In this paper, it is shown that the linearized Boltzmann-Enskog collision operator cannot be dissipative in the L2-space setting contrarily to the linearized Boltzmann operator. Some estimates useful for the spectral theory are given. The Enskog equation is a modification of the Boltzmann kinetic equation, in which each particle is considered as a hard sphere with nonzero diameter a > 0 (and th...

The problem of applying an energetically passive dissipative haptic interface to a path-following application is addressed. This consists of controlling a man-machine system where the human operator provides all motive power, and the machine may dissipate or redirect this power. The goal of a controller is to constrain the operator-induced motion to a single arbitrary degree-of-freedom. This re...

We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations of motion for an operator. It is our purpose to illustrate the accuracy of this approach by studying dissipative quantum systems on all timescales. In partic...

In this paper, we study q-Sturm-Liouville operators. We construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self-adjoint and other extensions of q-Sturm-Liouville operators in terms of boundary conditions. Then we prove a theorem on completeness of the system of eigenfunctions and associated functions of dissipative operators by ...

We determine the range of the incoming wave operator for the pair of operators (−∆,−∆+V1(x)−iεV2(x)) on L (R) under the conditions n ≥ 3 and 0 is a regular point of −∆ + V1, V2 ≥ 0 and ε > 0 is small enough. This implies that the dissipative scattering operator is bijective.

We consider a class of quantum dissipative semigroup on a von-Neumann algebra which admits a normal invariant state. We investigate asymptotic behavior of the dissipative dynamics and their relation to that of the canonical Markov shift. In case the normal invariant state is also faithful, we also extend the notion of ‘quantum detailed balance’ introduced by Frigerio-Gorini and prove that forwa...