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Titlebook: Number Theory and Physics; Proceedings of the W Jean-Marc Luck,Pierre Moussa,Michel Waldschmidt Conference proceedings 19901st edition Spri

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發(fā)表于 2025-3-21 18:38:24 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Number Theory and Physics
副標題Proceedings of the W
編輯Jean-Marc Luck,Pierre Moussa,Michel Waldschmidt
視頻videohttp://file.papertrans.cn/669/668876/668876.mp4
叢書名稱Springer Proceedings in Physics
圖書封面Titlebook: Number Theory and Physics; Proceedings of the W Jean-Marc Luck,Pierre Moussa,Michel Waldschmidt Conference proceedings 19901st edition Spri
描述7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu- tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string
出版日期Conference proceedings 19901st edition
關(guān)鍵詞Riemann zeta function; algebraic number theory; arithmetic; crystal; dynamical systems; number theory; qua
版次1
doihttps://doi.org/10.1007/978-3-642-75405-0
isbn_softcover978-3-642-75407-4
isbn_ebook978-3-642-75405-0Series ISSN 0930-8989 Series E-ISSN 1867-4941
issn_series 0930-8989
copyrightSpringer-Verlag Berlin Heidelberg 1990
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沙發(fā)
發(fā)表于 2025-3-22 00:07:54 | 只看該作者
Yang-Baxter Algebras and Quantum Groups (YBA) associated with all these two-dimensional models. These YBA allow one to construct the exact solution (spectrum, S-matrix, form-factors,…) for this class of theories. Braid groups and quantum groups are derived as limiting cases of YBA when θ (spectral parameter) goes to ±∞.
板凳
發(fā)表于 2025-3-22 03:19:59 | 只看該作者
A Topological Constraint on the Atomic Structure of Quasicrystals natural requirement on the geometry of the so-called “atomic surfaces” leads in a straightforward way to the study of their homology classes, and that the corresponding constraints on the density of quasicrystals are compatible with experimental results.
地板
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5#
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Spectral Properties of Schr?dinger’s Operator with a Thue-Morse Potentialre computed explicitly. The integrated density of states on the gaps are given by 1/2 or by k/3.2. where k and N are integers and k is not divisible by 3. At small coupling constant V, the gap widths scale according to V. Eigenfunctions for energies on the gap boundaries diverge faster than any polynomial at infinity.
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Affine Characters and Modular TransformationsWe describe the rational commutant of the modular action on .(.) affine characters.
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Representations of ,(2) for , a Root of UnityA review of .(2) representation theory for . a root of unity is given; physical applications to integrable systems or conformal theories are discussed.
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發(fā)表于 2025-3-22 22:19:28 | 只看該作者
Some Quasiperiodic Tilings as Modulated LatticesWe consider quasiperiodic structures obtained by the cut and project method and show that whenever the window satisfies a non-generic tiling property the associated structure can be transformed into a periodic lattice by bounded displacements. The case of the octagonal tiling is examined in detail.
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發(fā)表于 2025-3-23 05:00:34 | 只看該作者
The Topological Structure of Grain BoundariesIt is shown that grain boundaries are quasiperodic tilings made of inflatable sequences of structural units. A general grain boundary is a quasiperodic grid of dislocations with the same inflation multiplier (a quadratic irrational) in every direction.
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