Limitation of entanglement due to spatial qubit separation

We consider spatially separated qubits coupled to a thermal bosonic field that causes pure dephasing. Our focus is on the entanglement of two Bell states which for vanishing separation are known as robust and fragile entangled states. The reduced two-qubit dynamics is solved exactly and explicitly. Our results allow us to gain information about the robustness of two-qubit decoherence-free subspaces with respect to physical parameters such as temperature, qubit-bath coupling strength and spatial separation of the qubits. Moreover, we clarify the relation between single-qubit coherence and two-qubit entanglement and identify parameter regimes in which the terms robust and fragile are no longer appropriate.Comment: 7 pages, 3 figures; revised version, accepted for publication in Europhys. Let

Theoretical Studies of the Structure and Dynamics of Metal/Hydrogen Systems: Diffusion and Path Integral Monte Carlo Investigations of Nickel and Palladium Clusters

Using both classical and quantum mechanical Monte Carlo methods, a number of properties are investigated for a single hydrogen atom adsorbed on palladium and nickel clusters. In particular, the geometries, the preferred binding sites, site specific hydrogen normal mode frequencies, and finite temperature effects in clusters from two to ten metal atoms are examined. Our studies indicate that hydrogen is localized in the present systems. The preferred hydrogen binding sites are found to be tetrahedral in clusters with five or fewer metal atoms and ctahedral for clusters of six to ten atoms. The exceptions to this rule are Ni9H and Pd9H for which the outside, threefold hollow and the inside tetrahedral sites are preferred, respectively. Hydrogen induced ‘‘reconstruction’’ of bare cluster geometries is seen in seven and ten-atom clusters

Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state

Convergence Characteristics of the Cumulant Expansion for Fourier Path Integrals

The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables $N$ included. It is proved that when the cumulant expansion is truncated at order $p$, the asymptotic convergence rate of the density matrix behaves like $N^{-(2p+1)}$. The complex algebra associated with the proof is simplified by introducing a diagrammatic representation of the contributing terms along with an associated linked-cluster theorem. The cumulant terms at each order are expanded in a series such that the the asymptotic convergence rate is maintained without the need to calculate the full cumulant at order $p$. Using this truncated expansion of each cumulant at order $p$, the numerical cost in developing Fourier path integral expressions having convergence order $N^{-(2p+1)}$ is shown to be approximately linear in the number of required potential energy evaluations making the method promising for actual numerical implementation.Comment: 47 pages, 2 figures, submitted to PR

Theoretical Studies of the Effect of Hydrogen–Hydrogen Interactionson the Structural and Dynamical Properties of Metal/Hydrogen Clusters

Using a combination of ground state, equilibrium, and dynamical Monte Carlo methods, we examine the role of hydrogen-hydrogen interactions on selected structural and time-dependent properties of hydrogen containing metal clusters. Equilibrium simulations include studies of the classical and quantum-mechanical geometries and energetics for embedded atom potential models of both the ground states and low-lying structural isomers of NinH2 and PdnH2 clusters (4≤n≤9). In addition to these time-independent investigations, we utilize dynamical path integral methods to characterize the effects of hydrogen-hydrogen interactions on the hydrogen vibrational lineshapes in these systems

The Influence of Diffusion on Surface Reaction Kinetics

An analysis is given of diffusion-influenced surface reactions using models similar to those used in solution kinetics. It is shown that a pure two-dimensional model of surface reactions yields no steady state rate constant. By incorporation of adsorption and desorption processes the deficiencies in the two-dimensional results are eliminated. Expressions are derived for diffusion-controlled and diffusion-influenced rate constants for surface reactions. Expressions are also derived for the activation energies of these surface reactions. It is shown that the activation energy for diffusion-controlled reactions wiII approximately be given by the activation energy for surface diffusion. Bounding expressions are developed for the activation energy for diffusion-influenced reactions. Comparisons are made betweeen Langmuir-Hinshe1wood and Eley-Rideal mechanisms, and it is found that Langmuir-Hinshelwood mechanisms should be more important than Eley-Rideal processes for many surface reactions

Early oral contraceptive use and breast cancer: results of another case-control study.

We report the results of a case-control study of oral contraceptive use and breast cancer conducted in London, Oxford and Edinburgh between 1980 and 1984. One thousand one hundred and twenty-five women aged 16-64 years with newly diagnosed breast cancer and a like number of matched controls were interviewed and asked about their past due use of oral contraceptives (OCs). Among women aged 45 years or more at diagnosis there was no evidence of an association between OC use and breast cancer. Among the 351 pairs of women aged under 45 years at diagnosis there was a significantly elevated risk associated with increasing duration of use before first full term pregnancy (relative risk for 4+ years use versus never use = 2.6, 95% confidence limits, 1.3-5.4). Since this result is at variance with the findings in some other studies we have investigated the nature of this association with particular emphasis on possible bias, pill type and a latent effect

Comparative Monte Carlo Efficiency by Monte Carlo Analysis

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the $\lambda_2$ of various Markov chain transition matrices. We first computed ${\lambda_2}$ for several one and two dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as a function of temperature and applied magnetic field. Next, we computed $\lambda_2$ for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size $\Delta$. Based on the $\lambda_2$ criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule-of-thumb of adjusting $\Delta$ so the Metropolis acceptance rate is around 50% range is often sub-optimal. In general, as a function of temperature or $\Delta$, $\lambda_2$ for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure

Precise Measurement of Magnetic Field Gradients from Free Spin Precession Signals of 3^{3}He and 129^{129}Xe Magnetometers

We report on precise measurements of magnetic field gradients extracted from transverse relaxation rates of precessing spin samples. The experimental approach is based on the free precession of gaseous, nuclear spin polarized $^3$He and $^{129}$Xe atoms in a spherical cell inside a magnetic guiding field of about 400 nT using LT$_C$ SQUIDs as low-noise magnetic flux detectors. The transverse relaxation rates of both spin species are simultaneously monitored as magnetic field gradients are varied. For transverse relaxation times reaching 100 h, the residual longitudinal field gradient across the spin sample could be deduced to be$|\vec{\nabla}B_z|=(5.6 \pm 0.4)$ pT/cm. The method takes advantage of the high signal-to-noise ratio with which the decaying spin precession signal can be monitored that finally leads to the exceptional accuracy to determine magnetic field gradients at the sub pT/cm scale

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.