Related papers: Stopping the CCR flow and its isometric cocycles

In recent work of the authors, it was shown how to use any finite quantum stop time to stop the CCR flow and its strongly continuous isometric cocycles (Q. J. Math. 65:1145-1164, 2014). The stopped cocycle was shown to satisfy a stopped…

Let $P$ be a closed convex cone in $\mathbb{R}^{d}$ which we assume to be spanning and pointed i.e. $P-P=\mathbb{R}^{d}$ and $P \cap -P=\{0\}$. In this article, we consider CCR flows over $P$ associated to isometric representations that…

We initiate a study of E-semigroups over convex cones. We prove a structure theorem for E-semigroups which leave the algebra of compact operators invariant. Then we study in detail the CCR flows, E$_0$semigroups constructed from isometric…

An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…

For a uniformly locally finite metric space $(X, d)$, we investigate \emph{coarse} flows on its uniform Roe algebra $\mathrm{C}^*_u(X)$, defined as one-parameter groups of automorphisms whose differentiable elements include all partial…

A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…

In connection with parametric rescaling of free dynamics of CCR, we introduce a flow on the set of covariance forms and investigate its thermodynamic behavior at low temperature with the conclusion that every free state approaches to a…

Recently it is proved in arXiv:1906.05493v1 [math.OA] that CCR flows over convex cones are cocycle conjugate if and only if the associated isometric representations are conjugate. We provide a very short, simple and direct proof of that.…

Let $\A$ and $\B$ be operator algebras with $c_0$-isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically isomorphic, then $\A$ and $\B$ are isometrically isomorphic.…

The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…

The method of using periodic approximations to compute the spectral decomposition of the Koop- man operator is generalized to the class of measure-preserving flows on compact metric spaces. It is shown that the spectral decomposition of the…

Let $\sigma$ be an isometric representation of $\mathbb{N}^d$ on a Hilbert space $\mathcal{H}$. We induce $\sigma$ to an isometric representation $V$ of $\mathbb{R}_{+}^{d}$ on another Hilbert space $\mathcal{K}$. We show that the map…

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…

We introduce a cohomology theory for spatial super- product systems and compute the $2-$cocycles for some basic examples called as Clifford super-product systems, thereby distinguish them up to isomorphism. This consequently proves that a…

We study holographic c-theorems based on timelike entanglement entropy and show that a timelike c-function captures irreversible renormalization group (RG) flow. We demonstrate that timelike c-functions are applicable to both relativistic…

In this paper, we revisit Arveson's characterisation of CCR flows in terms of decomposibility of the product system in the multiparameter context. We show that a multiparameter $E_0$-semigroup is a CCR flow if and only if it is decomposable…

We show that a product subsystem of a time ordered system (that is, a product system of time ordered Fock modules), though type I, need not be isomorphic to a time ordered product system. In that way, we answer an open problem in the…

In this note, we exhibit an example of a multiparameter CCR flow which is not cocycle conjugate to its opposite. This is in sharp contrast to the one parameter situation

It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…

Let $M$ be a manifold equipped (locally) with a pair of complementary foliations. In Catuogno, da Silva and Ruffino (Stoch. Dyn. 2013), it is shown that, up to a stopping time $\tau$, a stochastic flow of local diffeomorphisms $\varphi_t$…