Random Control over Quantum Open Systems

Parametric fluctuations or stochastic signals are introduced into the control pulse sequence to investigate the feasibility of random control over quantum open systems. In a large parameter error region, the out-of-order control pulses work as well as the regular pulses for dynamical decoupling and dissipation suppression. Calculations and analysis are based on a non-perturbative control approach allowed by an exact quantum-state-diffusion equation. When the average frequency and duration of the pulse sequence take proper values, the random control sequence is robust, fault- tolerant, and insensitive to pulse strength deviations and interpulse temporal separation in the quasi-periodic sequence. This relaxes the operational requirements placed on quantum control experiments to a great deal.Comment: 7 pages, 6 firgure

Geometric phases in dressed state quantum computation

Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations and how one may take advantage of the dressed states producing them. Specifically, we show that that for a given, but arbitrary Hamiltonian, and at an arbitrary time {\tau}, there always exists a set of dressed states such that a given gate operation can be performed by the Hamiltonian up to a phase {\phi}. The phase is a sum of a dynamical phase and a geometric phase. We illustrate the new phase for several systems.Comment: 4 pages, 2 figure

Measuring infrastructure skills productivity

This chapter presents the concept and meaning of construction productivity and the techniques used in measuring workforce skills productivity in the construction industry. There are three major methods highlighted for monitoring and measuring productivity in the construction industry. The first relates to visual recording that requires taught watchers to be available on location to monitor and record work by specialists. The second is the physical recording technique which involves a direct surveillance technique that includes a qualified observer observing the site for the full duration of the working day operation using the work study method or work measurement. This method was typically illustrated with the application of regression model and learning curve theory to improve labour productivity. The third measuring technique discussed is the use of questionnaires and interview survey which involves information gathering through an interview with supervisors and workers working in the construction industry. Finally, the chapter discussed how infrastructure productivity can be improved through effective supervision, material management and supply chain management, project front-end planning (loading) and work face planning, training and certification of workforce and labour management and relations

Casimir Invariants for Systems Undergoing Collective Motion

Dicke states are states of a collection of particles which have been under active investigation for several reasons. One reason is that the decay rates of these states can be quite different from a set of independently evolving particles. Another reason is that a particular class of these states are decoherence-free or noiseless with respect to a set of errors. These noiseless states, or more generally subsystems, can avoid certain types of errors in quantum information processing devices. Here we provide a method for calculating invariants of systems of particles undergoing collective motions. These invariants can be used to determine a complete set of commuting observables for a class of Dicke states as well as identify possible logical operations for decoherence-free/noiseless subsystems. Our method is quite general and provides results for cases where the constituent particles have more than two internal states.Comment: 5 page

A perspective on algal biogas

Algae are suggested as a biomass source with significant growth rates, which may be cultivated in the ocean (seaweed) or on marginal land (microalgae). Biogas is suggested as a beneficial route to sustainable energy; however the scientific literature on algal biogas is relatively sparse. This report comprises a review of the literature and provides a state of the art in algal biogas and is aimed at an audience of academics and energy policy makers. It was produced by IEA Bioenergy Task 37 which addresses the challenges related to the economic and environmental sustainability of biogas production and utilisation.JRC.F.8-Sustainable Transpor

On the probability of a Pareto record

Given a sequence of independent random vectors taking values in ${\mathbb R}^d$ and having common continuous distribution function $F$, say that the $n^{\rm \scriptsize th}$ observation sets a (Pareto) record if it is not dominated (in every coordinate) by any preceding observation. Let $p_n(F) \equiv p_{n, d}(F)$ denote the probability that the $n^{\rm \scriptsize th}$ observation sets a record. There are many interesting questions to address concerning $p_n$ and multivariate records more generally, but this short paper focuses on how $p_n$ varies with $F$, particularly if, under $F$, the coordinates exhibit negative dependence or positive dependence (rather than independence, a more-studied case). We introduce new notions of negative and positive dependence ideally suited for such a study, called negative record-setting probability dependence (NRPD) and positive record-setting probability dependence (PRPD), relate these notions to existing notions of dependence, and for fixed $d \geq 2$ and $n \geq 1$ prove that the image of the mapping $p_n$ on the domain of NRPD (respectively, PRPD) distributions is $[p^*_n, 1]$ (resp., $[n^{-1}, p^*_n]$), where $p^*_n$ is the record-setting probability for any continuous $F$ governing independent coordinates.Comment: 16 pages, 1 figure; this revision responds to three anonymous reviews; paper accepted to Probability in the Engineering and Informational Science

Metastable lifetimes in a kinetic Ising model: Dependence on field and system size

The lifetimes of metastable states in kinetic Ising ferromagnets are studied by droplet theory and Monte Carlo simulation, in order to determine their dependences on applied field and system size. For a wide range of fields, the dominant field dependence is universal for local dynamics and has the form of an exponential in the inverse field, modified by universal and nonuniversal power-law prefactors. Quantitative droplet-theory predictions are numerically verified, and small deviations are shown to depend nonuniversally on the details of the dynamics. We identify four distinct field intervals in which the field dependence and statistical properties of the lifetimes are different. The field marking the crossover between the weak-field regime, in which the decay is dominated by a single droplet, and the intermediate-field regime, in which it is dominated by a finite droplet density, vanishes logarithmically with system size. As a consequence the slow decay characteristic of the former regime may be observable in systems that are macroscopic as far as their equilibrium properties are concerned.Comment: 18 pages single spaced. RevTex Version 3. FSU-SCRI-94-1

