Physics and Number theory

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2006

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2006

A single book is certainly not enough to describe the rich and historical relationships
between physics and number theory. This volume presents a selection of problems
which are currently in full development and inspire the research of many people. All
the papers begin with a survey which will make it possible even for non-specialists to
understand them and will give an idea of the great variety of subjects and techniques
in this frontier area.
The first paper, “The phase of oscillations and prime numbers: classical and quan-
tum”, by Michel Planat, is an example of the strong connection between physics and
mathematics. It starts from a concrete problem and brings into play an impressive va-
riety of mathematical techniques, especially in number theory. The paper provides an
accessible introduction to the problem of phase-locking in oscillating systems, both at
a classical level and at a quantum level. The mathematical formulation of the different
aspects of this problem requires numerous tools: first, you see how prime numbers
appear, together with continuous fractions and the Mangoldt function. Then, come
some hyperbolic geometry and the Riemann ζ-function. On the quantum side, roots
of unity and Ramanujan sums are related to noise in oscillations, and when discussing
phase in quantum information, the author uses Bost and Connes KMS states, Galois
rings and fields along with some finite projective geometry.
Next there are two papers about crystallography. From a physical point of view,
a crystal is a solid having an essentially discrete diffraction diagram. It can be pe-
riodic or not. From a mathematical point of view, lattices in R n are good tools to
describe periodic crystals, but not aperiodic ones. Very little is known about aperiodic
crystals, apart from the so called quasicrystals, whose diffraction diagrams present
some regularity: they are invariant under dilatation by a factor that may be irrational.
They are well described by some discrete sets called cut-and-project sets, which are a
generalisationoflattices. Inhispaper“OnSelf-SimilarFinitelyGeneratedUniformly
Discrete (SFU-)Sets and Sphere Packings”, Jean-LouisVerger-Gaugry is interested in
cut-and-projectsetsin R n . Thefirstpartofthepaperisasurveyofthelinkbetweenthe
geometry of numbers and aperiodic crystals in physics, from the mathematical point
of view. In the second part, the author proves some new results about the distances
between the points of cut-and-project sets. By considering each point as the centre of
asphere, onegetsaspherepackingproblemwhichishopefullyagoodmodelforatom
packing. In “Nested quasicrystalline discretisation of the line”, Jean-Pierre Gazeau,
Zuzana Masáková, and Edita Pelantová focus on cut-and-project sets obtained from a
square lattice in R 2 , with the idea of constructing aperiodic wavelets. They review the
geometrical properties of such sets, their combinatorial properties from the point of
view of language theory and their relation to nonstandard numeration systems based

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مغایرت عنوان کتاب با توضیحات و تصویر جلد
عدم رعایت حقوق نشر طبق قوانین جمهوری اسلامی ایران
محتوای مستهجن
توهین به قومیتها و محتوای نژادپرستی
توهین به اقیلیتهای مذهبی
اهانت به مقامات سیاسی و مذهبی
اشاعه ی کودک آزاری
سایر موارد

بستن

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2006

نویسنده

Vladimir G. Turaev

شابک

ISBN 9783037190289

20,000 تومان

خرید کتاب مطالعه نمونه درخواست ترجمه کتاب

خرید کتاب Physics and Number theory

Physics and Number theory

گزارش تخلف

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2006

نویسنده

شابک

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