404 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
Semiclassical approach to fidelity amplitude
The fidelity amplitude is a quantity of paramount importance in echo type
experiments. We use semiclassical theory to study the average fidelity
amplitude for quantum chaotic systems under external perturbation. We explain
analytically two extreme cases: the random dynamics limit --attained
approximately by strongly chaotic systems-- and the random perturbation limit,
which shows a Lyapunov decay. Numerical simulations help us bridge the gap
between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio
Entanglement-screening by nonlinear resonances
We show that nonlinear resonances in a classically mixed phase space allow to define generic, strongly entangled multi-partite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e. in the semiclassical limit, for those classes of diffusive noise which assist the quantum-classical transition
Quantum phase estimation algorithm in presence of static imperfections
We study numerically the effects of static imperfections and residual
couplings between qubits for the quantum phase estimation algorithm with two
qubits. We show that the success probability of the algorithm is affected
significantly more by static imperfections than by random noise errors in
quantum gates. An improvement of the algorithm accuracy can be reached by
application of the Pauli-random-error-correction method (PAREC).Comment: 5 pages, 5 figures. Research avilable at
http://www.quantware.ups-tlse.fr
Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
Quantum multifractality is a fundamental property of systems such as
non-interacting disordered systems at an Anderson transition and many-body
systems in Hilbert space. Here we discuss the origin of the presence or absence
of a fundamental symmetry related to this property. The anomalous multifractal
dimension is used to characterize the structure of quantum states in
such systems. Although the multifractal symmetry relation
\mbox{} is universally fulfilled in many known systems,
recently some important examples have emerged where it does not hold. We show
that this is the result of two different mechanisms. The first one was already
known and is related to Gaussian fluctuations well described by random matrix
theory. The second one, not previously explored, is related to the presence of
an algebraically localized envelope. While the effect of Gaussian fluctuations
can be removed by coarse graining, the second mechanism is robust to such a
procedure. We illustrate the violation of the symmetry due to algebraic
localization on two systems of very different nature, a 1D Floquet critical
system and a model corresponding to Anderson localization on random graphs.Comment: Closest to published versio
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
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
Phase space contraction and quantum operations
We give a criterion to differentiate between dissipative and diffusive
quantum operations. It is based on the classical idea that dissipative
processes contract volumes in phase space. We define a quantity that can be
regarded as ``quantum phase space contraction rate'' and which is related to a
fundamental property of quantum channels: non-unitality. We relate it to other
properties of the channel and also show a simple example of dissipative noise
composed with a chaotic map. The emergence of attaractor-like structures is
displayed.Comment: 8 pages, 6 figures. Changes added according to refferee sugestions.
(To appear in PRA
Frenkel-Kontorova model with cold trapped ions
We study analytically and numerically the properties of one-dimensional chain
of cold ions placed in a periodic potential of optical lattice and global
harmonic potential of a trap. In close similarity with the Frenkel-Kontorova
model, a transition from sliding to pinned phase takes place with the increase
of the optical lattice potential for the density of ions incommensurate with
the lattice period. Quantum fluctuations lead to a quantum phase transition and
melting of pinned instanton glass phase at large values of dimensional Planck
constant. The obtained results are also relevant for a Wigner crystal placed in
a periodic potential.Comment: RevTeX, 5 pages, 11 figures, research at
http://www.quantware.ups-tlse.f
- âŠ