92 research outputs found
Condensation of the roots of real random polynomials on the real axis
We introduce a family of real random polynomials of degree n whose
coefficients a_k are symmetric independent Gaussian variables with variance
= e^{-k^\alpha}, indexed by a real \alpha \geq 0. We compute exactly
the mean number of real roots for large n. As \alpha is varied, one finds
three different phases. First, for 0 \leq \alpha \sim
(\frac{2}{\pi}) \log{n}. For 1 < \alpha < 2, there is an intermediate phase
where grows algebraically with a continuously varying exponent,
\sim \frac{2}{\pi} \sqrt{\frac{\alpha-1}{\alpha}} n^{\alpha/2}. And finally for
\alpha > 2, one finds a third phase where \sim n. This family of real
random polynomials thus exhibits a condensation of their roots on the real line
in the sense that, for large n, a finite fraction of their roots /n are
real. This condensation occurs via a localization of the real roots around the
values \pm \exp{[\frac{\alpha}{2}(k+{1/2})^{\alpha-1} ]}, 1 \ll k \leq n.Comment: 13 pages, 2 figure
Fluctuation induced hopping and spin polaron transport
We study the motion of free magnetic polarons in a paramagnetic background of
fluctuating local moments. The polaron can tunnel only to nearby regions of
local moments when these fluctuate into alignment. We propose this fluctuation
induced hopping as a new transport mechanism for the spin polaron. We calculate
the diffusion constant for fluctuation induced hopping from the rate at which
local moments fluctuate into alignment. The electrical resistivity is then
obtained via the Einstein relation. We suggest that the proposed transport
mechanism is relevant in the high temperature phase of the Mn pyrochlore
colossal magneto resistance compounds and Europium hexaboride.Comment: 8 pages, 3 figure
Origin and pressure dependence of ferromagnetism in A2Mn2O7 pyrochlores (A=Y, In, Lu, and Tl)
Non-conventional mechanisms have been recently invoked in order to explain
the ferromagnetic ground state of A2Mn2O7 pyrochlores (A=Y, In, Lu and Tl) and
the puzzling decrease of their Curie temperatures with applied pressure. Here
we show, using a perturbation expansion in the Mn-O hopping term, that both
features can be understood within the superexhange model, provided that the
intra-atomic oxygen interactions are properly taken into account. An additional
coupling between the Mn ions mediated by the In(5s)/Tl(6s) bands yields the
higher Tc's of these two compounds, this mechamism enhancing their
ferromagnetism for higher pressures.Comment: 7 pages and 2 figures submitted to Phys. Rev. B, missing text adde
Stability and dynamics of free magnetic polarons
The stability and dynamics of a free magnetic polaron are studied by Monte
Carlo simulation of a classical two-dimensional Heisenberg model coupled to a
single electron. We compare our results to the earlier mean-field analysis of
the stability of the polaron, finding qualitative similarity but quantitative
differences. The dynamical simulations give estimates of the temperature
dependence of the polaron diffusion, as well as a crossover to a tunnelling
regime.Comment: 4 pages including 4 .eps figure
Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation
We study various statistical properties of real roots of three different
classes of random polynomials which recently attracted a vivid interest in the
context of probability theory and quantum chaos. We first focus on gap
probabilities on the real axis, i.e. the probability that these polynomials
have no real root in a given interval. For generalized Kac polynomials, indexed
by an integer d, of large degree n, one finds that the probability of no real
root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)
> 0 is the persistence exponent of the diffusion equation with random initial
conditions in spatial dimension d. For n \gg 1 even, the probability that they
have no real root on the full real axis decays like
n^{-2(\theta(2)+\theta(d))}. For Weyl polynomials and Binomial polynomials,
this probability decays respectively like \exp{(-2\theta_{\infty}} \sqrt{n})
and \exp{(-\pi \theta_{\infty} \sqrt{n})} where \theta_{\infty} is such that
\theta(d) = 2^{-3/2} \theta_{\infty} \sqrt{d} in large dimension d. We also
show that the probability that such polynomials have exactly k roots on a given
interval [a,b] has a scaling form given by \exp{(-N_{ab} \tilde
\phi(k/N_{ab}))} where N_{ab} is the mean number of real roots in [a,b] and
