Related papers: Bost-Connes systems for local fields of characteri…
In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between…
This paper introduces results for characteristically near vector fields that are stable or non-stable in the polar complex plane $\mathbb{C}$. All characteristic vectors (aka eigenvectors) emanate from the same fixed point in $\mathbb{C}$,…
It is shown how to map the quantum states of a system of free Bose particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group.
Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into…
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…
We study a Bose-Einstein condensate (BEC) at low energy limit and show that their collective dynamics exhibit interesting topological behavior. The system undergoes dynamical topological phase transition at its global periods if its…
We study an ergodic theorem for disjoint C*-dynamical systems, where disjointness here is a noncommutative version of the concept introduced by Furstenberg for classical dynamical systems. This is applied to W*-dynamical systems. We also…
These notes contain an extended version of lectures given at the ``Summer School on Large Coulomb Systems'' in Nordfjordeid, Norway, in august 2003. They furnish a short introduction to the theory of quantum harmonic systems, or free bose…
We revisit the problem of the existence of asymptotic massless boson fields in quantum field theory. The well-known construction of such fields by Buchholz [2], [4] is based on locality and the existence of vacuum vector, at least in…
Localic relations are relations internal to the category of locales, forming the point-free analogues of set-theoretic relations, and providing the general backdrop of localic order theory. This work studies 'open cone' localic relations,…
General methods of quantitative and qualitative continuity analysis of characteristics of composite quantum systems are described. Several modifications of the Alicki-Fannes-Winter method are considered, which make it applicable to a wide…
We consider the dynamics of systems of lattice bosons with infinitely many degrees of freedom. We show that their dynamics defines a group of automorphisms on a $C^*$--algebra introduced by Buchholz, which extends the resolvent algebra of…
The phase structure of ideal Bose gas system within different boundary conditions, i.e., the periodic boundary condition and Dirichlet boundary condition in this work, in an infinite volume, is investigated. It is found that the ground…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
The general approach for describing systems with Bose-Einstein condensate, where atoms interact through nonlocal pair potentials, is presented. A special attention is paid to nonintegrable potentials, such as the dipolar interaction…
We discuss the occurrence of Bose-Einstein condensation in systems of noninteracting charged particles in three in one dimensions and in presence of an external magnetic field. In the one dimensional, as well as in the magnetic field cases,…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
The Boolean autonomous dynamical systems, also called regular autonomous asynchronous systems are systems whose 'vector field' is a function {\Phi}:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the synchronous systems…
The condensation of the spinless ideal charged Bose gas in the presence of a magnetic field is revisited. The conventional approach is extended to include the macroscopic occupation of excited kinetic states lying in the lowest Landau…
We show that the KMS_beta-states of Bost-Connes type systems for number fields in the region 0<beta\le 1, as well as of the Connes-Marcolli GL_2-system for 1<beta\le 2, have type III_1. This is equivalent to ergodicity of various actions on…