Related papers: Opposite product system for the multiparameter CAR…
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
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…
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 $P$ 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…
We show an isomorphism stability property for Cartesian products of either flows with joining primeness property or flows which are $\alpha$-weakly mixing.
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
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…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…
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…
In this paper, we consider a simple test case of multiparameter product systems that arise out of random measures. We associate a product system to a stationary Poisson process and a stationary compound Poisson process. We show that the…
We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars…
By studying the weak closure of multidimensional off-diagonal self-joinings we provide a criterion for non-isomorphism of a flow with its inverse, hence the non-reversibility of a flow. This is applied to special flows over rigid…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
We study the structure of quantum Markov Processes from the point of view of product systems and their representations.
Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser system.
We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe such a system in terms of the coupling of the collective normal modes of the membrane array to the light fields. We show these…
Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.