Related papers: Bost-Connes systems for local fields of characteri…
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…
To each integral domain R with finite quotients we associate a purely infinite simple C*-algebra in a very natural way. Its stabilization can be identified with the crossed product of the algebra of continuous functions on the "finite adele…
We give a complete description of the phase transition of the Bost-Connes type systems for number fields recently introduced by Connes-Marcolli-Ramachandran and Ha-Paugam. We also introduce a notion of K-lattices and discuss an…
We consider a Hecke algebra naturally associated with the affine group with totally positive multiplicative part over an algebraic number field K and we show that the C*-algebra of the Bost-Connes system for K can be obtained from our Hecke…
The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of…
We consider the Hecke pair consisting of the group $P^+_K$ of affine transformations of a number field $K$ that preserve the orientation in every real embedding and the subgroup $P^+_O$ consisting of transformations with algebraic integer…
We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as…
We prove a version of the Cuntz--Krieger Uniqueness Theorem for $C^*$-algebras of arbitrary relative generalized Boolean dynamical systems. We then describe properties of a $C^*$-algebra of a relative generalized Boolean dynamical system…
In this note, using Borger's theory of periodic Witt vectors, we construct integral refinements of the arithmetic subalgebras associated with Bost-Connes systems for general number fields.
We construct a quantum statistical mechanical system $(A,s)$ analogous to the systems constructed by Bost-Connes and Connes-Marcolli in the case of Shimura varieties. Along the way, we define a new Bost-Connes system for number fields which…
A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the…
Thermodynamics properties of an interacting system of bosons are considered at finite temperatures and zero chemical potential within the Skyrme-like mean-field model. An interplay between attractive and repulsive interactions is…
A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a…
We describe the exact G-module F* for any cyclic extension F/K of locals fields of characteristic zero, where G is the Galois group of F/K. We also describe a parametrized space Wa,b,m,n which is most often a direct factor in F*.
Bose-condensed gases are considered with an effective interaction strength varying in the whole range of the values between zero and infinity. The consideration is based on the usage of a representative statistical ensemble for Bose systems…
Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is…
We prove rigorously the occurrence of zero-mode Bose-Einstein condensation for a class of continuous homogeneous systems of boson particles with superstable interactions. This is the first example of a translation invariant continuous…
Noncommutative duality for C*-dynamical systems is a vast generalization of Pontryagin duality for locally compact abelian groups. In this series of lectures, we give an introduction to the categorical aspects of this duality, focusing…
By KMS-classification theorem, the Dedekind zeta function is an invariant of Bost-Connes systems. In this paper, we show that it is in fact an invariant of Bost-Connes $C^*$-algebras. We examine second maximal primitive ideals of…
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are…