1,947 research outputs found
A Nonsteady Heat Diffusion Problem with Spherical Symmetry
A solution in successive approximations is presented for the heat diffusion across a spherical boundary with radial motion. The approximation procedure converges rapidly provided the temperature variations are appreciable only in a thin layer adjacent to the spherical boundary. An explicit solution for the temperature field is given in the zero order when the temperature at infinity and the temperature gradient at the spherical boundary are specified. The first-order correction for the temperature field may also be found. It may be noted that the requirements for rapid convergence of the approximate solution are satisfied for the particular problem of the growth or collapse of a spherical vapor bubble in a liquid when the translational motion of the bubble is neglected
Maximizing information on the environment by dynamically controlled qubit probes
We explore the ability of a qubit probe to characterize unknown parameters of
its environment. By resorting to quantum estimation theory, we analytically
find the ultimate bound on the precision of estimating key parameters of a
broad class of ubiquitous environmental noises ("baths") which the qubit may
probe. These include the probe-bath coupling strength, the correlation time of
generic bath spectra, the power laws governing these spectra, as well as their
dephasing times T2. Our central result is that by optimizing the dynamical
control on the probe under realistic constraints one may attain the maximal
accuracy bound on the estimation of these parameters by the least number of
measurements possible. Applications of this protocol that combines dynamical
control and estimation theory tools to quantum sensing are illustrated for a
nitrogen-vacancy center in diamond used as a probe.Comment: 8 pages + 6 pages (appendix), 3 Figure
Criticality of environmental information obtainable by dynamically controlled quantum probes
A universal approach to decoherence control combined with quantum estimation
theory reveals a critical behavior, akin to a phase transition, of the
information obtainable by a qubit probe concerning the memory time of
environmental fluctuations. This criticality emerges only when the probe is
subject to dynamical control. It gives rise to a sharp transition between two
dynamical phases characterized by either a short or long memory time compared
to the probing time. This phase-transition of the environmental information is
a fundamental feature that facilitates the attainment of the highest estimation
precision of the environment memory-time and the characterization of probe
dynamics.Comment: 3 pages, 4 figure
Quantum state transfer in disordered spin chains: How much engineering is reasonable?
The transmission of quantum states through spin chains is an important
element in the implementation of quantum information technologies. Speed and
fidelity of transfer are the main objectives which have to be achieved by the
devices even in the presence of imperfections which are unavoidable in any
manufacturing process. To reach these goals, several kinds of spin chains have
been suggested, which differ in the degree of fine-tuning, or engineering, of
the system parameters. In this work we present a systematic study of two
important classes of such chains. In one class only the spin couplings at the
ends of the chain have to be adjusted to a value different from the bulk
coupling constant, while in the other class every coupling has to have a
specific value. We demonstrate that configurations from the two different
classes may perform similarly when subjected to the same kind of disorder in
spite of the large difference in the engineering effort necessary to prepare
the system. We identify the system features responsible for these similarities
and we perform a detailed study of the transfer fidelity as a function of chain
length and disorder strength, yielding empirical scaling laws for the fidelity
which are similar for all kinds of chain and all disorder models. These results
are helpful in identifying the optimal spin chain for a given quantum
information transfer task. In particular, they help in judging whether it is
worthwhile to engineer all couplings in the chain as compared to adjusting only
the boundary couplings.Comment: 20 pages, 13 figures. Revised version, title changed, accepted by
Quantum Information & Computatio
Robustness of spin-chain state-transfer schemes
This is a shortened and slightly edited version of a chapter in the
collection "Quantum State Transfer and Network Engineering", edited by G.M.
Nikolopoulos and I. Jex, where we review our own research about the robustness
of spin-chain state-transfer schemes along with other approaches to the topic.
Since our own research is documented elsewhere to a large extent we here
restrict ourselves to a review of other approaches which might be useful to
other researchers in the field
URBAN PLACE-CONSCIOUS EDUCATION: PRIDE IN THE INNER CITY
Many educators are turning to place-conscious education as a means of making studentsâ education relevant and meaningful, as well as encouraging them to contribute to their local communities in positive ways. While many scholars focus their research on place-conscious education on rural areas, a growing body of scholarship examines how place-conscious principles can be applied in inner city schools. Differences in emphasis and approach exist between the rural and urban scholarship, however. This work analyzes some key differences as well as examining why they might exist. Urban studentsâ relationship with place is complicated by societal messages which make fostering a pride of place a difficult but necessary task for place-conscious educators
Combining All Pairs Shortest Paths and All Pairs Bottleneck Paths Problems
We introduce a new problem that combines the well known All Pairs Shortest
Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to
compute the shortest paths for all pairs of vertices for all possible flow
amounts. We call this new problem the All Pairs Shortest Paths for All Flows
(APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with
unit edge costs and real edge capacities in
time,
where is the number of vertices, is the number of distinct edge
capacities (flow amounts) and is the time taken
to multiply two -by- matrices over a ring. Secondly we extend the problem
to graphs with positive integer edge costs and present an algorithm with
worst case time complexity, where is
the upper bound on edge costs
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