3,815 research outputs found
Ground-state Stabilization of Open Quantum Systems by Dissipation
Control by dissipation, or environment engineering, constitutes an important
methodology within quantum coherent control which was proposed to improve the
robustness and scalability of quantum control systems. The system-environment
coupling, often considered to be detrimental to quantum coherence, also
provides the means to steer the system to desired states. This paper aims to
develop the theory for engineering of the dissipation, based on a ground-state
Lyapunov stability analysis of open quantum systems via a Heisenberg-picture
approach. Algebraic conditions concerning the ground-state stability and
scalability of quantum systems are obtained. In particular, Lyapunov stability
conditions expressed as operator inequalities allow a purely algebraic
treatment of the environment engineering problem, which facilitates the
integration of quantum components into a large-scale quantum system and draws
an explicit connection to the classical theory of vector Lyapunov functions and
decomposition-aggregation methods for control of complex systems. The
implications of the results in relation to dissipative quantum computing and
state engineering are also discussed in this paper.Comment: 18 pages, to appear in Automatic
Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity
In this work we analyze the relation between the multiplicative decomposition
of the deformation gradient as a product
of the elastic and plastic factors and the theory of uniform materials. We
prove that postulating such a decomposition is equivalent to having a uniform
material model with two configurations - total and the inelastic
. We introduce strain tensors characterizing different types of
evolutions of the material and discuss the form of the internal energy and that
of the dissipative potential. The evolution equations are obtained for the
configurations and the material metric .
Finally the dissipative inequality for the materials of this type is
presented.It is shown that the conditions of positivity of the internal
dissipation terms related to the processes of plastic and metric evolution
provide the anisotropic yield criteria
Bloch Equations and Completely Positive Maps
The phenomenological dissipation of the Bloch equations is reexamined in the
context of completely positive maps. Such maps occur if the dissipation arises
from a reduction of a unitary evolution of a system coupled to a reservoir. In
such a case the reduced dynamics for the system alone will always yield
completely positive maps of the density operator. We show that, for Markovian
Bloch maps, the requirement of complete positivity imposes some Bloch
inequalities on the phenomenological damping constants. For non-Markovian Bloch
maps some kind of Bloch inequalities involving eigenvalues of the damping basis
can be established as well. As an illustration of these general properties we
use the depolarizing channel with white and colored stochastic noise.Comment: Talk given at the Conference "Quantum Challenges", Falenty, Poland,
September 4-7, 2003. 21 pages, 3 figure
Dissipation time and decay of correlations
We consider the effect of noise on the dynamics generated by
volume-preserving maps on a d-dimensional torus. The quantity we use to measure
the irreversibility of the dynamics is the dissipation time. We focus on the
asymptotic behaviour of this time in the limit of small noise. We derive
universal lower and upper bounds for the dissipation time in terms of various
properties of the map and its associated propagators: spectral properties,
local expansivity, and global mixing properties. We show that the dissipation
is slow for a general class of non-weakly-mixing maps; on the opposite, it is
fast for a large class of exponentially mixing systems which include uniformly
expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit
Lagrangian Framework for Systems Composed of High-Loss and Lossless Components
Using a Lagrangian mechanics approach, we construct a framework to study the
dissipative properties of systems composed of two components one of which is
highly lossy and the other is lossless. We have shown in our previous work that
for such a composite system the modes split into two distinct classes,
high-loss and low-loss, according to their dissipative behavior. A principal
result of this paper is that for any such dissipative Lagrangian system, with
losses accounted by a Rayleigh dissipative function, a rather universal
phenomenon occurs, namely, selective overdamping: The high-loss modes are all
overdamped, i.e., non-oscillatory, as are an equal number of low-loss modes,
but the rest of the low-loss modes remain oscillatory each with an extremely
high quality factor that actually increases as the loss of the lossy component
increases. We prove this result using a new time dynamical characterization of
overdamping in terms of a virial theorem for dissipative systems and the
breaking of an equipartition of energy.Comment: 53 pages, 1 figure; Revision of our original manuscript to
incorporate suggestions from refere
Effective dissipative dynamics for polarized photons
In the framework of open quantum systems, the propagation of polarized
photons can be effectively described using quantum dynamical semigroups. These
extended time-evolutions induce irreversibility and dissipation. Planned, high
sensitive experiments, both in the laboratory and in space, will be able to put
stringent bounds on these non-standard effects.Comment: 15 pages, plain-TeX, no figure
Massless neutrino oscillations
Quantum dynamical semigroups provide a general framework for studying the
evolution of open systems. Neutrino propagation both in vacuum and in matter
can be analyzed using these techniques: they allow a consistent treatment of
non-standard, dissipative effects that can alter the pattern of neutrino
oscillations. In particular, initially massless neutrinos can give rise to a
nonvanishing flavour transition probability, involving in addition the Majorana
CP-violating mixing phase.Comment: 27 pages, plain-TeX, no figure
Quantum Markov Channels for Qubits
We examine stochastic maps in the context of quantum optics. Making use of
the master equation, the damping basis, and the Bloch picture we calculate a
non-unital, completely positive, trace-preserving map with unequal damping
eigenvalues. This results in what we call the squeezed vacuum channel. A
geometrical picture of the effect of stochastic noise on the set of pure state
qubit density operators is provided. Finally, we study the capacity of the
squeezed vacuum channel to transmit quantum information and to distribute EPR
states.Comment: 18 pages, 4 figure
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