We consider hermitian dissipative mappings δ which are densely defined in unital C∗-algebras A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij) → (δ(aij)), are dissipative on the n by n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completel...

Stability analysis of the numerical Method of characteristics applied to energy-preserving systems. Abstract We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Eu...

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial st...

Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that when the...

Excitation functions for the strongly dissipative collision 19F (Elab = 135 − 140 MeV)+89Y with an energy step of 250 keV in the lab. system have been measured. The data are consistent with previous measurements and exhibit oscillations, which are interpreted as an indication of quantum chaotic phenomena in dissipative heavy-ion collisions. The Fourier component of the energy autocorrelation of...

We propose a new perspective on the intermittency in weakly dissipative systems. It is focused on the elementary (burst-like) event separating states with different properties. This event is seen as a real-space-time manifestation of an instanton connecting in an extended space-time states with distinct topology of the idealized version of the system.

Conditions for nonlocal existence of a continuous storage function for nonlinear dissipative system are presented. More precisely, it is shown that under the local ω-uniform reachability assumption at one point x∗ the required supply function is continuous on the set of points reachable from x∗. Conditions for the local ωuniform reachability based on the local controllability properties of the ...