In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

Lattice dynamical systems arise in various application fields, for instance, in chemical reaction theory, material science, biology, laser systems, image processing and pattern recognition, and electrical engineering (cf. [6, 7, 13]). In each field, they have their own forms, but in some other cases, they appear as spatial discretizations of partial differential equations (PDEs). Recently, many...

For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been obse...

Abstract Velocity measurements in turbulent superfluid helium between co-rotating propellers are reported. The parameters chosen such that the flow is fully turbulent, and its dissipative scales partly resolved by velocity sensors. This allows for first experimental comparison of spectra quantum versus classical turbulence where resolved. In some specific conditions, differences observed, with ...

Localized States in Driven Dissipative Systems

This article contains the outline of a 3-hour course that will be given by the authors at the ECC 2003. The course consists of 4 parts: 1. The basic concepts, 2. Linear differential systems, 3. Control in a behavioral setting, and 4. The synthesis of dissipative systems.