291 research outputs found
Multifractality of quantum wave functions in the presence of perturbations
We present a comprehensive study of the destruction of quantum
multifractality in the presence of perturbations. We study diverse
representative models displaying multifractality, including a pseudointegrable
system, the Anderson model and a random matrix model. We apply several types of
natural perturbations which can be relevant for experimental implementations.
We construct an analytical theory for certain cases, and perform extensive
large-scale numerical simulations in other cases. The data are analyzed through
refined methods including double scaling analysis. Our results confirm the
recent conjecture that multifractality breaks down following two scenarios. In
the first one, multifractality is preserved unchanged below a certain
characteristic length which decreases with perturbation strength. In the second
one, multifractality is affected at all scales and disappears uniformly for a
strong enough perturbation. Our refined analysis shows that subtle variants of
these scenarios can be present in certain cases. This study could guide
experimental implementations in order to observe quantum multifractality in
real systems.Comment: 20 pages, 27 figure
Two scenarios for quantum multifractality breakdown
We expose two scenarios for the breakdown of quantum multifractality under
the effect of perturbations. In the first scenario, multifractality survives
below a certain scale of the quantum fluctuations. In the other one, the
fluctuations of the wave functions are changed at every scale and each
multifractal dimension smoothly goes to the ergodic value. We use as generic
examples a one-dimensional dynamical system and the three-dimensional Anderson
model at the metal-insulator transition. Based on our results, we conjecture
that the sensitivity of quantum multifractality to perturbation is universal in
the sense that it follows one of these two scenarios depending on the
perturbation. We also discuss the experimental implications.Comment: 5 pages, 4 figures, minor modifications, published versio
Numerical representation of internal waves propagation
Similar to surface waves propagating at the interface of two fluid of different densities (like air and water), internal waves in the oceanic interior travel along surfaces separating waters of different densities (e.g. at the thermocline). Due to their key role in the global distribution of (physical) diapycnal mixing and mass transport, proper representation of internal wave dynamics in numerical models should be considered a priority since global climate models are now configured with increasingly higher horizontal/vertical resolution. However, in most state-of-the-art oceanic models, important terms involved in the propagation of internal waves (namely the horizontal pressure gradient and horizontal divergence in the continuity equation) are generally discretized using very basic numerics (i.e. second-order approximations) in space and time. In this paper, we investigate the benefits of higher-order approximations in terms of the discrete dispersion relation (in the linear theory) on staggered and nonstaggered computational grids. A fourth-order scheme discretized on a C-grid to approximate both pressure gradient and horizontal divergence terms provides clear improvements but, unlike nonstaggered grids, prevents the use of monotonic or non- oscillatory schemes. Since our study suggests that better numerics is required, second and fourth order direct space-time algorithms are designed, thus paving the way toward the use of efficient high-order discretizations of internal gravity waves in oceanic models, while maintaining good sta- bility properties (those schemes are stable for Courant numbers smaller than 1). Finally, important results obtained at a theoretical level are illustrated at a discrete level using two-dimensional (x,z) idealized experiments
Universality of the Anderson transition with the quasiperiodic kicked rotor
We report a numerical analysis of the Anderson transition in a
quantum-chaotic system, the quasiperiodic kicked rotor with three
incommensurate frequencies. It is shown that this dynamical system exhibits the
same critical phenomena as the truly random 3D-Anderson model. By taking proper
account of systematic corrections to one-parameter scaling, the universality of
the critical exponent is demonstrated. Our result is in
perfect agreement with the value found for the Anderson model.Comment: 4 figures, 3 tables (published version
Universal scaling of the order-parameter distribution in strongly disordered superconductors
We investigate theoretically and experimentally the statistical properties of
the inhomogeneous order-parameter distribution (OPD) at the verge of the
superconductor-insulator transition (SIT). We find within two prototype
fermionic and bosonic models for disordered superconductors that one can
identify a universal rescaling of the OPD. By performing scanning-tunneling
microscopy experiments in three samples of NbN with increasing disorder we show
that such a rescaling describes also with an excellent accuracy the
experimental data. These results can provide a breakthrough in our
understanding of the SIT.Comment: 11 pages, 8 figures, revised version submitted to PR
Two critical localization lengths in the Anderson transition on random graphs
We present a full description of the nonergodic properties of wave functions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths: the largest one describes localization along rare branches and diverges with a critical exponent ν∥=1 at the transition. The second length, which describes localization along typical branches, reaches at the transition a finite universal value (which depends only on the connectivity of the graph), with a singularity controlled by a new critical exponent ν⊥=1/2. We show numerically that these two localization lengths control the finite-size scaling properties of key observables: wave-function moments, correlation functions, and spectral statistics. Our results are identical to the theoretical predictions for the typical localization length in the many-body localization transition, with the same critical exponent. This strongly suggests that the two transitions are in the same universality class and that our techniques could be directly applied in this context
Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1<K<2, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales. In the critical regime, multifractal wave functions are located on a few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusual volumic scaling on the delocalized side. The critical scalings and exponents are independent of the branching parameter, which strongly supports the universality of our results
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