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 students’ 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 students’ 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 $\tilde{O}(\sqrt{t}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}n^{2.843})$ time, where $n$ is the number of vertices, $t$ is the number of distinct edge capacities (flow amounts) and $O(n^{\omega}) < O(n^{2.373})$ is the time taken to multiply two $n$-by-$n$ matrices over a ring. Secondly we extend the problem to graphs with positive integer edge costs and present an algorithm with $\tilde{O}(\sqrt{t}c^{(\omega+5)/4}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}c^{1.843}n^{2.843})$ worst case time complexity, where $c$ is the upper bound on edge costs