2,664 research outputs found
Electronic properties of ternary quasicrystals in one dimension
The one-electron properties of a certain class of one-dimensional ternary
quasicrystals are investigated. In particular, we show in detail the presence
of a special kind of critical states called marginal critical states in these
QCs. By the use of a real-space renormalization-group method, it is shown that
the scaling properties of marginal critical states are characterized by
stretched exponentials. These states are virtually localized, so that their
presence may make a QC less conductive.Comment: 19 pages, 9 figures, 2 tables, uses REVTeX. (V3) Title, abstract, and
introduction have been modified. To appear in Phys. Rev.
Quantum speedup for active learning agents
Can quantum mechanics help us in building intelligent robots and agents? One
of the defining characteristics of intelligent behavior is the capacity to
learn from experience. However, a major bottleneck for agents to learn in any
real-life situation is the size and complexity of the corresponding task
environment. Owing to, e.g., a large space of possible strategies, learning is
typically slow. Even for a moderate task environment, it may simply take too
long to rationally respond to a given situation. If the environment is
impatient, allowing only a certain time for a response, an agent may then be
unable to cope with the situation and to learn at all. Here we show that
quantum physics can help and provide a significant speed-up for active learning
as a genuine problem of artificial intelligence. We introduce a large class of
quantum learning agents for which we show a quadratic boost in their active
learning efficiency over their classical analogues. This result will be
particularly relevant for applications involving complex task environments.Comment: Minor updates, 14 pages, 3 figure
Generalized calculation of magnetic coupling constants for Mott-Hubbard insulators: Application to ferromagnetic Cr compounds
Using a Rayleigh-Schr\"odinger perturbation expansion of multi-band Hubbard
models, we present analytic expressions for the super-exchange coupling
constants between magnetic transition metal ions of arbitrary separation in
Mott-Hubbard insulators. The only restrictions are i) all ligand ions are
closed shell anions and ii) all contributing interaction paths are of equal
length. For short paths, our results essentially confirm the
Goodenough-Kanamori-Anderson rules, yet in general there does not exist any
simple rule to predict the sign of the magnetic coupling constants. The most
favorable situation for ferromagnetic coupling is found for ions with less than
half filled d shells, the (relative) tendency to ferromagnetic coupling
increases with increasing path length. As an application, the magnetic
interactions of the Cr compounds RbCrCl, CrCl, CrBr and CrI
are investigated, all of which except CrCl are ferromagnets.Comment: 13 pages, 6 eps figures, submitted to Phys Rev
Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization
Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise
to optimal frequency-hopping sequences and optimal comma-free codes. New
constructions for PCDPs, based on almost difference sets and cyclic difference
matrices, are given. These produce new infinite families of optimal PCDPs (and
hence optimal frequency-hopping sequences and optimal comma-free codes). The
existence problem for optimal PCDPs in , with base blocks
of size three, is also solved for all .Comment: to appear in IEEE Transactions on Information Theor
Fermions in three-dimensional spinfoam quantum gravity
We study the coupling of massive fermions to the quantum mechanical dynamics
of spacetime emerging from the spinfoam approach in three dimensions. We first
recall the classical theory before constructing a spinfoam model of quantum
gravity coupled to spinors. The technique used is based on a finite expansion
in inverse fermion masses leading to the computation of the vacuum to vacuum
transition amplitude of the theory. The path integral is derived as a sum over
closed fermionic loops wrapping around the spinfoam. The effects of quantum
torsion are realised as a modification of the intertwining operators assigned
to the edges of the two-complex, in accordance with loop quantum gravity. The
creation of non-trivial curvature is modelled by a modification of the pure
gravity vertex amplitudes. The appendix contains a review of the geometrical
and algebraic structures underlying the classical coupling of fermions to three
dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER
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