Multifractal wave functions of simple quantum maps.

  title={Multifractal wave functions of simple quantum maps.},
  author={John Martin and Ignacio Garc{\'i}a-Mata and Olivier Giraud and Bertrand Georgeot},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={82 4 Pt 2},
We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet… 
Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems.
It is shown that finite statistics has remarkably strong effects, so that even random matrix computations deviate from analytic results (and show strong sample-to-sample variation), such that restoring agreement requires exponentially large sample sizes.
Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos
  • Qian Wang, M. Robnik
  • Computer Science, Medicine
  • 2021
It is shown that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space and the probability distribution of expansion coefficients is investigated.
Multifractal Eigenfunctions for a Singular Quantum Billiard
Whereas much work in the mathematical literature on quantum chaos has focused on phenomena such as quantum ergodicity and scarring, relatively little is known at the rigorous level about the
Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing
Abstract We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in
Multifractality of open quantum systems.
It is conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy.
On the generalized dimensions of multifractal eigenstates
Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, Dq and , of the eigenstates of critical random matrix ensembles: , 1 ⩽
Disordered Kitaev chains with long-range pairing.
  • Xiaoming Cai
  • Physics, Medicine
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2017
This work focuses on the transition from the topological superconducting phase to the topologically trivial Anderson localized phase, and effects of the exponent α on this phase transition.
Quantum localization measures in phase space.
A general scheme to define localization in measure spaces, based on what is called Rényi occupations, is presented, from which any measure of localization can be derived, and is applied to the four-dimensional unbounded phase space of the interacting spin-boson Dicke model.
Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields
Abstract Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the
Many-Body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases.
It is shown that the scaling of the derivative of any generalized fractal dimension with respect to the interaction strength encodes the critical point of the superfluid to the Mott insulator transition, and provides an efficient way to accurately estimate its position.


Theory and Applications
Infinitary rewriting generalises usual finitary rewriting by providing infinite reduction sequences with a notion of convergence. The idea of – at least conceptually – assigning a meaning to infinite
Journal of Geophysical Research
FROM March 1949 the journal Terrestrial Magnetism and Almespheric Electricity will appear under the new title Journal of Geophysical Research. The change the name marks the transfer of editorship
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
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