相关论文: Topos Analogues of the KMS State
From a non-constant holomorphic map on a connected Riemann surface we construct an 'etale second countable locally compact Hausdorff groupoid whose associated groupoid C*-algebra admits a one-parameter group of automorphisms with the…
A continuous groupoid homomorphism $c$ on a locally compact second countable Hausdorff \'etale groupoid $\mathcal{G}$ gives rise to a $C^{*}$-dynamical system in which every $\beta$-KMS state can be associated to a $e^{-\beta…
Recent progress on the question of the size of the class of connected and hyperconnected geometric morphisms from a given topos has led to the definition of {\em local state classifier}. We discuss a historical precedent which leads to the…
We study the KMS states on local quantum Cuntz-Krieger algebras associated to quantum graphs. Using their isomorphism to the Cuntz-Pimsner algebra of the quantum edge correspondence, we show that the general criteria for KMS states can be…
Given a positive function on the set of edges of an arbitrary directed graph $E=(E^0,E^1)$, we define a one-parameter group of automorphisms on the C*-algebra of the graph $C^*(E)$, and study the problem of finding KMS states for this…
In this paper, we study KMS states for the gauge actions on C${}^*$-algebras associated with self-similar sets whose branch points are finite. If the self-similar set does not contain any branch point, the Hutchinson measure gives the…
In the framework of deformation quantization we define formal KMS states on the deformed algebra of power series of functions with compact support in phase space as C[[\lambda]]-linear functionals obeying a formal variant of the usual KMS…
We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting…
We study KMS states for gauge actions with potential functions on Cuntz--Krieger algebras whose underlying one-sided topological Markov shifts are continuous orbit equivalent. As a result, we have a certain relationship between topological…
We consider self-similar actions of groupoids on the path spaces of finite directed graphs, and construct examples of such self-similar actions using a suitable notion of graph automaton. Self-similar groupoid actions have a Cuntz-Pimsner…
Let $G$ be a countable discrete amenable group, and $\Lambda$ be a strongly connected finite $k$-graph. If $(G,\Lambda)$ is a pseudo free and locally faithful self-similar action which satisfies the finite-state condition, then the…
We consider a family of Cuntz-Pimsner algebras associated to self-similar group actions, and their Toeplitz analogues. Both families carry natural dynamics implemented by automorphic actions of the real line, and we investigate the…
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped…
We want to relate the concepts of entropy and pressure to that of KMS states for $C^*$-Algebras. Several different definitions of entropy are known in our days. The one we describe here is quite natural and extends the usual one for…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
To any periodic, unital and full C*-dynamical system (A, \alpha, R) an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive…
Given a topologically free action of a countable group $G$ on a compact metric space $X$, there is a canonical correspondence between continuous 1-cocycles for this group action and diagonal 1-parameter groups of automorphisms of the…
In the topos approach to quantum theory, the spectral presheaf plays the role of the state space of a quantum system. We show how a notion of entropy can be defined within the topos formalism using the equivalence between states and…
Recent results about topological coset models are summarized. The action of a topological ${G\over H}$ coset model ($rank\ H = rank\ G$) is written down as a sum of ``decoupled" matter, gauge and ghost sectors. The physical states are in…