126 research outputs found
Geometric phases in quantum control disturbed by classical stochastic processes
We describe the geometric (Berry) phases arising when some quantum systems
are driven by control classical parameters but also by outer classical
stochastic processes (as for example classical noises). The total geometric
phase is then divided into an usual geometric phase associated with the control
parameters and a second geometric phase associated with the stochastic
processes. The geometric structure in which these geometric phases take place
is a composite bundle (and not an usual principal bundle), which is explicitely
built in this paper. We explain why the composite bundle structure is the more
natural framework to study this problem. Finally we treat a very simple example
of a two level atom driven by a phase modulated laser field with a phase
instability described by a gaussian white noise. In particular we compute the
average geometric phase issued from the noise
Exotic Smoothness and Physics
The essential role played by differentiable structures in physics is reviewed
in light of recent mathematical discoveries that topologically trivial
space-time models, especially the simplest one, , possess a rich
multiplicity of such structures, no two of which are diffeomorphic to each
other and thus to the standard one. This means that physics has available to it
a new panoply of structures available for space-time models. These can be
thought of as source of new global, but not properly topological, features.
This paper reviews some background differential topology together with a
discussion of the role which a differentiable structure necessarily plays in
the statement of any physical theory, recalling that diffeomorphisms are at the
heart of the principle of general relativity. Some of the history of the
discovery of exotic, i.e., non-standard, differentiable structures is reviewed.
Some new results suggesting the spatial localization of such exotic structures
are described and speculations are made on the possible opportunities that such
structures present for the further development of physical theories.Comment: 13 pages, LaTe
Natural extensions and entropy of -continued fractions
We construct a natural extension for each of Nakada's -continued
fractions and show the continuity as a function of of both the entropy
and the measure of the natural extension domain with respect to the density
function . In particular, we show that, for all , the product of the entropy with the measure of the domain equals .
As a key step, we give the explicit relationship between the -expansion
of and of
Separation of trajectories and its Relation to Entropy for Intermittent Systems with a Zero Lyapunov exponent
One dimensional intermittent maps with stretched exponential separation of
nearby trajectories are considered. When time goes infinity the standard
Lyapunov exponent is zero. We investigate the distribution of
,
where is determined by the nonlinearity of the map in the vicinity of
marginally unstable fixed points. The mean of is determined
by the infinite invariant density. Using semi analytical arguments we calculate
the infinite invariant density for the Pomeau-Manneville map, and with it
obtain excellent agreement between numerical simulation and theory. We show
that \alpha \left is equal to Krengel's entropy and
to the complexity calculated by the Lempel-Ziv compression algorithm. This
generalized Pesin's identity shows that \left and
Krengel's entropy are the natural generalizations of usual Lyapunov exponent
and entropy for these systems.Comment: 12 pages, 10 figure
Pesin-type relation for subexponential instability
We address here the problem of extending the Pesin relation among positive
Lyapunov exponents and the Kolmogorov-Sinai entropy to the case of dynamical
systems exhibiting subexponential instabilities. By using a recent rigorous
result due to Zweim\"uller, we show that the usual Pesin relation can be
extended straightforwardly for weakly chaotic one-dimensional systems of the
Pomeau-Manneville type, provided one introduces a convenient subexponential
generalization of the Kolmogorov-Sinai entropy. We show, furthermore, that
Zweim\"uller's result provides an efficient prescription for the evaluation of
the algorithm complexity for such systems. Our results are confirmed by
exhaustive numerical simulations. We also point out and correct a misleading
extension of the Pesin relation based on the Krengel entropy that has appeared
recently in the literature.Comment: 10 pages, 4 figures. Final version to appear in Journal of
Statistical Mechanics (JSTAT
The entropy of alpha-continued fractions: numerical results
We consider the one-parameter family of interval maps arising from
generalized continued fraction expansions known as alpha-continued fractions.
