25,494 research outputs found
Emergent SU(N) symmetry in disordered SO(N) spin chains
Strongly disordered spin chains invariant under the SO(N) group are shown to
display random-singlet phases with emergent SU(N) symmetry without fine tuning.
The phases with emergent SU(N) symmetry are of two kinds: one has a ground
state formed of randomly distributed singlets of strongly bound pairs of SO(N)
spins (a `mesonic' phase), while the other has a ground state composed of
singlets made out of strongly bound integer multiples of N SO(N) spins (a
`baryonic' phase). The established mechanism is general and we put forward the
cases of and as prime candidates for experimental
realizations in material compounds and cold-atoms systems. We display universal
temperature scaling and critical exponents for susceptibilities distinguishing
these phases and characterizing the enlarging of the microscopic symmetries at
low energies.Comment: 5 pages, 2 figures, Contribution to the Topical Issue "Recent
Advances in the Theory of Disordered Systems", edited by Ferenc Igl\'oi and
Heiko Riege
Highly-symmetric random one-dimensional spin models
The interplay of disorder and interactions is a challenging topic of
condensed matter physics, where correlations are crucial and exotic phases
develop. In one spatial dimension, a particularly successful method to analyze
such problems is the strong-disorder renormalization group (SDRG). This method,
which is asymptotically exact in the limit of large disorder, has been
successfully employed in the study of several phases of random magnetic chains.
Here we develop an SDRG scheme capable to provide in-depth information on a
large class of strongly disordered one-dimensional magnetic chains with a
global invariance under a generic continuous group. Our methodology can be
applied to any Lie-algebra valued spin Hamiltonian, in any representation. As
examples, we focus on the physically relevant cases of SO(N) and Sp(N)
magnetism, showing the existence of different randomness-dominated phases.
These phases display emergent SU(N) symmetry at low energies and fall in two
distinct classes, with meson-like or baryon-like characteristics. Our
methodology is here explained in detail and helps to shed light on a general
mechanism for symmetry emergence in disordered systems.Comment: 26 pages, 12 figure
Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows
We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN],
on the vanishing viscosity limit of circularly symmetric viscous flow in a disk
with rotating boundary, shown there to converge to the inviscid limit in
-norm as long as the prescribed angular velocity of the
boundary has bounded total variation. Here we establish convergence in stronger
and -Sobolev spaces, allow for more singular angular velocities
, and address the issue of analyzing the behavior of the boundary
layer. This includes an analysis of concentration of vorticity in the vanishing
viscosity limit. We also consider such flows on an annulus, whose two boundary
components rotate independently.
[LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J.,
Vanishing viscosity limit for incompressible flow inside a rotating circle,
preprint 2006
Developing a site-conditions map for seismic hazard Assessment in Portugal
The evaluation of site effects on a broad scale is a critical issue for seismic hazard and risk assessment, land use planning and emergency planning. As characterization of site conditions based on the shear-wave velocity has become increasingly important, several methods have been proposed in the literature to estimate its average over the first thirty meters (Vs30) from more extensively available data. These methods include correlations with geologic-geographic defined units and topographic slope. In this paper we present the first steps towards the development of a site–conditions map for Portugal, based on a regional database of shear-wave velocity data, together with geological, geographic, and lithological information. We computed Vs30 for each database site and classified it according to the corresponding geological-lithological information using maps at the smallest scale available (usually 1:50000). We evaluated the consistency of Vs30 values within generalized-geological classes, and assessed the performance of expedient methodologies proposed in the literature
Experimental determination of the non-extensive entropic parameter
We show how to extract the parameter from experimental data, considering
an inhomogeneous magnetic system composed by many Maxwell-Boltzmann homogeneous
parts, which after integration over the whole system recover the Tsallis
non-extensivity. Analyzing the cluster distribution of
LaSrMnO manganite, obtained through scanning tunnelling
spectroscopy, we measure the parameter and predict the bulk magnetization
with good accuracy. The connection between the Griffiths phase and
non-extensivity is also considered. We conclude that the entropic parameter
embodies information about the dynamics, the key role to describe complex
systems.Comment: Submitted to Phys. Rev. Let
Eigenfunctions of the Laplacian and associated Ruelle operator
Let be a co-compact Fuchsian group of isometries on the Poincar\'e
disk \DD and the corresponding hyperbolic Laplace operator. Any
smooth eigenfunction of , equivariant by with real
eigenvalue , where , admits an integral
representation by a distribution \dd_{f,s} (the Helgason distribution) which
is equivariant by and supported at infinity \partial\DD=\SS^1. The
geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension
over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the
so-called Bowen-Series transformation. Let be the complex Ruelle
transfer operator associated to the jacobian . M. Pollicott showed
that \dd_{f,s} is an eigenfunction of the dual operator for the
eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic
eigenfunction of for the eigenvalue 1, given by an
integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}}
\dd_{f,s} (d\eta), \noindent where is a -valued
piecewise constant function whose definition depends upon the geometry of the
Dirichlet fundamental domain representing the surface \DD/\Gamma
A neuronal network model of interictal and recurrent ictal activity
We propose a neuronal network model which undergoes a saddle-node bifurcation
on an invariant circle as the mechanism of the transition from the interictal
to the ictal (seizure) state. In the vicinity of this transition, the model
captures important dynamical features of both interictal and ictal states. We
study the nature of interictal spikes and early warnings of the transition
predicted by this model. We further demonstrate that recurrent seizures emerge
due to the interaction between two networks.Comment: 9 pages, 7 figure
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