عنوان

Number Theory and Physics :

3642754058

3642754074

9783642754050

9783642754074

b573395

Number Theory and Physics :

[Book]

Proceedings of the Winter School, Les Houches, France, March 7-16, 1989

edited by Jean-Marc Luck, Pierre Moussa, Michel Waldschmidt.

Berlin, Heidelberg

Springer Berlin Heidelberg

1990

(XIII, 311 pages 45 illustrations)

Springer proceedings in physics, 47.

I Conformally Invariant Field Theories, Integrability, Quantum Groups --; Z/NZ Conformal Field Theories --; Affine Characters and Modular Transformations --; Conformal Field Theory on a Riemann Surface --; Modular Invariance of Field Theories and String Compactifications --; Yang-Baxter Algebras and Quantum Groups --; Representations of Uq sl(2) for q a Root of Unity --; II Quasicrystals and Related Geometrical Structures --; Some Quasiperiodic Tilings as Modulated Lattices --; Types of Order and Diffraction Spectra for Tilings of the Line --; A Topological Constraint on the Atomic Structure of Quasicrystals --; From Approximants to Quasicrystals: A Non-standard Approach --; The Topological Structure of Grain Boundaries --; Calculation of 6D Atomic Surfaces from a Given Approximant Crystalline Structure Using Approximate Icosahedral Periodic Tilings --; III Spectral Problems, Automata and Substitutions --; Spectral Properties of Schrödinger's Operator with a Thue-Morse Potential --; On the Non-commutative Torus of Real Dimension Two --; Topological Invariants Associated with Quasi-Periodic Quantum Hamiltonians --; Spectra of Some Almost Periodic Operators --; The Quantum Hall Effect and the Schrödinger Equation with Competing Periods --; Finite Automata in 1-D and 2-D Physics --; Summation Formulae for Substitutions on a Finite Alphabet --; The Inhomogeneous Ising Chain and Paperfolding --; IV Dynamical and Stochastic Systems --; A Nonlinear Evolution with Travelling Waves --; Iterating Random Maps and Applications --; Hannay Angles and Classical Perturbation Theory --; Nekhoroshev Stability Estimates for Symplectic Maps and Physical Applications --; p-adic Dynamical Systems --; V Further Arithmetical Problems, and Their Relationship to Physics --; Dirichlet Series Associated with a Polynomial --; Some Remarks on Random Number Generators --; Bounds for Non-blocking Switch Networks --; The Ising Model and the Diophantine Moment Problem --; Statistical Theory of Numbers --; Algebraic Number Theory and Hamiltonian Chaos --; Semiclassical Properties of the Cat Maps --; Index of Contributors.

The contributions to this book can be divided into two categories: those in which mathematicians write on problems relevant to theoretical physics, and those dealing with problems relevant to number theory, written by physicists. Many recent developments in theoretical physics display aspects related to number theory, and this cooperation will be furthered by this volume. The authors from each discipline have taken pains to present their contributions in a manner that is attractive and understandable to readers from the other discipline. The subjects covered include: modular forms and applications to quantum field theory for strings, number theoretical aspects of the spectra of operators applied to the Hall effect, quasicrystals, almost periodic systems, the Riemann zeta function, applications of number theory to dynamical systems, statistical mechanics, lattices, stochastic processes and integrable systems.

Crystallography.

Number theory.

Physics.

edited by Jean-Marc Luck, Pierre Moussa, Michel Waldschmidt.

Jean-Marc Luck

Michel Waldschmidt

Pierre Moussa

[Book]

Y