Sharpened localization of the trailing point of the Pareto record frontier

For $d\ge2$ and iid $d$-dimensional observations $X^{(1)},X^{(2)},\dots$ with independent Exponential$(1)$ coordinates, we revisit the study by Fill and Naiman (Electron. J. Probab., 2020) of the boundary (relative to the closed positive orthant), or "frontier", $F_n$ of the closed Pareto record-setting (RS) region \mbox{RS}_n:=\{0\le x\in{\mathbb R}^d:x\not\prec X^{(i)}\mbox{\ for all $1\le i\le n$}\} at time $n$, where $0\le x$ means that $0\le x_j$ for $1\le j\le d$ and $x\prec y$ means that $x_j<y_j$ for $1\le j\le d$. With $x_+:=\sum_{j=1}^d x_j$, let F_n^-:=\min\{x_+:x\in F_n\}\quad\mbox{and}\quad F_n^+:=\max\{x_+:x\in F_n\}. Almost surely, there are for each $n$ unique vectors $\lambda_n\in F_n$ and $\tau_n\in F_n$ such that $F_n^+=(\lambda_n)_+$ and $F_n^-=(\tau_n)_+$; we refer to $\lambda_n$ and $\tau_n$ as the leading and trailing points, respectively, of the frontier. Fill and Naiman provided rather sharp information about the typical and almost sure behavior of $F^+$, but somewhat crude information about $F^-$, namely, that for any $\varepsilon >0$ and $c_n\to\infty$ we have $${\mathbb P}(F_n^- -\ln n\in (-(2+\varepsilon)\ln\ln\ln n,c_n))\to 1$$ (describing typical behavior) and almost surely \limsup \frac{F_n^- - \ln n}{\ln \ln n} \le 0 \quad \mbox{and} \quad \liminf \frac{F_n^- - \ln n}{\ln \ln \ln n} \in [-2, -1]. In this paper we use the theory of generators (minima of $F_n$) together with the first- and second-moment methods to improve considerably the trailing-point location results to $$F_n^- - (\ln n - \ln \ln \ln n) \overset{\mathrm{P}}{\longrightarrow} - \ln(d - 1)$$ (describing typical behavior) and, for $d \ge 3$, almost surely \begin{align*} &\limsup [F_n^- - (\ln n - \ln \ln \ln n)] \leq -\ln(d - 2) + \ln 2 \\ \mbox{and }&\liminf [F_n^- - (\ln n - \ln \ln \ln n)] \ge - \ln d - \ln 2. \end{align*}Comment: 32 pages, 2 figures. arXiv admin note: text overlap with arXiv:1901.0562

Sharpened Localization of the Trailing Point of the Pareto Record Frontier

For d ≥ 2 and i.i.d. d-dimensional observations X^{(1)}, X^{(2)}, … with independent Exponential(1) coordinates, we revisit the study by Fill and Naiman (Electron. J. Probab., 25:Paper No. 92, 24 pp., 2020) of the boundary (relative to the closed positive orthant), or "frontier", F_n of the closed Pareto record-setting (RS) region RS_n := {0 ≤ x ∈ R^d: x ⊀ X^(i) for all 1 ≤ i ≤ n} at time n, where 0 ≤ x means that 0 ≤ x_j for 1 ≤ j ≤ d and x ≺ y means that x_j < y_j for 1 ≤ j ≤ d. With x_+ : = ∑_{j = 1}^d x_j = ‖x‖₁, let F_n^- := min{x_+: x ∈ F_n} and F_n^+ : = max{x_+: x ∈ F_n}. Almost surely, there are for each n unique vectors λ_n ∈ F_n and τ_n ∈ F_n such that F_n^+ = (λ_n)_+ and F_n^- = (τ_n)_+; we refer to λ_n and τ_n as the leading and trailing points, respectively, of the frontier. Fill and Naiman provided rather sharp information about the typical and almost sure behavior of F^+, but somewhat crude information about F^-, namely, that for any ε > 0 and c_n → ∞ we have P(F_n^- - ln n ∈ (- (2 + ε) ln ln ln n, c_n)) → 1 (describing typical behavior) and almost surely limsup (F_n^- - ln n)/(ln ln n) ≤ 0 and liminf (F_n^- - ln n)/(ln ln ln n) ∈ [-2, -1]. In this extended abstract we use the theory of generators (minima of F_n) together with the first- and second-moment methods to improve considerably the trailing-point location results to F_n^- - (ln n - ln ln ln n) ⟶P -ln(d - 1) (describing typical behavior) and, for d ≥ 3, almost surely limsup [F_n^- -(ln n - ln ln ln n)] ≤ -ln(d - 2) + ln 2 and liminf [F_n^- -(ln n - ln ln ln n)] ≥ -ln d - ln 2