Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods

We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to the Fermionic Gaussian state that optimally approximates the quantum state of the fermions. The methods apply to relatively large systems, since their complexity only scales quadratically with the number of lattice sites. Moreover, they are specially suited to describe inhomogenous systems, as those typically found in recent experiments with atoms in optical lattices, at least in the weak interaction regime. As a benchmark, we have applied them to the two-dimensional Hubbard model on a 10x10 lattice with and without an external confinement.Comment: 16 pages, 22 figure

Microwave amplification with nanomechanical resonators

Sensitive measurement of electrical signals is at the heart of modern science and technology. According to quantum mechanics, any detector or amplifier is required to add a certain amount of noise to the signal, equaling at best the energy of quantum fluctuations. The quantum limit of added noise has nearly been reached with superconducting devices which take advantage of nonlinearities in Josephson junctions. Here, we introduce a new paradigm of amplification of microwave signals with the help of a mechanical oscillator. By relying on the radiation pressure force on a nanomechanical resonator, we provide an experimental demonstration and an analytical description of how the injection of microwaves induces coherent stimulated emission and signal amplification. This scheme, based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices, and, at the same time, has a high potential to reach quantum limited operation. With a measured signal amplification of 25 decibels and the addition of 20 quanta of noise, we anticipate near quantum-limited mechanical microwave amplification is feasible in various applications involving integrated electrical circuits.Comment: Main text + supplementary information. 14 pages, 3 figures (main text), 18 pages, 6 figures (supplementary information

A prospective cohort study of long-term cognitive changes in older Medicare beneficiaries

<p>Abstract</p> <p>Background</p> <p>Promoting cognitive health and preventing its decline are longstanding public health goals, but long-term changes in cognitive function are not well-documented. Therefore, we first examined long-term changes in cognitive function among older Medicare beneficiaries in the Survey on Assets and Health Dynamics among the Oldest Old (AHEAD), and then we identified the risk factors associated with those changes in cognitive function.</p> <p>Methods</p> <p>We conducted a secondary analysis of a prospective, population-based cohort using baseline (1993-1994) interview data linked to 1993-2007 Medicare claims to examine cognitive function at the final follow-up interview which occurred between 1995-1996 and 2006-2007. Besides traditional risk factors (i.e., aging, age, race, and education) and adjustment for baseline cognitive function, we considered the reason for censoring (entrance into managed care or death), and post-baseline continuity of care and major health shocks (hospital episodes). Residual change score multiple linear regression analysis was used to predict cognitive function at the final follow-up using data from telephone interviews among 3,021 to 4,251 (sample size varied by cognitive outcome) baseline community-dwelling self-respondents that were ≥ 70 years old, not in managed Medicare, and had at least one follow-up interview as self-respondents. Cognitive function was assessed using the 7-item Telephone Interview for Cognitive Status (TICS-7; general mental status), and the 10-item immediate and delayed (episodic memory) word recall tests.</p> <p>Results</p> <p>Mean changes in the number of correct responses on the TICS-7, and 10-item immediate and delayed word recall tests were -0.33, -0.75, and -0.78, with 43.6%, 54.9%, and 52.3% declining and 25.4%, 20.8%, and 22.9% unchanged. The main and most consistent risks for declining cognitive function were the baseline values of cognitive function (reflecting substantial regression to the mean), aging (a strong linear pattern of increased decline associated with greater aging, but with diminishing marginal returns), older age at baseline, dying before the end of the study period, lower education, and minority status.</p> <p>Conclusions</p> <p>In addition to aging, age, minority status, and low education, substantial and differential risks for cognitive change were associated with sooner vs. later subsequent death that help to clarify the terminal drop hypothesis. No readily modifiable protective factors were identified.</p

Differential Impact of Monsoon and Large Amplitude Internal Waves on Coral Reef Development in the Andaman Sea

The Andaman Sea and other macrotidal semi-enclosed tropical seas feature large amplitude internal waves (LAIW). Although LAIW induce strong fluctuations i.e. of temperature, pH, and nutrients, their influence on reef development is so far unknown. A better-known source of disturbance is the monsoon affecting corals due to turbulent mixing and sedimentation. Because in the Andaman Sea both, LAIW and monsoon, act from the same westerly direction their relative contribution to reef development is difficult to discern. Here, we explore the framework development in a number of offshore island locations subjected to differential LAIW- and SW-monsoon impact to address this open question. Cumulative negative temperature anomalies – a proxy for LAIW impact – explained a higher percentage of the variability in coral reef framework height, than sedimentation rates which resulted mainly from the monsoon. Temperature anomalies and sediment grain size provided the best correlation with framework height suggesting that so far neglected subsurface processes (LAIW) play a significant role in shaping coral reefs