NUMBER THEORY, DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS

DOI10.1142/S0129055X99000325zbMath0956.11019WikidataQ56566820 ScholiaQ56566820MaRDI QIDQ3365286

Andreas Knauf

Publication date: 1999

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Markov chainsdynamical systemsscatteringRiemann zeta-functionequilibrium statistical mechanics\(p\)-adic analysisRamanujan graphsFarey tesselation

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Classical equilibrium statistical mechanics (general) (82B05) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Miscellaneous applications of number theory (11Z05) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Zeta and (L)-functions: analytic theory (11M99)

Related Items (6)

Graphs, local zeta functions, log-Coulomb gases, and phase transitions at finite temperature ⋮ Quantization of non-standard Hamiltonians and the Riemann zeros ⋮ Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman ⋮ Generalized Farey trees, transfer operators and phase transitions ⋮ Positive limit-Fourier transform of Farey fractions ⋮ A thermodynamic classification of real numbers

Cites Work

• Supersymmetry and the Möbius inversion function
• On the thermodynamic formalism for the Gauss map
• The first 50 million prime numbers
• The number-theoretical spin chain and the Riemann zeroes
• The zeta function, non-differentiability of pressure, and the critical exponent of transition
• Extension of spontaneous symmetry breaking of Bost-Connes in case of arbitrary global fields
• On a ferromagnetic spin chain
• A Farey fraction spin chain
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
• Some remarks on the location of zeroes of the partition function for lattice systems
• Phases of the number-theoretic spin chain
• Statistical mechanics of a one-dimensional lattice gas
• The Modular Surface and Continued Fractions
• The thermodynamic formalism approach to Selberg’s zeta function for 𝑃𝑆𝐿(2,𝐙)
• Is our mathematics natural? The case of equilibrium statistical mechanics
• Scattering theory for automorphic functions
• Gaussian correlation inequalities for ferromagnets
• Free energy and correlations of the number-theoretical spin chain
• On a ferromagnetic spin chain. II. Thermodynamic limit
• The phase transition of the number-theoretical spin chain
• The low activity phase of some Dirichlet series

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