Related papers: Complete positivity and dissipative factorized dyn…

We investigate the asymptotic behavior, as t goes to infinity, for a semilinear hyperbolic equation with asymptotically smal dissipation and convex potential. We prove that if the damping term behaves like K/t^\alpha for t large enough, k>0…

We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero ("L\'evy's Theorem"). Our proof of this fact that does not require the matrices to…

Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the…

For a commutative semigroup $S$ with 0, the zero-divisor graph of $S$ denoted by $\Gamma(S)$ is the graph whose vertices are nonzero zero-divisor of $S$, and two vertices $x$, $y$ are adjacent in case $xy=0$ in $S$. In this paper we study…

Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…

We show that for every "locally finite" unit-preserving completely positive map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of another unital C*-algebra such that the two sequences P, P^2,P^3,... and \alpha,…

For any $\theta, \omega > 1/2$ we prove that, if any $d$-pseudotrajectory of length $\sim 1/d^{\omega}$ of a diffeomorphism $f\in C^2$ can be $d^{\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable. Previously it was…

We consider semigroups $\{\alpha_t: \; t\geq 0\}$ of normal, unital, completely positive maps $\alpha_t$ on a von Neumann algebra ${\mathcal M}$. The (predual) semigroup $\nu_t (\rho):= \rho \circ \alpha_t$ on normal states $\rho$ of…

We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy…

For a class of linear maps on a von Neumann factor, we associate two objects, bounded operators and trace class operators, both of which play the roles of Choi matrices. Each of them is positive if and only if the original map on the factor…

Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian…

Let $\Gamma$ be a finitely generated group equipped with a symmetric and nondegenerate probability measure $\mu$ with finite second moment, and $Y$ a CAT(0) space which is either proper or of finite telescopic dimension. We show that if an…

Hermitian positive definite, totally positive, and nonsingular M-matrices enjoy many common properties, in particular: (A) positivity of all principal minors, (B) weak sign symmetry, (C) eigenvalue monotonicity, (D) positive stability. The…

Let $\Gamma$ be a sub-semigroup of $G=GL(d,\mathbb R),$ $d>1.$ We assume that the action of $\Gamma$ on $\R^d$ is strongly irreducible and that $\Gamma$ contains a proximal and expanding element. We describe contraction properties of the…

Let $\mathbb{P}_G([0,\infty))$ and $\mathbb{P}_G^{'}([0,\infty))$ be the sets of positive semidefinite and positive definite matrices of order $n$, respectively, with nonnegative entries, where some positions of zero entries are restricted…

We propose and explore a notion of decomposably divisible (D-divisible) differentiable quantum evolution families on matrix algebras. This is achieved by replacing the complete positivity requirement, imposed on the propagator, by more…

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…

We show that each positive map from B(K) to B(H) with K and H finite dimensional Hilbert spaces is a scalar multiple of a map of the form $Tr - \psi$ with $\psi$ completely positive. This is used to give necessary and sufficient conditions…

We investigate conditions for logarithmic complete monotonicity of a quotient of two products of gamma functions, where the argument of each gamma function has different scaling factor. We give necessary and sufficient conditions in terms…

By using an exact analytical non-Hermitian formalism involving the full set of resonance (quasinormal) states and complex energy eigenvalues for quantum tunneling decay, we show that unitarity holds at any instant of time for the…