Related papers: CCR and CAR flows over convex cones

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…

Let $P$ be a pointed, closed convex cone in $\mathbb{R}^d$. We prove that for two pure isometric representations $V^{(1)}$ and $V^{(2)}$ of $P$, the associated CAR flows $\beta^{V^{(1)}}$ and $\beta^{V^{(2)}}$ are cocycle conjugate if and…

Let $P$ be a closed convex cone in $\mathbb{R}^d$ which is assumed to be spanning $\mathbb{R}^d$ and contains no line. In this article, we consider a family of CAR flows over $P$ and study the decomposability of the associated product…

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

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…

In this paper using one of the necessary conditions obtained for extendability in [BISSar], we prove that the CAR flows ([Amo01]) on type III factors arising from most quasi-free states are not extendable. As a consequence we find the super…

We consider the multiparameter CAR flows and describe its opposite. We also characterize the symmeticity of CAR flows in terms of associated isometric representations.

In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric…

We consider the CR Yamabe flow on a compact strictly pseudoconvex CR manifold $M$ of real dimension $2n+1$. We prove convergence of the CR Yamabe flow when $n=1$ or $M$ is spherical.

In this paper, we construct uncountably many examples of multiparameter CCR flows, which are not pullbacks of $1$-parameter CCR flows, with index one. Moreover, the constructed CCR flows are type I in the sense that the associated product…

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…

It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e., left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism…

We show that the metric of nonpositively curved graph manifolds is determined by its geodesic flow. More precisely we show that if the geodesic flows of two nonpositively curved graph manifolds are $C^0$ conjugate then the spaces are…

In [8], Arveson proved that a $1$-parameter decomposable product system is isomorphic to the product system of a CCR flow. We show that the structure of a generic decomposable product system, over higher dimensional cones, modulo twists by…

We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the…

Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be seen as a consequence of the (infinite dimensional) group of…

In this paper we study some generic properties of the geodesic flows on a convex sphere. We prove that, $C^r$ generically ($2\le r\le\infty$), every hyperbolic closed geodesic admits some transversal homoclinic orbits.

We provide an affirmative answer to the Cr Closing Lemma, r>1, for a large class of flows defined on every closed surface.

In this paper, we study curve shortening flows on rotational surfaces in $\mathbb{R}^3$. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of embedded curve…

We give an overview of the existence and regularity results for curvature flows and how these flows can be used to solve some problems in geometry and physics.