41,419 research outputs found
Nonlocality of nucleon interaction and an anomalous off shell behavior of the two-nucleon amplitudes
The problem of the ultraviolet divergences that arise in describing the
nucleon dynamics at low energies is considered. By using the example of an
exactly solvable model it is shown that after renormalization the interaction
generating nucleon dynamics is nonlocal in time. Effects of such nonlocality on
low-energy nucleon dynamics are investigated. It is shown that nonlocality in
time of nucleon-nucleon interactions gives rise to an anomalous off-shell
behavior of the two-nucleon amplitudes that have significant effects on the
dynamics of many-nucleon systems.Comment: 9 pages, 4 figures, ReVTeX
Parameterization of Stabilizing Linear Coherent Quantum Controllers
This paper is concerned with application of the classical Youla-Ku\v{c}era
parameterization to finding a set of linear coherent quantum controllers that
stabilize a linear quantum plant. The plant and controller are assumed to
represent open quantum harmonic oscillators modelled by linear quantum
stochastic differential equations. The interconnections between the plant and
the controller are assumed to be established through quantum bosonic fields. In
this framework, conditions for the stabilization of a given linear quantum
plant via linear coherent quantum feedback are addressed using a stable
factorization approach. The class of stabilizing quantum controllers is
parameterized in the frequency domain. Also, this approach is used in order to
formulate coherent quantum weighted and control problems for
linear quantum systems in the frequency domain. Finally, a projected gradient
descent scheme is proposed to solve the coherent quantum weighted control
problem.Comment: 11 pages, 4 figures, a version of this paper is to appear in the
Proceedings of the 10th Asian Control Conference, Kota Kinabalu, Malaysia, 31
May - 3 June, 201
Covariance Dynamics and Entanglement in Translation Invariant Linear Quantum Stochastic Networks
This paper is concerned with a translation invariant network of identical
quantum stochastic systems subjected to external quantum noise. Each node of
the network is directly coupled to a finite number of its neighbours. This
network is modelled as an open quantum harmonic oscillator and is governed by a
set of linear quantum stochastic differential equations. The dynamic variables
of the network satisfy the canonical commutation relations. Similar large-scale
networks can be found, for example, in quantum metamaterials and optical
lattices. Using spatial Fourier transform techniques, we obtain a sufficient
condition for stability of the network in the case of finite interaction range,
and consider a mean square performance index for the stable network in the
thermodynamic limit. The Peres-Horodecki-Simon separability criterion is
employed in order to obtain sufficient and necessary conditions for quantum
entanglement of bipartite systems of nodes of the network in the Gaussian
invariant state. The results on stability and entanglement are extended to the
infinite chain of the linear quantum systems by letting the number of nodes go
to infinity. A numerical example is provided to illustrate the results.Comment: 11 pages, 3 figures, submitted to the 54th IEEE Conference on
Decision and Control, December 15-18, 2015, Osaka, Japa
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