Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic Oscillators in a General Environment

In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D \textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to $N$, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations and dissipation of mesoscopic objects towards the construction of a theoretical framework for macroscopic quantum phenomena.Comment: 35 pages, revtex, no figures, 2nd version, references added, to appear in PR

Initial Geometrical Imperfections in Three-Storey Modular Steel Scaffolds

Modular steel scaffolds are commonly used as supporting scaffolds in building construction. They are highly susceptible to global and local instability, and traditionally, the load carrying capacities of these scaffolds are obtained from limited full-scale tests with little rational design. Structural failure of these scaffolds occurs from time to time due to inadequate design, poor installation and over-loads on sites. Initial geometrical imperfections are considered to be very important to the structural behaviour of multi-storey modular steel scaffolds. This paper presents an extensive numerical investigation on three different approaches in analyzing and designing multi-story modular steel scaffolds, namely, a) Notional Load Approach, b) Eigenmode Imperfection Approach, and c) Critical Load Approach. It should be noted that all these three approaches adopt different ways to allow for the presence of initial geometrical imperfections in the scaffolds when determining their load carrying capacities. Moreover, their suitability and accuracy in predicting the structural instability of typical modular steel scaffolds are presented and discussed in details

Decoherence of a Josephson qubit due to coupling to two level systems

Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two level systems in the oxide barrier produce fluctuations and 1/f noise in the Josephson junction critical current I_o. This in turn leads to fluctuations in the qubit energy splitting that degrades the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.Comment: 23 pages, Latex, 6 encapsulated postscript figure

Ultra-high energy neutrino scattering

Estimates are made of the ultra-high energy neutrino cross sections based on an extrapolation to very small Bjorken x of the logarithmic Froissart dependence in x shown previously to provide an excellent fit to the measured proton structure function F_2^p(x,Q^2) over a broad range of the virtuality Q^2. Expressions are obtained for both the neutral current and the charged current cross sections. Comparison with an extrapolation based on perturbative QCD shows good agreement for energies where both fit data, but our rates are as much as a factor of 10 smaller for neutrino energies above 10^9 GeV, with important implications for experiments searching for extra-galactic neutrinos.Comment: 4 pages, 1 figure, 1 table; Title, abstract and text changed, conclusions unchanged. Version accepted for publication in Physical Review

A comparison of sampling designs in a Hainan tropical rain forest

Different sampling strategies are simulated by changing quadrat size, quadrat shape, sample size and the arrangement of quadrats in a tropical rain forest of Hainan (South China). The simulation uses enumeration data of trees, and derived variables such as species richness, species importance, and species population density, to compare the efficiency of the sampling. The results verify that greater sampling efficiency is to be expected using systematic sampling than random sampling. Quadrat size has substantial influence on parameter estimation, but quadrat shape has negligible effect except when the quadrat is extremely long and narrow

Review of a partial care program for severely emotionally disturbed youth

The need for research on programs for Emotionally Disturbed (ED) children and adolescents is great. The present study examined a partial care program for ED youth in New Jersey. There were 120 subjects in this study. Several characteristics of these subjects were examined – gender, race, age, diagnosis, and family status. The study also examined the subjects\u27 average length of stay in the program.and reasons for being discharged. In addition, the ratio of clients to staff was studied. The data was collected by examining the files of past and present clients to gather the necessary information. Descriptive statistics were used to analyze the results. The majority of the subjects were African American males between the ages of 12 and 15 years. Most were either diagnosed Conduct Disorder or Oppositional Defiant Disorder and most lived with a single parent. The overall length of stay for the subjects was 8 months. Most of them were discharged due to refusal of service or to another placement. The ratio of clients to staff varied from 6 to 1 to 3 to 1 over the three year period studied

Evidence of Dynamical Spin Shielding in Ce from Spin-Resolved Photoelectron Spectroscopy

Using Fano effect measurements upon polycrystalline Ce, we have observed a phase reversal between the spectral structure at the Fermi edge and the other 4f derived feature near a binding energy of 2 eV. The Fano effect is the observation of spin polarized photoelectron emission from nonmagnetic materials, under chirally selective excitation, such as circularly polarized photons. The observation of phase reversal between the two peaks is a direct experimental proof of Kondo shielding in Ce, confirming the predictions of Gunnarsson and Shoenhammer, albeit with a small modification