1,049 research outputs found
Output Feedback Invariants
The paper is concerned with the problem of determining a complete set of
invariants for output feedback. Using tools from geometric invariant theory it
is shown that there exists a quasi-projective variety whose points parameterize
the output feedback orbits in a unique way. If the McMillan degree ,
the product of number of inputs and number of outputs, then it is shown that in
the closure of every feedback orbit there is exactly one nondegenerate system.Comment: 15 page
Output feedback invariants
The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree n ≥ mp, the product of the number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system
Relative "-Numerical Ranges for Applications in Quantum Control and Quantum Information
Motivated by applications in quantum information and quantum control, a new
type of "-numerical range, the relative "-numerical range denoted
, is introduced. It arises upon replacing the unitary group U(N) in
the definition of the classical "-numerical range by any of its compact and
connected subgroups .
The geometric properties of the relative "-numerical range are analysed in
detail. Counterexamples prove its geometry is more intricate than in the
classical case: e.g. is neither star-shaped nor simply-connected.
Yet, a well-known result on the rotational symmetry of the classical
"-numerical range extends to , as shown by a new approach based on
Lie theory. Furthermore, we concentrate on the subgroup , i.e. the -fold tensor product of SU(2),
which is of particular interest in applications. In this case, sufficient
conditions are derived for being a circular disc centered at
origin of the complex plane. Finally, the previous results are illustrated in
detail for .Comment: accompanying paper to math-ph/070103
Numerical modelling of methyl iodide in the eastern tropical Atlantic
Methyl iodide (CH3I) is a volatile organic halogen compound that contributes significantly to the transport of iodine from the ocean to the atmosphere, where it plays an important role in tropospheric chemistry. CH3I is naturally produced and occurs in the global ocean. The processes involved in the formation of CH3I, however, are not fully understood. In fact, there is an ongoing debate whether production by phytoplankton or photochemical degradation of organic matter is the main source term. Here, both the biological and photochemical production mechanisms are considered in a biogeochemical module that is coupled to a one-dimensional water column model for the eastern tropical Atlantic. The model is able to reproduce observed subsurface maxima of CH3I concentrations. But, the dominating source process cannot be clearly identified as subsurface maxima can occur due to both direct biological and photochemical production. However, good agreement between the observed and simulated difference between surface and subsurface methyl iodide concentrations is achieved only when direct biological production is taken into account. Production rates for the biological CH3I source that were derived from published laboratory studies are shown to be inappropriate for explaining CH3I concentrations in the eastern tropical Atlantic
The Significance of the -Numerical Range and the Local -Numerical Range in Quantum Control and Quantum Information
This paper shows how C-numerical-range related new strucures may arise from
practical problems in quantum control--and vice versa, how an understanding of
these structures helps to tackle hot topics in quantum information.
We start out with an overview on the role of C-numerical ranges in current
research problems in quantum theory: the quantum mechanical task of maximising
the projection of a point on the unitary orbit of an initial state onto a
target state C relates to the C-numerical radius of A via maximising the trace
function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one
may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii)
in restricting the dynamics to {\em local} operations on each qubit, i.e. to
the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2).
Interestingly, the latter then leads to a novel entity, the {\em local}
C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither
star-shaped nor simply connected in contrast to the conventional C-numerical
range. This is shown in the accompanying paper (math-ph/0702005).
We present novel applications of the C-numerical range in quantum control
assisted by gradient flows on the local unitary group: (1) they serve as
powerful tools for deciding whether a quantum interaction can be inverted in
time (in a sense generalising Hahn's famous spin echo); (2) they allow for
optimising witnesses of quantum entanglement. We conclude by relating the
relative C-numerical range to problems of constrained quantum optimisation, for
which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200
The Optimal Control Landscape for the Generation of Unitary Transformations with Constrained Dynamics
The reliable and precise generation of quantum unitary transformations is
essential to the realization of a number of fundamental objectives, such as
quantum control and quantum information processing. Prior work has explored the
optimal control problem of generating such unitary transformations as a surface
optimization problem over the quantum control landscape, defined as a metric
for realizing a desired unitary transformation as a function of the control
variables. It was found that under the assumption of non-dissipative and
controllable dynamics, the landscape topology is trap-free, implying that any
reasonable optimization heuristic should be able to identify globally optimal
solutions. The present work is a control landscape analysis incorporating
specific constraints in the Hamiltonian corresponding to certain dynamical
symmetries in the underlying physical system. It is found that the presence of
such symmetries does not destroy the trap-free topology. These findings expand
the class of quantum dynamical systems on which control problems are
intrinsically amenable to solution by optimal control.Comment: Submitted to Journal of Mathematical Physic
Leukotriene receptor expression in esophageal squamous cell cancer and non-transformed esophageal epithelium: a matched case control study
Study questionnaire. (DOC 21 kb
Hamiltonian statistical mechanics
A framework for statistical-mechanical analysis of quantum Hamiltonians is
introduced. The approach is based upon a gradient flow equation in the space of
Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve
toward those of the reference Hamiltonian. The nonlinear double-bracket
equation governing the flow is such that the eigenvalues of the initial
Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by
compact invariant subspaces, which permits the construction of statistical
distributions over the Hamiltonians. In two dimensions, an explicit dynamical
model is introduced, wherein the density function on the space of Hamiltonians
approaches an equilibrium state characterised by the canonical ensemble. This
is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde
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