Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived explicitly. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic

A bipartite class of entanglement monotones for N-qubit pure states

We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.Comment: 6 page

Normal forms and entanglement measures for multipartite quantum states

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence and the 3-tangle), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover a natural extension of the definition of GHZ-states to e.g. $2\times 2\times N$ systems is obtained.Comment: Proof of uniqueness of normal form adde

Multipartite entanglement in 2 x 2 x n quantum systems

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally entangled state, and some applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure

Measurement of the Branching Fractions for D^0 → π^-e^+v_e and D^0 → + K^-e^+V_e and Determination of │V_(cd)/V_(cs)│^2

Measurements of the exclusive branching fractions B(D^0→π^-e^+ν_e) and B(D^0→K^-e^+ν_e), using data collected at the ψ(3770) with the Mark III detector at the SLAC e^+e^- storage ring SPEAR, are used to determine the ratio of the Kobayashi-Maskawa matrix elements │V_(cd)/V_(cs)│^2 =0.057_(-0.015)^(+0.038)±0.005

Search for the decay D^0→K^0e^+e^-

A search for the decay of the charmed meson D^0→K^0e^+e^- is presented, based on data collected at the ψ(3770) resonance with the Mark III detector at the SLAC storage ring SPEAR. No evidence for this process is found, resulting in an upper limit on the decay branching ratio of 1.7×10^(-3) at the 90% confidence level

Revenue Management of Reusable Resources with Advanced Reservations

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/1/poms12672_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/2/poms12672.pd

Testing Fuel Efficiency of a Tractor with a Continuously Variable Transmission

A John Deere 8530 IVT tractor (Waterloo, Iowa) with a continuously variable transmission (CVT) that could be operated in automatic (CVT) or manual (fixed gear ratio) mode was tested for fuel consumption at a setpoint travel speed of 9 km·h‐1 with 17 different drawbar loads. Linear regression analysis results showed that with the throttle set to maximum in both transmission modes, operating the tractor with the transmission in the automatic mode was more fuel efficient than operating with the transmission in the manual mode when the drawbar power was approximately 78%, or less, of maximum power. When load transition portions of the data were filtered out, there was no significant effect of load sequencing in the remaining data. On the other hand, there was a noticeable effect of travel direction which could occur due to a minor slope of the test track in the direction of travel. Testing of more tractor models from different manufacturers and at different travel speeds is needed to determine if these results can be applied to different tractor models produced by the same and/or other manufacturers

Some entanglement features of three-atoms Tavis-Cummings model: Cooperative case

In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are taken initially to be either in the uppermost excited state "$|eee>$" or The $\textmd{GHZ}$-state or the $\textmd{W}$-state. For this system we investigate different kinds of atomic inversion and entanglement, which arise between the different parts of the system due to the interaction. Also the relationship, between entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear, is discussed. The $Q$-functions for different cases are discussed. Most remarkably it is found that the $\textmd{GHZ}$-state is more robust against energy losses, showing almost coherent trapping and Schr\"odinger-cat states can not be produced from such state. Also the entanglement of $\textmd{GHZ}$-state is more robust than the $\textmd{W}$-state. Another interesting feature found is that the state which has no pairwise entanglement initially will have a much improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms-pairwise entanglement are produced with the $\textmd{W}$-state.Comment: 14 pages, 7 figure

Moments of generalized Husimi distributions and complexity of many-body quantum states

We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to the systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution.Comment: published version, 33 pages, 7 figre