4,687 research outputs found
Strong Stationarity Conditions for Optimal Control of Hybrid Systems
We present necessary and sufficient optimality conditions for finite time
optimal control problems for a class of hybrid systems described by linear
complementarity models. Although these optimal control problems are difficult
in general due to the presence of complementarity constraints, we provide a set
of structural assumptions ensuring that the tangent cone of the constraints
possesses geometric regularity properties. These imply that the classical
Karush-Kuhn-Tucker conditions of nonlinear programming theory are both
necessary and sufficient for local optimality, which is not the case for
general mathematical programs with complementarity constraints. We also present
sufficient conditions for global optimality.
We proceed to show that the dynamics of every continuous piecewise affine
system can be written as the optimizer of a mathematical program which results
in a linear complementarity model satisfying our structural assumptions. Hence,
our stationarity results apply to a large class of hybrid systems with
piecewise affine dynamics. We present simulation results showing the
substantial benefits possible from using a nonlinear programming approach to
the optimal control problem with complementarity constraints instead of a more
traditional mixed-integer formulation.Comment: 30 pages, 4 figure
The outer crust of non-accreting cold neutron stars
The properties of the outer crust of non-accreting cold neutron stars are
studied by using modern nuclear data and theoretical mass tables updating in
particular the classic work of Baym, Pethick and Sutherland. Experimental data
from the atomic mass table from Audi, Wapstra, and Thibault of 2003 is used and
a thorough comparison of many modern theoretical nuclear models, relativistic
and non-relativistic ones, is performed for the first time. In addition, the
influences of pairing and deformation are investigated. State-of-the-art
theoretical nuclear mass tables are compared in order to check their
differences concerning the neutron dripline, magic neutron numbers, the
equation of state, and the sequence of neutron-rich nuclei up to the dripline
in the outer crust of non-accreting cold neutron stars.Comment: 20 pages, 10 figures, accepted for publication in Phys. Rev.
EIT ground-state cooling of long ion strings
Electromagnetically-induced-transparency (EIT) cooling is a ground-state
cooling technique for trapped particles. EIT offers a broader cooling range in
frequency space compared to more established methods. In this work, we
experimentally investigate EIT cooling in strings of trapped atomic ions. In
strings of up to 18 ions, we demonstrate simultaneous ground state cooling of
all radial modes in under 1 ms. This is a particularly important capability in
view of emerging quantum simulation experiments with large numbers of trapped
ions. Our analysis of the EIT cooling dynamics is based on a novel technique
enabling single-shot measurements of phonon numbers, by rapid adiabatic passage
on a vibrational sideband of a narrow transition
Quantum simulation of the Klein paradox with trapped ions
We report on quantum simulations of relativistic scattering dynamics using
trapped ions. The simulated state of a scattering particle is encoded in both
the electronic and vibrational state of an ion, representing the discrete and
continuous components of relativistic wave functions. Multiple laser fields and
an auxiliary ion simulate the dynamics generated by the Dirac equation in the
presence of a scattering potential. Measurement and reconstruction of the
particle wave packet enables a frame-by-frame visualization of the scattering
processes. By precisely engineering a range of external potentials we are able
to simulate text book relativistic scattering experiments and study Klein
tunneling in an analogue quantum simulator. We describe extensions to solve
problems that are beyond current classical computing capabilities.Comment: 3 figures, accepted for publication in PR
Observation of Entangled States of a Fully Controlled 20-Qubit System
We generate and characterise entangled states of a register of 20
individually controlled qubits, where each qubit is encoded into the electronic
state of a trapped atomic ion. Entanglement is generated amongst the qubits
during the out-of-equilibrium dynamics of an Ising-type Hamiltonian, engineered
via laser fields. Since the qubit-qubit interactions decay with distance,
entanglement is generated at early times predominantly between neighbouring
groups of qubits. We characterise entanglement between these groups by
designing and applying witnesses for genuine multipartite entanglement. Our
results show that, during the dynamical evolution, all neighbouring qubit
pairs, triplets, most quadruplets, and some quintuplets simultaneously develop
genuine multipartite entanglement. Witnessing genuine multipartite entanglement
in larger groups of qubits in our system remains an open challenge.Comment: 20 pages, 4 figure
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