Related papers: Bost-Connes-Marcolli systems for Shimura varieties…
We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explict class field theory for such fields. This system…
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…
After recalling some basic notions of quantum statistical mechanics, we explain the Bost-Connes system that relates the structure of the maximal abelian extension of $\mathbb{Q}$ to the space of \kms states of a \cs-dynamical system.…
In this article we develop a broad generalization of the classical Bost-Connes system, where roots of unit are replaced by an algebraic datum consisting of an abelian group and a semi-group of endomorphisms. Examples include roots of unit,…
With a global function field K with constant field F_q, a finite set S of primes in K and an abelian extension L of K, finite or infinite, we associate a C*-dynamical system. The systems, or at least their underlying groupoids, defined…
We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show…
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arithmetic properties of KMS states in the corresponding quantum…
The theory of limiting modular symbols provides a noncommutative geometric model of the boundary of modular curves that includes irrational points in addition to cusps. A noncommutative space associated to this boundary is constructed, as…
We develop a general framework for analyzing KMS-states on C*-algebras arising from actions of Hecke pairs. We then specialize to the system recently introduced by Connes and Marcolli and classify its KMS-states for inverse temperatures…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral…
After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the…
The Bost-Connes system is a $C^*$-dynamical system which has a relation with the class field theory. The purpose of this paper is to generalize the notion of Bost-Connes systems to local fields of characteristic zero. The notable phenomenon…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
By using the theory of Complex Multiplication for general Siegel modular varieties we construct arithmetic subalgebras for BC-type systems attached to number fields containing a CM field. Our approach extends the construction of Connes,…
In contrast to classical physics, quantum mechanics divides particles into two classes-bosons and fermions-whose exchange statistics dictate the dynamics of systems at a fundamental level. In two dimensions quasi-particles known as 'anyons'…
It is well-known that thermal equilibrium states in quantum statistical mechanics and quantum field theory can be described in a mathematically rigorous manner by means of the so-called Kubo-Martin-Schwinger (KMS) condition, which is based…
We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum…
We use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quantum systems by means of a set of equations resembling the…