11,325 research outputs found
Spectral properties of the trap model on sparse networks
One of the simplest models for the slow relaxation and aging of glasses is
the trap model by Bouchaud and others, which represents a system as a point in
configuration-space hopping between local energy minima. The time evolution
depends on the transition rates and the network of allowed jumps between the
minima. We consider the case of sparse configuration-space connectivity given
by a random graph, and study the spectral properties of the resulting master
operator. We develop a general approach using the cavity method that gives
access to the density of states in large systems, as well as localisation
properties of the eigenvectors, which are important for the dynamics. We
illustrate how, for a system with sparse connectivity and finite temperature,
the density of states and the average inverse participation ratio have
attributes that arise from a non-trivial combination of the corresponding mean
field (fully connected) and random walk (infinite temperature) limits. In
particular, we find a range of eigenvalues for which the density of states is
of mean-field form but localisation properties are not, and speculate that the
corresponding eigenvectors may be concentrated on extensively many clusters of
network sites.Comment: 41 pages, 15 figure
Tuna dreams revisited: economic contributions from a tuna enterprise in Solomon Islands
Tuna is one of the few renewable resources available on a large scale for Pacific island countries, and many countries want to develop onshore value-adding processing to generate more domestic economic development from tuna fisheries in the region. The case of Soltai Fishing and Processing (formerly Solomon Taiyo Ltd) provides many useful lessons about the benefits and pitfalls of this development strategy
Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
Many-body localisation is studied in a disordered quantum spin-1/2 chain with
long-ranged power-law interactions, and distinct power-law exponents for
interactions between longitudinal and transverse spin components. Using a
self-consistent mean-field theory centring on the local propagator in Fock
space and its associated self-energy, a localisation phase diagram is obtained
as a function of the power-law exponents and the disorder strength of the
random fields acting on longitudinal spin-components. Analytical results are
corroborated using the well-studied and complementary numerical diagnostics of
level statistics, entanglement entropy, and participation entropy, obtained via
exact diagonalisation. We find that increasing the range of interactions
between transverse spin components hinders localisation and enhances the
critical disorder strength. In marked contrast, increasing the interaction
range between longitudinal spin components is found to enhance localisation and
lower the critical disorder.Comment: 30 pages, 4 figure
Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method
Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes. (C) 2009 Elsevier B.V. All rights reserved
Decohering d-dimensional quantum resistance
The Landauer scattering approach to 4-probe resistance is revisited for the
case of a d-dimensional disordered resistor in the presence of decoherence. Our
treatment is based on an invariant-embedding equation for the evolution of the
coherent reflection amplitude coefficient in the length of a 1-dimensional
disordered conductor, where decoherence is introduced at par with the disorder
through an outcoupling, or stochastic absorption, of the wave amplitude into
side (transverse) channels, and its subsequent incoherent re-injection into the
conductor. This is essentially in the spirit of B{\"u}ttiker's
reservoir-induced decoherence. The resulting evolution equation for the
probability density of the 4-probe resistance in the presence of decoherence is
then generalised from the 1-dimensional to the d-dimensional case following an
anisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namely
that the disorder evolves in one arbitrarily chosen direction only, is the main
approximation here that makes the analytical treatment possible. A
qualitatively new result is that arbitrarily small decoherence reduces the
localisation-delocalisation transition to a crossover making resistance moments
of all orders finite.Comment: 14 pages, 1 figure, revised version, to appear in Phys. Rev.
More than skin deep: body representation beyond primary somatosensory cortex
The neural circuits underlying initial sensory processing of somatic information are relatively well understood. In contrast, the processes that go beyond primary somatosensation to create more abstract representations related to the body are less clear. In this review, we focus on two classes of higher-order processing beyond somatosensation. Somatoperception refers to the process of perceiving the body itself, and particularly of ensuring somatic perceptual constancy. We review three key elements of somatoperception: (a) remapping information from the body surface into an egocentric reference frame (b) exteroceptive perception of objects in the external world through their contact with the body and (c) interoceptive percepts about the nature and state of the body itself. Somatorepresentation, in contrast, refers to the essentially cognitive process of constructing semantic knowledge and attitudes about the body, including: (d) lexical-semantic knowledge about bodies generally and one’s own body specifically, (e) configural knowledge about the structure of bodies, (f) emotions and attitudes directed towards one’s own body, and (g) the link between physical body and psychological self. We review a wide range of neuropsychological, neuroimaging and neurophysiological data to explore the dissociation between these different aspects of higher somatosensory function
Spectra of Modular and Small-World Matrices
We compute spectra of symmetric random matrices describing graphs with
general modular structure and arbitrary inter- and intra-module degree
distributions, subject only to the constraint of finite mean connectivities. We
also evaluate spectra of a certain class of small-world matrices generated from
random graphs by introducing short-cuts via additional random connectivity
components. Both adjacency matrices and the associated graph Laplacians are
investigated. For the Laplacians, we find Lifshitz type singular behaviour of
the spectral density in a localised region of small values. In the
case of modular networks, we can identify contributions local densities of
state from individual modules. For small-world networks, we find that the
introduction of short cuts can lead to the creation of satellite bands outside
the central band of extended states, exhibiting only localised states in the
band-gaps. Results for the ensemble in the thermodynamic limit are in excellent
agreement with those obtained via a cavity approach for large finite single
instances, and with direct diagonalisation results.Comment: 18 pages, 5 figure
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