17,115 research outputs found
Dissipativity preserving model reduction by retention of trajectories of minimal dissipation
We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas (Syst Control Lett 54:361-374, 2005) and Sorensen (Syst Control Lett 54:347-360, 2005) is shown to be a particular case of this more general class of model reduction procedures
Phase space contraction and quantum operations
We give a criterion to differentiate between dissipative and diffusive
quantum operations. It is based on the classical idea that dissipative
processes contract volumes in phase space. We define a quantity that can be
regarded as ``quantum phase space contraction rate'' and which is related to a
fundamental property of quantum channels: non-unitality. We relate it to other
properties of the channel and also show a simple example of dissipative noise
composed with a chaotic map. The emergence of attaractor-like structures is
displayed.Comment: 8 pages, 6 figures. Changes added according to refferee sugestions.
(To appear in PRA
Monte Carlo simulations of dissipative quantum Ising models
The dynamical critical exponent is a fundamental quantity in
characterizing quantum criticality, and it is well known that the presence of
dissipation in a quantum model has significant impact on the value of .
Studying quantum Ising spin models using Monte Carlo methods, we estimate the
dynamical critical exponent and the correlation length exponent for
different forms of dissipation. For a two-dimensional quantum Ising model with
Ohmic site dissipation, we find as for the corresponding
one-dimensional case, whereas for a one-dimensional quantum Ising model with
Ohmic bond dissipation we obtain the estimate .Comment: 9 pages, 8 figures. Submitted to Physical Review
Regulation and robust stabilization: a behavioral approach
In this thesis we consider a number of control synthesis problems within the behavioral approach to systems and control. In particular, we consider the problem of regulation, the H! control problem, and the robust stabilization problem. We also study the problems of regular implementability and stabilization with constraints on the input/output structure of the admissible controllers. The systems in this thesis are assumed to be open dynamical systems governed by linear constant coefficient ordinary differential equations. The behavior of such system is the set of all solutions to the differential equations. Given a plant with its to-be-controlled variable and interconnection variable, control of the plant is nothing but restricting the behavior of the to-be-controlled plant variable to a desired subbehavior. This restriction is brought about by interconnecting the plant with a controller (that we design) through the plant interconnection variable. In the interconnected system the plant interconnection variable has to obey the laws of both the plant and the controller. The interconnected system is also called the controlled system, in which the controller is an embedded subsystem. The interconnection of the plant and the controller is said to be regular if the laws governing the interconnection variable are independent from the laws governing the plant. We call a specification regularly implementable if there exists a controller acting on the plant interconnection variable, such that, in the interconnected system, the behavior of the to-becontrolled variable coincides with the specification and the interconnection is regular. Within the framework of regular interconnection we solve the control problems listed in the first paragraph. Solvability conditions for these problems are independent of the particular representations of the plant and the desired behavior.
Semiclassical Evolution of Dissipative Markovian Systems
A semiclassical approximation for an evolving density operator, driven by a
"closed" hamiltonian operator and "open" markovian Lindblad operators, is
obtained. The theory is based on the chord function, i.e. the Fourier transform
of the Wigner function. It reduces to an exact solution of the Lindblad master
equation if the hamiltonian operator is a quadratic function and the Lindblad
operators are linear functions of positions and momenta.
Initially, the semiclassical formulae for the case of hermitian Lindblad
operators are reinterpreted in terms of a (real) double phase space, generated
by an appropriate classical double Hamiltonian. An extra "open" term is added
to the double Hamiltonian by the non-hermitian part of the Lindblad operators
in the general case of dissipative markovian evolution. The particular case of
generic hamiltonian operators, but linear dissipative Lindblad operators, is
studied in more detail. A Liouville-type equivariance still holds for the
corresponding classical evolution in double phase, but the centre subspace,
which supports the Wigner function, is compressed, along with expansion of its
conjugate subspace, which supports the chord function.
Decoherence narrows the relevant region of double phase space to the
neighborhood of a caustic for both the Wigner function and the chord function.
This difficulty is avoided by a propagator in a mixed representation, so that a
further "small-chord" approximation leads to a simple generalization of the
quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.
Global time estimates for solutions to equations of dissipative type
Global time estimates of Lp-Lq norms of solutions to general strictly
hyperbolic partial differential equations are considered. The case of special
interest in this paper are equations exhibiting the dissipative behaviour.
Results are applied to discuss time decay estimates for Fokker-Planck equations
and for wave type equations with negative mass.Comment: Journees "Equations aux Derivees Partielles
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