In this paper, the exact transient quantum transport of non-interacting nanostructures is investigated in the presence of initial system-lead correlations and initial lead-lead correlations for a device system coupled to general electronic leads. The
exact master equation incorporating with initial correlations is derived through the extended quantum Langevin equation. The effects of the initial correlations are manifested through the time-dependent fluctuations contained explicitly in the exact master equation. The transient transport current incorporating with initial correlations is obtained from the exact master equation. The resulting transient transport current can be expressed in terms of the single-particle propagating and correlation Green functions of the device system. We show that the initial correlations can affect quantum transport not only in the transient regime, but also in the steady-state limit when system-lead couplings are strong enough so that electron localized bound states occur in the device system.
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with differing costs. T
his model captures more of the difficulty of certain natural problems. We test this model on a simple problem, Search with Two Oracles, for which we create a quantum algorithm that we prove is asymptotically optimal. We further give some evidence, using a geometric picture of Grovers algorithm, that our algorithm is exactly optimal.
Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity $Q(f)$, and sh
ow that $B(f)=Theta(Q(f)^2)$. This result gives a new method to upper bound the quantum query complexity: we give a method of finding bomb query algorithms from classical algorithms, which then provide nonconstructive upper bounds on $Q(f)=Theta(sqrt{B(f)})$. We subsequently were able to give explicit quantum algorithms matching our upper bound method. We apply this method on the single-source shortest paths problem on unweighted graphs, obtaining an algorithm with $O(n^{1.5})$ quantum query complexity, improving the best known algorithm of $O(n^{1.5}sqrt{log n})$ [arXiv:quant-ph/0606127]. Applying this method to the maximum bipartite matching problem gives an $O(n^{1.75})$ algorithm, improving the best known trivial $O(n^2)$ upper bound.
We conducted the observational tests of a phase correction scheme for the Atacama Compact Array (ACA) of the Atacama Large Millimeter and submillimeter Array (ALMA) using the Submillimeter Array (SMA). Interferometers at millimeter- and submillimeter
-wave are highly affected by the refraction induced by water vapor in the troposphere, which results as phase fluctuations. The ACA is planning to compensate the atmospheric phase fluctuations using the phase information of the outermost antennas with interpolating to the inner antennas by creating a phase screen. The interpolation and extrapolation phase correction schemes using phase screens are tested with the SMA to study how effective these schemes are. We produce a plane of a wavefront (phase screen) from the phase information of three antennas for each integration, and this phase screen is used for the interpolation and extrapolation of the phases of inner and outer antennas, respectively. The interpolation scheme obtains apparently improved results, suggesting that the ACA phase correction scheme will work well. On the other hand, the extrapolation scheme often does not improve the results. After the extrapolation, unexpectedly large phase fluctuations show up to the antennas at the distance of ~140 m away from the center of the three reference antennas. These direction vectors are almost perpendicular to the wind direction, suggesting that the phase fluctuations can be well explained by the frozen phase screen.
