Abstract For a prototype quadratic Hamiltonian describing driven, dissipative system, exact matrix elements of the reduced density are obtained from generating function in terms normal characteristic functions. The approach is based on Heisenberg equations motion and operator calculus. special limiting cases discussed.

Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator AD in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation e K of ...

The article is devoted to building various dilatations of linear operators. explicit construction a unitary dilation compression operator considered. Then the J-unitary dilatation bounded constructed by means knot concept operator. Using Pavlov method, we construct self-adjoint dissipative We consider spectral and translational representations densely defined with nonempty set regular points. a...

This paper surveys several alternative but equivalent definitions of “input to state stability” (iss), a property which provides a natural framework in which to formulate notions of stability with respect to input perturbations. Relations to classical Lyapunov as well as operator theoretic approaches, connections to dissipative systems, and applications to stabilization of several cascade struc...

We have derived an equation of motion for coarse-grained particles by using a projection operator. Because the derived coarse-grained equation is based on microscopic description, it can be the basis for models of various coarse-grained simulations. We show that by substitution of random forces into fluctuating forces in the coarse-grained equation, the equations for Brownian dynamics and dissi...

We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order systems with fairly general operator coefficients and apply our bound to the perturbation of the damping term. The result is illustrated on a dissipative wave equa...

We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispe...

We explore the phase diagram of the dissipative Rabi-Hubbard model, as could be realized by a Raman-pumping scheme applied to a coupled cavity array. There exist various exotic attractors, including ferroelectric, antiferroelectric, and incommensurate fixed points, as well as regions of persistent oscillations. Many of these features can be understood analytically by truncating to the two lowes...