For such maps, we perform a numerical study of the behaviour of metric entropy
as a function of the parameter. The behaviour of entropy is known to be quite
regular for parameters for which a matching condition on the orbits of the
endpoints holds. We give a detailed description of the set M where this
condition is met: it consists of a countable union of open intervals,
corresponding to different combinatorial data, which appear to be arranged in a
hierarchical structure. Our experimental data suggest that the complement of M
is a proper subset of the set of bounded-type numbers, hence it has measure
zero. Furthermore, we give evidence that the entropy on matching intervals is
smooth; on the other hand, we can construct points outside of M on which it is
not even locally monotone.Comment: 33 pages, 14 figure
Exotic Differentiable Structures and General Relativity
We review recent developments in differential topology with special concern
for their possible significance to physical theories, especially general
relativity. In particular we are concerned here with the discovery of the
existence of non-standard (``fake'' or ``exotic'') differentiable structures on
topologically simple manifolds such as , \R and
Because of the technical difficulties involved in the smooth case, we begin
with an easily understood toy example looking at the role which the choice of
complex structures plays in the formulation of two-dimensional vacuum
electrostatics. We then briefly review the mathematical formalisms involved
with differentiable structures on topological manifolds, diffeomorphisms and
their significance for physics. We summarize the important work of Milnor,
Freedman, Donaldson, and others in developing exotic differentiable structures
on well known topological manifolds. Finally, we discuss some of the geometric
implications of these results and propose some conjectures on possible physical
implications of these new manifolds which have never before been considered as
physical models.Comment: 11 pages, LaTe
The Standard Model with gravity couplings
In this paper, we examine the coupling of matter fields to gravity within the
framework of the Standard Model of particle physics. The coupling is described
in terms of Weyl fermions of a definite chirality, and employs only
(anti)self-dual or left-handed spin connection fields. It is known from the
work of Ashtekar and others that such fields can furnish a complete description
of gravity without matter. We show that conditions ensuring the cancellation of
perturbative chiral gauge anomalies are not disturbed. We also explore a global
anomaly associated with the theory, and argue that its removal requires that
the number of fundamental fermions in the theory must be multiples of 16. In
addition, we investigate the behavior of the theory under discrete
transformations P, C and T; and discuss possible violations of these discrete
symmetries, including CPT, in the presence of instantons and the
Adler-Bell-Jackiw anomaly.Comment: Extended, and replaced with LaTex file. 25 Page
Inactivation of promoter 1B of APC causes partial gene silencing: evidence for a significant role of the promoter in regulation and causative of familial adenomatous polyposis
Familial adenomatous polyposis (FAP) is caused by germline mutations in the adenomatous polyposis coli (APC) gene. Two promoters, 1A and 1B, have been recognized in APC, and 1B is thought to have a minor role in the regulation of the gene. We have identified a novel deletion encompassing half of this promoter in the largest family (Family 1) of the Swedish Polyposis Registry. The mutation leads to an imbalance in allele-specific expression of APC, and transcription from promoter 1B was highly impaired in both normal colorectal mucosa and blood from mutation carriers. To establish the significance of promoter 1B in normal colorectal mucosa (from controls), expression levels of specific transcripts from each of the promoters, 1A and 1B, were examined, and the expression from 1B was significantly higher compared with 1A. Significant amounts of transcripts generated from promoter 1B were also determined in a panel of 20 various normal tissues examined. In FAP-related tumors, the APC germline mutation is proposed to dictate the second hit. Mutations leaving two or three out of seven 20-amino-acid repeats in the central domain of APC intact seem to be required for tumorigenesis. We examined adenomas from mutation carriers in Family 1 for second hits in the entire gene without any findings, however, loss of the residual expression of the deleterious allele was observed. Three major conclusions of significant importance in relation to the function of APC can be drawn from this study; (i) germline inactivation of promoter 1B is disease causing in FAP; (ii) expression of transcripts from promoter 1B is generated at considerable higher levels compared with 1A, demonstrating a hitherto unknown importance of 1B; (iii) adenoma formation in FAP, caused by impaired function of promoter 1B, does not require homozygous inactivation of APC allowing for alternative genetic models as basis for adenoma formation
Increased Risk of Temporomandibular Joint Closed Lock: A Case-Control Study of ANKH Polymorphisms
Objectives: This study aimed to carry out a histological examination of the temporomandibular joint (TMJ) in ank mutant mice and to identify polymorphisms of the human ANKH gene in order to establish the relationship between the type of temporomandibular disorders (TMD) and ANKH polymorphisms.\ud
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Materials and Methods: Specimens from the TMJ of ank mutant and wild-type mice were inspected with a haematoxylin and eosin staining method. A sample of 55 TMD patients were selected. Each was examined with standard clinical procedures and genotyping techniques.\ud
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Results: The major histological finding in ank mutant mice was joint space narrowing. Within TMD patients, closed lock was more prevalent among ANKH-OR homozygotes (p = 0.011, OR = 7.7, 95% CI 1.6–36.5) and the elder (p = 0.005, OR = 2.4, 95% CI 1.3–4.3).\ud
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Conclusions: Fibrous ankylosis was identified in the TMJ of ank mutant mice. In the human sample, ANKH-OR polymorphism was found to be a genetic marker associated with TMJ closed lock. Future investigations correlating genetic polymorphism to TMD are indicated
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