504 research outputs found
Unbounded rough drivers
We propose a theory of linear differential equations driven by unbounded
operator-valued rough signals. As an application we consider rough linear
transport equations and more general linear hyperbolic symmetric systems of
equations driven by time-dependent vector fields which are only distributions
in the time direction.Comment: 38 pages. some improvements and precision
Paracontrolled calculus and regularity structures
International audienceWe start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the space of admissible models
Ground states of a frustrated spin-1/2 antifferomagnet: Cs_2CuCl_4 in a magnetic field
We present detailed calculations of the magnetic ground state properties of
CsCuCl in an applied magnetic field, and compare our results with
recent experiments. The material is described by a spin Hamiltonian, determined
with precision in high field measurements, in which the main interaction is
antiferromagnetic Heisenberg exchange between neighboring spins on an
anisotropic triangular lattice. An additional, weak Dzyaloshinkii-Moriya
interaction introduces easy-plane anisotropy, so that behavior is different for
transverse and longitudinal field directions. We determine the phase diagram as
a function of field strength for both field directions at zero temperature,
using a classical approximation as a first step. Building on this, we calculate
the effect of quantum fluctuations on the ordering wavevector and components of
the ordered moments, using both linear spinwave theory and a mapping to a Bose
gas which gives exact results when the magnetization is almost saturated. Many
aspects of the experimental data are well accounted for by this approach.Comment: 13 Pages, 9 Figure
Extreme sensitivity of a frustrated quantum magnet: Cs_2CuCl_4
We report a thorough theoretical study of the low temperature phase diagram
of Cs_2CuCl_4, a spatially anisotropic spin S=1/2 triangular lattice
antiferromagnet, in a magnetic field. Our results, obtained in a
quasi-one-dimensional limit in which the system is regarded as a set of weakly
coupled Heisenberg chains, are in excellent agreement with experiment. The
analysis reveals some surprising physics. First, we find that, when the
magnetic field is oriented within the triangular layer, spins are actually most
strongly correlated within planes perpendicular to the triangular layers. This
is despite the fact that the inter-layer exchange coupling in Cs_2CuCl_4 is
about an order of magnitude smaller than the weakest (diagonal) exchange in the
triangular planes themselves. Second, the phase diagram in such orientations is
exquisitely sensitive to tiny interactions, heretofore neglected, of order a
few percent or less of the largest exchange couplings. These interactions,
which we describe in detail, induce entirely new phases, and a novel
commensurate-incommensurate transition, the signatures of which are identified
in NMR experiments. We discuss the differences between the behavior of
Cs_2CuCl_4 and an ideal two-dimensional triangular model, and in particular the
occurrence of magnetization plateaux in the latter. These and other related
results are presented here along with a thorough exposition of the theoretical
methods, and a discussion of broader experimental consequences to Cs_2CuCl_4
and other materials.Comment: 43 pages, 20 figures; typos correcte
On Partial Response Signaling for MIMO Equalization on Multi-Gbit/s Electrical Interconnects
Because of its ability to deal with intersymbol interference (ISI) and crosstalk (XT) over mutually coupled electrical interconnects, multiple-input multiple-output (MIMO) decision feedback equalization (DFE) has proven to be a promising low-cost solution for achieving multi-Gbit/s wireline communication on- and off-chip. However, not only does the channel become very sensitive to manufacturing tolerances at very high symbol rates, the latency in the feedback loop becomes prohibitively large as well. Whereas the former issue has been addressed by adopting a stochastic MIMO approach where (part of) the equalization filters depend on the channel statistics rather than on the actual channel, we tackle in this paper the latency issue by setting to zero the first N taps of the feedback filters. Moreover, we show that precoded partial response (PR) signaling can improve the performance of the resulting scheme, although the achieved gain is smaller than in the case of single-input single-output (SISO) equalization
Curvature Diffusions in General Relativity
We define and study on Lorentz manifolds a family of covariant diffusions in
which the quadratic variation is locally determined by the curvature. This
allows the interpretation of the diffusion effect on a particle by its
interaction with the ambient space-time. We will focus on the case of warped
products, especially Robertson-Walker manifolds, and analyse their asymptotic
behaviour in the case of Einstein-de Sitter-like manifolds.Comment: 34 page
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