Number Theory and Physics

Number Theory and Physics consists of two types of contributions: mathematicians write on problems relevant to theoretical physics, and theoretical physicists present problems relevant to number theory. This combination aims to promote understanding between the two fields, which will undoubtedly aid further developments. The topics treated include: - modular forms - spectra of operators - the Hall effect - quasicrystals - the Riemann zeta function - stochastic processes - integrable systems

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 NumberGenerators.- 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.