\tilde \phi(x) a universal scaling function. We develop a simple Mean Field
(MF) theory reproducing qualitatively these scaling behaviors, and improve
systematically this MF approach using the method of persistence with partial
survival, which in some cases yields exact results. Finally, we show that the
probability density function of the largest absolute value of the real roots
has a universal algebraic tail with exponent {-2}. These analytical results are
confirmed by detailed numerical computations.Comment: 32 pages, 16 figure
Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model
We revisit the ground-state phase diagram of the one-dimensional half-filled
extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive
interactions. In the first half of the paper, using the weak-coupling
renormalization-group approach (g-ology) including second-order corrections to
the coupling constants, we show that bond-charge-density-wave (BCDW) phase
exists for U \approx 2V in between charge-density-wave (CDW) and
spin-density-wave (SDW) phases. We find that the umklapp scattering of
parallel-spin electrons disfavors the BCDW state and leads to a bicritical
point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into
the CDW-SDW first-order transition line. In the second half of the paper, we
investigate the phase diagram of the extended Hubbard model with either
additional staggered site potential \Delta or bond alternation \delta. Although
the alternating site potential \Delta strongly favors the CDW state (that is, a
band insulator), the BCDW state is not destroyed completely and occupies a
finite region in the phase diagram. Our result is a natural generalization of
the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014
(1999)], who predicted the existence of a spontaneously dimerized insulating
state between a band insulator and a Mott insulator in the phase diagram of the
ionic Hubbard model. The bond alternation \delta destroys the SDW state and
changes it into the BCDW state (or Peierls insulating state). As a result the
phase diagram of the model with \delta contains only a single critical line
separating the Peierls insulator phase and the CDW phase. The addition of
\Delta or \delta changes the universality class of the CDW-BCDW transition from
the Gaussian transition into the Ising transition.Comment: 24 pages, 20 figures, published versio
First order transition and phase separation in pyrochlores with colossal-magnetoresistance
TlMnO pyrochlores present colossal magnetoresistance (CMR)
around the long range ferromagnetic ordering temperature (T). The
character of this magnetic phase transition has been determined to be first
order, by purely magnetic methods, in contrast to the second order character
previously reported by Zhao et al. (Phys. Rev. Lett. 83, 219 (1999)). The
highest CMR effect, as in TlCdMnO, corresponds to a
stronger first order character. This character implies a second type of
magnetic interaction, besides the direct superexchange between the Mn
ions, as well as a phase coexistence. A model is proposed, with a complete
Hamiltonian (including superexchange and an indirect interaction), which
reproduce the observed phenomenology.Comment: 6 pages. Figures include
Processing of aluminum-graphite particulate metal matrix composites by advanced shear technology
Copyright @ 2009 ASM International. This paper was published in Journal of Materials Engineering and Performance 18(9) and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.To extend the possibilities of using aluminum/graphite composites as structural materials, a novel process is developed. The conventional methods often produce agglomerated structures exhibiting lower strength and ductility. To overcome the cohesive force of the agglomerates, a melt conditioned high-pressure die casting
(MC-HPDC) process innovatively adapts the well-established, high-shear dispersive mixing action of a twin screw mechanism. The distribution of particles and properties of composites are quantitatively evaluated.
The adopted rheo process significantly improved the distribution of the reinforcement in the matrix with a strong interfacial bond between the two. A good combination of improved ultimate tensile strength (UTS) and tensile elongation (e) is obtained compared with composites produced by conventional processes.EPSR
Long-range Angular Correlations On The Near And Away Side In P-pb Collisions At √snn=5.02 Tev
7191/Mar294
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