6,024 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
Marginal and irrelevant disorder in Einstein-Maxwell backgrounds
We study analytically the effect of a weak random chemical potential of zero
average in an Einstein-Maxwell background. For uncorrelated disorder this
perturbation is relevant however we show that it can become marginal or even
irrelevant by tuning disorder correlations. At zero temperature we find that,
to leading order in the disorder strength, the correction to the conductivity
for irrelevant perturbations vanishes. In the marginal case, in order to
renormalize a logarithmic divergence, we carry out a resummation of the
perturbative expansion of the metric that leads to a Lifshitz-like geometry in
the infrared. Disorder in this case also induces a positive correction to the
conductivity. At finite temperature the black hole acquires an effective charge
and the thermal conductivity has the expected Drude peak that signals the
breaking of translational invariance. However the electric conductivity is not
affected by the random chemical potential to leading order in the disorder
strength.A. M. G. thanks Hong Liu and Elias Kiritsis for illuminating discussions. A. M. G. acknowledges partial support from EPSRC, grant No. EP/I004637/1. B. L. thanks Andrew Lucas for interesting discussions and suggestions concerning the conductivity. B.L. is supported by a CAPES/COT grant No. 11469/13-17. Both authors are grateful to the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society
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Conductivity and entanglement entropy of high dimensional holographic superconductors
We investigate the dependence of the conductivity and the entanglement
entropy on the space-time dimensionality in two holographic
superconductors: one dual to a quantum critical point with spontaneous symmetry
breaking, and the other modeled by a charged scalar that condenses at a
sufficiently low temperature in the presence of a Maxwell field. In both cases
the gravity background is asymptotically Anti de Sitter (AdS). In the large
limit we obtain explicit analytical results for the conductivity at zero
temperature and the entanglement entropy by a expansion. We show that the
entanglement entropy is always smaller in the broken phase. As dimensionality
increases, the entanglement entropy decreases, the coherence peak in the
conductivity becomes narrower and the ratio between the energy gap and the
critical temperature decreases. These results suggest that the condensate
interactions become weaker in high spatial dimensions.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/JHEP09(2015)03
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.âM.âC. is supported by the Fundamental Laws Initiative of the Center for the Fundamental Laws of Nature at Harvard University. The work of H.âL. is partially supported by the U.S. Department of Energy (DOE) under Cooperative Research Agreement No. DE-FG0205ER41360. A.âM.âG.-G. was supported by Engineering and Physical Sciences Research Council, Grant No. EP/I004637/1; Fundação para a CiĂȘncia 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 Ï 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 Ï 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
Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the k-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the fourth- and sixth-order energy cumulants vanish in the limit of a large number of particles Nââ, which is consistent with a Gaussian spectral density. However, for finite N, the tail of the average spectral density is well approximated by a semicircle law. The specific heat coefficient, determined numerically from the low-temperature behavior of the partition function, is consistent with the value obtained by previous analytical calculations. For energy scales of the order of the mean level spacing we show that level statistics are well described by random matrix theory. Due to the underlying Clifford algebra of the model, the universality class of the spectral correlations depends on N. For larger energy separations we identify an energy scale that grows with N, reminiscent of the Thouless energy in mesoscopic physics, where deviations from random matrix theory are observed. Our results are a further confirmation that the Sachdev-Ye-Kitaev model is quantum chaotic for all time scales. According to recent claims in the literature, this is an expected feature in field theories with a gravity dual.EPSRC, Grant No. EP/I004637/1; U.S. Department of Energy Grant No. DE-FG-88FR4038
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Drude weight and Mazur-Suzuki bounds in holography
We investigate the Drude weight and the related Mazur-Suzuki (MS) bound in a
broad variety of strongly coupled field theories with a gravity dual at finite
temperature and chemical potential. We revisit the derivation of the recently
proposed universal expression for the Drude weight for Einstein-Maxwell-dilaton
(EMd) theories and extend it to the case of theories with multiple massless
gauge fields. We show that the MS bound, which in the context of condensed
matter provides information on the integrability of the theory, is saturated in
these holographic theories including R-charged backgrounds. We then explore the
limits of this universality by studying EMd theories with spontaneous
symmetry breaking and gravity duals of non-relativistic field theories
including an asymptotically Lifshitz EMd model with two massless gauge fields
and the Einstein-Proca model. In all these cases, the Drude weight, computed
analytically, deviates from the universal result and the MS bound is not
saturated. In general it is not possible to deduce the low temperature
dependence of the Drude weight by simple dimensional analysis. Finally we study
the effect of a weak breaking of translational symmetry by coupling the EMd
action, with and without spontaneous symmetry breaking, to an axion
field. We show the coherent part of the conductivity in this limit is simply
the product of the MS bound and the scattering time obtained from the leading
quasinormal mode. For asymptotically theories it seems that the MS bound
sets a lower bound on the DC conductivity for a given scattering time.A. R. B. thanks Kostas Skenderis and Yegor Korovin for illuminating discussions. A. M. G. thanks Carlos Hoyos for illuminating discussions and acknowledges partial support from EPSRC, grant No. EP/I004637/1. A. R. B. has been supported by the Department of Physics of the University of Cambridge. Both authors are grateful to the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society
Environmental epigenomics: Current approaches to assess epigenetic effects of endocrine disrupting compounds (EDC's) on human health
Environmental Epigenomics is a developing field to study the epigenetic effect on human health from exposure to environmental factors. Endocrine disrupting chemicals have been detected primarily in pharmaceutical drugs, personal care products, food additives, and food containers. Exposure to endocrine-disrupting chemicals (EDCs) has been associated with a high incidence and prevalence of many endocrine-related disorders in humans. Nevertheless, further evidence is needed to establish a correlation between exposure to EDC and human disorders. Conventional detection of EDCs is based on chemical structure and concentration sample analysis. However, substantial evidence has emerged, suggesting that cell exposure to EDCs leads to epigenetic changes, independently of its chemical structure with non-monotonic low-dose responses. Consequently, a paradigm shift in toxicology assessment of EDCs is proposed based on a comprehensive review of analytical techniques used to evaluate the epigenetic effects. Fundamental insights reported elsewhere are compared in order to establish DNA methylation analysis as a viable method for assessing endocrine disruptors beyond the conventional study approach of chemical structure and concentration analysis
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
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