6,009 research outputs found
Global critical temperature in disordered superconductors with weak multifractality
There is growing evidence, from experiments and numerical simulations, that a
key feature of sufficiently disordered superconductors is the spatial
inhomogeneity of the order parameter. However not much is known analytically
about the details of its spatial distribution or the associated global critical
temperature that signals the breaking of long-range order. Here we address this
problem for disordered systems around an Anderson transition characterized by
multifractal one-body eigenstates. In the limit of weak multifractality and for
weakly coupled superconductors we compute the superconducting order parameter
analytically, including its energy dependence and statistical distribution in
space. The spatial distribution of the order parameter is found to be always
log-normal. The global critical temperature, computed by percolation techniques
and neglecting phase fluctuations, is enhanced with respect to the clean limit
only for very weakly coupled superconductors. Some enhancement still persists
even in the presence of moderate phase fluctuations crudely modelled by
increasing the percolation threshold. Our results are also consistent with
experiments, where enhancement of the critical temperature is observed in Al
thin films, a very weakly coupled metallic superconductor, but not in more
strongly coupled materials.A.M.G. was supported by EPSRC, Grant No. EP/I004637/1, FCT, Grant PTDC/FIS/111348/2009, and a Marie Curie International Reintegration Grant PIRG07-GA-2010-268172. J.M. acknowledges the support of an EPSRC Ph.D. studentship.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevB.92.17452
Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
We study a one-dimensional (1d) XXZ spin-chain in a random field on the
metallic side of the many-body localization transition by level statistics. For
a fixed interaction, and intermediate disorder below the many-body localization
transition, we find that, asymptotically, the number variance grows faster than
linear with a disorder dependent exponent. This is consistent with the
existence of an anomlaous Thouless energy in the spectrum. In non-interacting
disordered metals this is an energy scale related to the typical time for a
particle to diffuse across the sample. In the interacting case it seems related
to a more intricate anomalous diffusion process. This interpretation is not
fully consistent with recent claims that, for intermediate disorder, level
statistics are described by a plasma model with power-law decaying interactions
whose number variance grows slower than linear. As disorder is further
increased, still on the metallic side, the Thouless energy is gradually washed
out. In the range of sizes we can explore, level statistics are scale invariant
and approach Poisson statistics at the many-body localization transition.
Slightly below the many-body localization transition, spectral correlations,
well described by critical statistics, are quantitatively similar to those of a
high dimensional, non-interacting, disordered conductor at the Anderson
transition.A.M.G. acknowledges support from EPSRC, Grant No. EP/I004637/1.This is the author accepted manuscript. The final version is available from the American Physical Society via https://doi.org/10.1103/PhysRevB.94.14420
Defect formation beyond kibble-zurek mechanism and holography
We study the dynamic after a smooth quench across a continuous transition
from the disordered phase to the ordered phase. Based on scaling ideas, linear
response and the spectrum of unstable modes, we develop a theoretical
framework, valid for any second order phase transition, for the early-time
evolution of the condensate in the broken phase. Our analysis unveils a novel
period of non-adiabatic evolution after the system passes through the phase
transition, where a parametrically large amount of coarsening occurs before a
well-defined condensate forms. Our formalism predicts a rate of defect
formation parametrically smaller than the Kibble-Zurek prediction and yields a
criterion for the break-down of Kibble-Zurek scaling for sufficiently fast
quenches. We numerically test our formalism for a thermal quench in a 2 + 1
dimensional holographic superfluid. These findings, of direct relevance in a
broad range of fields including cold atom, condensed matter, statistical
mechanism and cosmology, are an important step towards a more quantitative
understanding of dynamical phase transitions.We thank Laurence Yaffe for useful discussions. The work of P. M. C. is supported by the Fundamental Laws Initiative of the Center for the Fundamental Laws of Nature at Harvard University. The work of H. L. is partially supported by the U.S. Department of Energy (DOE) under Cooperative Research Agreement No. DE-FG0205ER41360. A. M. G.-G. was supported by Engineering and Physical Sciences Research Council, Grant No. EP/I004637/1; Fundação para a Ciência e a Tecnologia, Grant No. PTDC/FIS/111348/2009; and a Marie Curie International Reintegration Grant No. PIRG07-GA-2010-268172.This is the final version of the article. It first appeared from APS via http://dx.doi.org/10.1103/PhysRevX.5.02101
Transport in a gravity dual with a varying gravitational coupling constant
We study asymptotically AdS Brans-Dicke (BD) backgrounds, where the Ricci tensor R is coupled to a scalar in the radial dimension, as effective models of metals with a varying coupling constant. We show that, for translationally invariant backgrounds, the regular part of the dc conductivity σ deviates from the universal result of Einstein-Maxwell-dilaton (EMD) models. However, the shear viscosity to entropy ratio saturates the Kovtun-Son-Starinets (KSS) bound. Similar results apply to more general f(R) gravity models. In four bulk dimensions we study momentum relaxation induced by gravitational and electromagnetic axion-dependent couplings. For sufficiently strong momentum dissipation induced by the former, a recently proposed bound on the dc conductivity σ is violated for any finite electromagnetic axion coupling. Interestingly, in more than four bulk dimensions, the dc conductivity for strong momentum relaxation decreases with temperature in the low temperature limit. In line with other gravity backgrounds with momentum relaxation, the shear viscosity to entropy ratio is always lower than the KSS bound. The numerical computation of the optical conductivity reveals a linear growth with the frequency in the limit of low temperature, low frequency and large momentum relaxation. We have also shown that the module and argument of the optical conductivity for intermediate frequencies are not consistent with cuprates' experimental results, even assuming several channel of momentum relaxation.A.M.G. acknowledges support from EPSRC, Grant No. EP/I004637/1. B.L. is supported by CAPES/COT Grant No. 11469/13-17. A.R.B. acknowledges support from the Department of Physics and the Theory of Condensed Matter group of the University of Cambridge as well as the Cambridge Philosophical Society
WiBAF into a CMS: Personalization in learning environments made easy
Adaptivity has proven successful in reducing navigation and comprehension problems in hypermedia documents. Authoring of adaptive hypermedia documents and especially of the adaptivity in these documents has been problematic or at least labour intensive throughout AH history. This paper shows how the integration of a CMS with an adaptive framework greatly simplifies the inclusion of personalization in existing educational applications. It does this within the context of European project Autism&Uni that uses adaptive hypermedia to offer information for students transitioning from high school to university, especially to cater for students on the autism spectrum as well as for non-autistic students. The use of our Within Browser adaptation framework (WiBAF) reduces privacy concerns because the user model is stored on the end-user's machine, and eliminates performance issues that currently prevent the adoption of adaptivity in MOOC platforms by having the adaptation performed on the end-user's machine as well (within the browser). Authoring of adaptive applications within the educational domain with the system proposed was tried out with first year students from the Design-Based Learning Hypermedia course at the Eindhoven University of Technology (TU/e) to gather feedback on the problems they faced with the platform
Adaptive web-based educational application for autistic students
Adaptive web-based applications have proven successful in reducing navigation and comprehension problems in hypermedia documents. In this paper, we describe a toolkit that is offered as an adaptive Web-based application to help autistic students incorporate to high education. The toolkit has been developed using a popular CMS in which we have integrated a client-side adaptation library. The toolkit described here was tried out during workshops with autistic students at Leeds Becketts University to gather (mostly qualitative) feedback on the adaptation and privacy aspects of the Autism&Uni platform. That feedback was later used to improve the toolkit
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