9,665 research outputs found
The improper infinite derivatives of Takagi's nowhere-differentiable function
Let T be Takagi's continuous but nowhere-differentiable function. Using a
representation in terms of Rademacher series due to N. Kono, we give a complete
characterization of those points where T has a left-sided, right-sided, or
two-sided infinite derivative. This characterization is illustrated by several
examples. A consequence of the main result is that the sets of points where
T'(x) is infinite have Hausdorff dimension one. As a byproduct of the method of
proof, some exact results concerning the modulus of continuity of T are also
obtained.Comment: 16 page
B meson light-cone wavefunctions in the heavy quark limit
We present a systematic study of the B meson light-cone wavefunctions in QCD
in the heavy-quark limit. We construct model-independent formulae for the
light-cone wavefunctions in terms of independent dynamical degrees of freedom,
which exactly satisfy the QCD equations of motion and constraints from
heavy-quark symmetry. The results demonstrate novel behaviors of longitudinal
as well as transverse momentum distribution in the B mesons.Comment: 5 pages LaTeX, 1 style file. Talk presented at RADCOR/Loops and Legs
2002, Kloster Banz, Germany, September 8-13, 200
Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbor interaction
The ordering property of the classical pyrochlore Heisenberg antiferromagnet
with the ferromagnetic next-nearest-neighbor interaction is investigated by
means of a Monte Carlo simulation. The model is found to exhibit a first-order
transition at a finite temperature into a peculiar ordered state. While the
spin structure factor, i.e., the thermal average of the squared Fourier
amplitude of the spin, exhibits a finite long-range order characterized by the
commensurate spin order of the period four, the thermal average of the spin
itself almost vanishes. It means that, although the amplitude of the spin
Fourier component is long-range ordered, the associated phase degree of freedom
remains to be fluctuating.Comment: Proceedings of the Highly Frustrated Magnetism (HFM2006) conference.
To appear in a special issue of J. Phys. Condens. Matte
Novel spin-liquid states in the frustrated Heisenberg antiferromagnet on the honeycomb lattice
Recent experiment on a honeycomb-lattice Heisenberg antiferromagnet (AF)
BiMnO(NO) revealed a novel spin-liquid-like behavior down to
low temperature, which was ascribed to the frustration effect due to the
competition between the AF nearest- and next-nearest-neighbor interactions
and . Motivated by the experiment, we study the ordering of the
- frustrated classical Heisenberg AF on a honeycomb lattice both by
a low-temperature expansion and a Monte Carlo simulation. The model has been
known to possess a massive degeneracy of the ground state, which, however,
might be lifted due to thermal fluctuations leading to a unique ordered state,
the effect known as 'order-by-disorder'. We find that the model exhibits an
intriguing ordering behavior, particularly near the AF phase boundary. The
energy scale of the order-by-disorder is suppressed there down to extremely low
temperatures, giving rise to exotic spin-liquid states like a "ring-liquid" or
a "pancake-liquid" state accompanied by the characteristic spin structure
factor and the field-induced antiferromagnetism. We argue that the recent
experimental data are explicable if the system is in such exotic spin-liquid
states
Nature of the vortex-glass order in strongly type-II superconductors
The stability and the critical properties of the three-dimensional
vortex-glass order in random type-II superconductors with point disorder is
investigated in the unscreened limit based on a lattice {\it XY} model with a
uniform field. By performing equilibrium Monte Carlo simulations for the system
with periodic boundary conditions, the existence of a stable vortex-glass order
is established in the unscreened limit. Estimated critical exponents are
compared with those of the gauge-glass model.Comment: Error in the reported value of the exponent eta is correcte
Ordering of the Heisenberg spin glass in two dimensions
The spin and the chirality orderings of the Heisenberg spin glass in two
dimensions with the nearest-neighbor Gaussian coupling are investigated by
equilibrium Monte Carlo simulations. Particular attention is paid to the
behavior of the spin and the chirality correlation lengths. In order to observe
the true asymptotic behavior, fairly large system size L\gsim 20 (L the linear
dimension of the system) appears to be necessary. It is found that both the
spin and the chirality order only at zero temperature. At high temperatures,
the chiral correlation length stays shorter than spin correlation length,
whereas at lower temperatures below the crossover temperature T_\times, the
chiral correlation length exceeds the spin correlation length. The spin and the
chirality correlation-length exponents are estimated above T_\times to be
\nu_SG=0.9+-0.2 and \nu_CG=2.1+-0.3, respectively. These values are close to
the previous estimates on the basis of the domain-wall-energy calculation.
Discussion is given about the asymptotic critical behavior realized below
T_\times.Comment: to appear in a special issue of J. Phys.
Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes
Characteristic versus critical features of earthquakes are studied on the
basis of the Olami-Feder-Christensen model. It is found that the local
recurrence-time distribution exhibits a sharp -function-like peak
corresponding to rhythmic recurrence of events with a fixed ``period'' uniquely
determined by the transmission parameter of the model, together with a
power-law-like tail corresponding to scale-free recurrence of events. The model
exhibits phenomena closely resembling the asperity known in seismology
Probing SO(10) symmetry breaking patterns through sfermion mass relations
We consider supersymmetric SO(10) grand unification where the unified gauge
group can break to the Standard Model gauge group through different chains. The
breaking of SO(10) necessarily involves the reduction of the rank, and
consequent generation of non-universal supersymmetry breaking scalar mass
terms. We derive squark and slepton mass relations, taking into account these
non-universal contributions to the sfermion masses, which can help distinguish
between the different chains through which the SO(10) gauge group breaks to the
Standard Model gauge group. We then study some implications of these
non-universal supersymmetry breaking scalar masses for the low energy
phenomenology.Comment: 13 pages, latex using revtex4, contains 2 figures, replaced with
version accepted for publicatio
Generating functional analysis of CDMA detection dynamics
We investigate the detection dynamics of the parallel interference canceller
(PIC) for code-division multiple-access (CDMA) multiuser detection, applied to
a randomly spread, fully syncronous base-band uncoded CDMA channel model with
additive white Gaussian noise (AWGN) under perfect power control in the
large-system limit. It is known that the predictions of the density evolution
(DE) can fairly explain the detection dynamics only in the case where the
detection dynamics converge. At transients, though, the predictions of DE
systematically deviate from computer simulation results. Furthermore, when the
detection dynamics fail to convergence, the deviation of the predictions of DE
from the results of numerical experiments becomes large. As an alternative,
generating functional analysis (GFA) can take into account the effect of the
Onsager reaction term exactly and does not need the Gaussian assumption of the
local field. We present GFA to evaluate the detection dynamics of PIC for CDMA
multiuser detection. The predictions of GFA exhibits good consistency with the
computer simulation result for any condition, even if the dynamics fail to
convergence.Comment: 14 pages, 3 figure
Squark and slepton masses as probes of supersymmetric SO(10) unification
We carry out an analysis of the non-universal supersymmetry breaking scalar
masses arising in SO(10) supersymmetric unification. By considering patterns of
squark and slepton masses, we derive a set of sum rules for the sfermion masses
which are independent of the manner in which SO(10) breaks to the Standard
Model gauge group via its SU(5) subgroups. The phenomenology arising from such
non-universality is unaffected by the symmetry breaking pattern, so long as the
breaking occurs via any of the SU(5) subgroups of the SO(10) group.Comment: 15 pages using RevTe
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