2,954 research outputs found
On the reversibility and the closed image property of linear cellular automata
When is an arbitrary group and is a finite-dimensional vector space,
it is known that every bijective linear cellular automaton is reversible and that the image of every linear cellular automaton is closed in for the prodiscrete topology. In this
paper, we present a new proof of these two results which is based on the
Mittag-Leffler lemma for projective sequences of sets. We also show that if
is a non-periodic group and is an infinite-dimensional vector space, then
there exist a linear cellular automaton which is
bijective but not reversible and a linear cellular automaton whose image is not closed in for the prodiscrete topology
Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions
A language L over a finite alphabet is growth-sensitive (or entropy
sensitive) if forbidding any set of subwords F yields a sub-language L^F whose
exponential growth rate (entropy) is smaller than that of L. Let (X, E, l) be
an infinite, oriented, labelled graph. Considering the graph as an (infinite)
automaton, we associate with any pair of vertices x,y in X the language
consisting of all words that can be read as the labels along some path from x
to y. Under suitable, general assumptions we prove that these languages are
growth-sensitive. This is based on using Markov chains with forbidden
transitions.Comment: to appear in Theoretical Computer Science, 201
Expansive actions on uniform spaces and surjunctive maps
We present a uniform version of a result of M. Gromov on the surjunctivity of
maps commuting with expansive group actions and discuss several applications.
We prove in particular that for any group and any field \K, the
space of -marked groups such that the group algebra \K[G] is
stably finite is compact.Comment: 21 page
A numerical ab initio study of harmonic generation from a ring-shaped model molecule in laser fields
When a laser pulse impinges on a molecule which is invariant under certain
symmetry operations selection rules for harmonic generation (HG) arise. In
other words: symmetry controls which channels are open for the deposition and
emission of laser energy---with the possible application of filtering or
amplification. We review the derivation of HG selection rules and study
numerically the interaction of laser pulses with an effectively one-dimensional
ring-shaped model molecule. The harmonic yields obtained from that model and
their dependence on laser frequency and intensity are discussed. In a real
experiment obvious candidates for such molecules are benzene, other aromatic
compounds, or even nanotubes.Comment: 5 pages, 3 figure
Two-color stabilization of atomic hydrogen in circularly polarized laser fields
Dynamic stabilization of atomic hydrogen against ionization in high-frequency
single- and two-color, circularly polarized laser pulses is observed by
numerically solving the three-dimensional, time-dependent Schr\"odinger
equation. The single-color case is revisited and numerically determined
ionization rates are compared with both, exact and approximate high-frequency
Floquet rates. The position of the peaks in the photoelectron spectra can be
explained with the help of dressed initial states. In two-color laser fields of
opposite circular polarization the stabilized probability density may be shaped
in various ways. For laser frequencies and ,
and sufficiently large excursion amplitudes distinct
probability density peaks are observed. This may be viewed as the
generalization of the well-known ``dichotomy'' in linearly polarized laser
fields, i.e, as ``trichotomy,'' ``quatrochotomy,'' ``pentachotomy'' etc. All
those observed structures and their ``hula-hoop''-like dynamics can be
understood with the help of high-frequency Floquet theory and the two-color
Kramers-Henneberger transformation. The shaping of the probability density in
the stabilization regime can be realized without additional loss in the
survival probability, as compared to the corresponding single-color results.Comment: 10 pages, REVTeX4, 11 eps-figures, see also
http://www.physik.tu-darmstadt.de/tqe/dieter/publist.html for a manuscript
with higher-quality figure
On surjunctive monoids
A monoid is called surjunctive if every injective cellular automata with
finite alphabet over is surjective. We show that all finite monoids, all
finitely generated commutative monoids, all cancellative commutative monoids,
all residually finite monoids, all finitely generated linear monoids, and all
cancellative one-sided amenable monoids are surjunctive. We also prove that
every limit of marked surjunctive monoids is itself surjunctive. On the other
hand, we show that the bicyclic monoid and, more generally, all monoids
containing a submonoid isomorphic to the bicyclic monoid are non-surjunctive
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