There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the regularization error depend on the given smoothness assumptions, and for general accretive operators these may be both with respect to the operator or...

We present an iterative path integral algorithm for computing multitime correlation functions of a quantum system coupled to a dissipative bath of harmonic oscillators. By splitting the Boltzmann operator into two parts and reordering the propagators in the expression for canonical correlation functions, we are able to transform the evolution time contour into a symmetric one so that a forward ...

In granular matter, consisting of discrete particles, long-range interactions imply that each of the particles is interacting with all others. For many charged granular materials with Coulomb repulsion or large-scale gravitationally attractive systems, a Molecular Dynamics environment is developed. In granular systems with long-range interaction forces and dissipative collisions, both effects c...

A characterisation of the quantum stochastic bounded generators of irreversible quantum state evolutions is given. This suggests the general form of quantum stochastic evolution equation with respect to the Poisson (jumps), Wiener (diffusion) or general Quantum Noise. The corresponding irreversible Heisenberg evolution in terms of stochastic completely positive (CP) cocycles is also characteriz...

0. Introduction Our object is to study domains which are the region of negative definiteness of an operator-valued Hermitian form defined on a space of operators and to investigate the biholomorphic linear fractional transformations between them. This is a unified setting in which to consider operator balls, operator half-planes, strictly J-contractive operators, strictly J-dissipative operator...

We introduce and discuss certain models of dilute granular systems of spheres with dissipative collisions and variable coefficient of restitution, under the assumption of weak inelasticity. The dissipation is taken into account by introducing a correction to the Boltzmann collision operator in the form of a nonlinear friction type operator. Using this correction we obtain formally from the Bolt...

The space of Null Lagrangians is the least investigated territory in dynamics since they are identically sent to zero by their Euler-Lagrange operator and thereby having no effects on equations motion. A humble effort discover relevance these made introducing a generalized procedure (with respect recent introduced authors this paper) that takes advantage null-ness construct non-standard represe...

Quantum chaos—the study of quantized nonintegrable Hamiltonian systems—is an extremely well-developed and sophisticated field. By contrast, very little work has been done in looking at quantum versions of systems which classically exhibit dissipative chaos. Using the decoherence formalism of Gell-Mann and Hartle, I find a quantum mechanical analog of one such system, the forced damped Duffing o...

We develop an information theoretic interpretation of the numberphase complementarity in atomic systems, where phase is treated as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as an upper bound on a sum of knowledge of these two observables for the case of two-level systems. A tighter bound characterizing the uncertainty relation is obtain...

The water wave theory traditionally assumes the fluid to be perfect, thus neglecting all effects of the viscosity. However, the explanation of several experimental data sets requires the explicit inclusion of dissipative effects. In order to meet these practical problems, the theory of visco-potential flows has been developed (see P.-F. Liu & A. Orfila [42] and D. Dutykh & F. Dias [25]). Then, ...