In this note, we consider the feedback connection of a plant M with a random matrix gain , and study the statistical properties of the loop gain L = M , under the hypothesis that the random feedback has a unitarily invariant distribution. This setup has interesting connections with two open problems related to the entropy of the plant, and to a probabilistic version of the multivariate Nyquist ...

We present a generally covariant and parity-invariant two-frame field ("zwei-dreibein") action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models and extends them, in the context of the...

In this paper, we show a multiple-term refinement of Young?s type inequality and its reverse via the Kantorovich constants, which extends unifies two recent important results due to L. Nasiri et al. (Result. Math (74), 2019), C. Yang (Journal. Math. Inequalities, (14), 2020). An application these scalars give inequalities for operators, Hilbert-Schmidt norms, traces unitarily invariant norms.

We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood terms conditional probabilities, which are defined from solutions constraint equation a generalization Page-Wootters formalism. In this regard, show how expectation values worldline tensor fields related to averages suitabl...

The separability modulus l(ρ) of a state ρ of an arbitrary finite composite quantum system, is the largest t in [0, 1] such that t.ρ+(1− t).τ is unentangled, where τ is the normalized trace. The basic properties of l, introduced by Vidal & Tarrach [1] in another guise, are briefly established. With these properties, we obtain conditions on the spectrum of a state which imply that it is separabl...