266,888 research outputs found
Optimal trajectories for efficient atomic transport without final excitation
We design optimal harmonic-trap trajectories to transport cold atoms without
final excitation, combining an inverse engineering techniqe based on
Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are
not really harmonic, we keep the relative displacement between the center of
mass and the trap center bounded. Under this constraint, optimal protocols are
found according to different physical criteria. The minimum time solution has a
"bang-bang" form, and the minimum displacement solution is of "bang-off-bang"
form. The optimal trajectories for minimizing the transient energy are also
discussed.Comment: 10 pages, 7 figure
Energy Complexity of Distance Computation in Multi-hop Networks
Energy efficiency is a critical issue for wireless devices operated under
stringent power constraint (e.g., battery). Following prior works, we measure
the energy cost of a device by its transceiver usage, and define the energy
complexity of an algorithm as the maximum number of time slots a device
transmits or listens, over all devices. In a recent paper of Chang et al. (PODC
2018), it was shown that broadcasting in a multi-hop network of unknown
topology can be done in energy. In this paper, we continue
this line of research, and investigate the energy complexity of other
fundamental graph problems in multi-hop networks. Our results are summarized as
follows.
1. To avoid spending energy, the broadcasting protocols of Chang
et al. (PODC 2018) do not send the message along a BFS tree, and it is open
whether BFS could be computed in energy, for sufficiently large . In
this paper we devise an algorithm that attains energy
cost.
2. We show that the framework of the round lower bound proof
for computing diameter in CONGEST of Abboud et al. (DISC 2017) can be adapted
to give an energy lower bound in the wireless network model
(with no message size constraint), and this lower bound applies to -arboricity graphs. From the upper bound side, we show that the energy
complexity of can be attained for bounded-genus graphs
(which includes planar graphs).
3. Our upper bounds for computing diameter can be extended to other graph
problems. We show that exact global minimum cut or approximate -- minimum
cut can be computed in energy for bounded-genus graphs
Opaque perfect lenses
The response of the ``perfect lens'', consisting of a slab of lossless
material of thickness with at one frequency is
investigated. It is shown that as time progresses the lens becomes increasingly
opaque to any physical TM line dipole source located a distance from
the lens and which has been turned on at time . Here a physical source is
defined as one which supplies a bounded amount of energy per unit time. In fact
the lens cloaks the source so that it is not visible from behind the lens
either. For sources which are turned on exponentially slowly there is an exact
correspondence between the response of the perfect lens in the long time
constant limit and the response of lossy lenses in the low loss limit. Contrary
to the usual picture where the field intensity has a minimum at the front
interface we find that the field diverges to infinity there in the long time
constant limit.Comment: The 7th International Conference on the Electrical transport and
Optical Properties of Inhomogenous Media (ETOPIM7
Time minimal trajectories for two-level quantum systems with two bounded controls
In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we tackle the time-optimal control problem with techniques of optimal synthesis on 2-D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the starting point
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