We use the
multiple scales method to show the possibility of constructing different kinds
of wavepackets of transverse magnetic (TM) modes propagating through the fiber.
This procedure allows us to generate different hierarchies of nonlinear partial
differential equations (PDEs) which describe the propagation of optical pulses
along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium
and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order
derivative nonlinearity, governing the dynamics for the amplitude of the
wavepacket. In this derivation the dispersion, self-focussing and diffraction
in the nematic are taken into account. Although the resulting nonlinear
may be reduced to the modified Korteweg de Vries equation (mKdV), it also has
additional complex solutions which include two-parameter families of bright and
dark complex solitons. We show analytically that under certain conditions, the
bright solitons are actually double embedded solitons. We explain why these
solitons do not radiate at all, even though their wavenumbers are contained in
the linear spectrum of the system. Finally, we close the paper by making
comments on the advantages as well as the limitations of our approach, and on
further generalizations of the model and method presented.Comment: "Physical Review E, in press
Hyphal Orientation of Candida albicans Is Regulated by a Calcium-Dependent Mechanism
SummaryEukaryotic cells from fungal hyphae to neurites that grow by polarized extension must coordinate cell growth and cell orientation to enable them to exhibit growth tropisms and to respond to relevant environmental cues. Such cells generally maintain a tip-high Ca2+ cytoplasmic gradient, which is correlated with their ability to exhibit polarized tip growth and to respond to growth-directing extracellular signals [1–5]. In yeast and other fungi, the polarisome, exocyst, Arp2/3, and Spitzenkörper protein complexes collectively orchestrate tip growth and cell polarity, but it is not clear whether these molecular complexes also regulate cell orientation or whether they are influenced by cytoplasmic Ca2+ gradients. Hyphae of the human pathogenic fungus Candida albicans reorient their growth axis in response to underlying surface topography (thigmotropism) [6] and imposed electric fields (galvanotropism) [7]. The establishment and maintenance of directional growth in relation to these environmental cues was Ca2+ dependent. Tropisms were attenuated in media containing low Ca2+, or calcium-channel blockers, and in mutants where calcium channels or elements of the calcium signaling pathway were deleted. Therefore galvanotropism and thigmotropism may both be mediated by localized Ca2+ influx at sites of polarized growth via Ca2+ channels that are activated by appropriate environmental signals
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