7,674 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
Implementation of Spin Hamiltonians in Optical Lattices
We propose an optical lattice setup to investigate spin chains and ladders.
Electric and magnetic fields allow us to vary at will the coupling constants,
producing a variety of quantum phases including the Haldane phase, critical
phases, quantum dimers etc. Numerical simulations are presented showing how
ground states can be prepared adiabatically. We also propose ways to measure a
number of observables, like energy gap, staggered magnetization, end-chain
spins effects, spin correlations and the string order parameter
Anderson localization in a periodic photonic lattice with a disordered boundary
We investigate experimentally the light evolution inside a two-dimensional
finite periodic array of weakly- coupled optical waveguides with a disordered
boundary. For a completely localized initial condition away from the surface,
we find that the disordered boundary induces an asymptotic localization in the
bulk, centered around the initial position of the input beam.Comment: 3 pages, 4 figure
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
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 Îœâ„=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 Îœâ„=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
Nutritional intervention in early life to manipulate rumen microbial colonization and methane output by kid goats post-weaning
Non-abelian D=11 Supermembrane
We obtain a U(M) action for supermembranes with central charges in the Light
Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of
the supermembrane together with the invariance under a U(M) gauge group with M
arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it
corresponds to M parallel supermembranes minimally immersed on the target M9xT2
(MIM2). In order to ensure the invariance under the symmetries and to close the
corresponding algebra, a star-product determined by the central charge
condition is introduced. It is constructed with a nonconstant symplectic
two-form where curvature terms are also present. The theory is in the strongly
coupled gauge-gravity regime. At low energies, the theory enters in a
decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for
any number of M2-branes.Comment: Contribution to the Proceedings of the Dubna International SQS'09
Workshop ("Supersymmetries and Quantum Symmetries-2009", July 29 - August 3,
2009. 12pg, Late
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