Quantum-limited metrology in the presence of collisional dephasing

Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $\chi$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $\hat{J}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2\gamma)^{1/3}$ below super-Heisenberg limit $\propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<\!<\gamma<N^{3/4}$. With a $\hat{J}_y$ measurement, our analytical results confirm that the phase $\phi=\chi t\sim 0$ can be detected at the limit even in the presence of the dephasing.Comment: 3.2 pages, 3 figure

The Abel-Zeilberger Algorithm

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.Comment: 18 page

Spin squeezing: transforming one-axis-twisting into two-axis-twisting

Squeezed spin states possess unique quantum correlation or entanglement that are of significant promises for advancing quantum information processing and quantum metrology. In recent back to back publications [C. Gross \textit{et al, Nature} \textbf{464}, 1165 (2010) and Max F. Riedel \textit{et al, Nature} \textbf{464}, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2dB and -2.5dB respectively in two-component atomic condensates exhibiting one-axis-twisting interactions (OAT). The noise reduction limit for the OAT interaction scales as $\propto 1/{N^{2/3}}$, which for a condensate with $N\sim 10^3$ atoms, is about 100 times below standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the OAT spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction $\propto 1/N$, or an extra 10-fold improvement for $N\sim 10^3$.Comment: 4 pages, 3 figure

Global Models of Planet Formation and Evolution

Despite the increase in observational data on exoplanets, the processes that lead to the formation of planets are still not well understood. But thanks to the high number of known exoplanets, it is now possible to look at them as a population that puts statistical constraints on theoretical models. A method that uses these constraints is planetary population synthesis. Its key element is a global model of planet formation and evolution that directly predicts observable planetary properties based on properties of the natal protoplanetary disk. To do so, global models build on many specialized models that address one specific physical process. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disk (gas and solids), the (proto)planet (solid core, gaseous envelope, and atmosphere), and finally the interactions (migration and N-body interaction). We compare the approaches in different global models and identify physical processes that require improved descriptions in future. We then address important results of population synthesis like the planetary mass function or the mass-radius relation. In these results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Due to their nature as meta models, global models depend on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that global models will in future undergo significant modifications. Despite this, they can already now yield many testable predictions. With future global models addressing the geophysical characteristics, it should eventually become possible to make predictions about the habitability of planets.Comment: 30 pages, 16 figures. Accepted for publication in the International Journal of Astrobiology (Cambridge University Press

A review of microgrid development in the United States – A decade of progress on policies, demonstrations, controls, and software tools

Microgrids have become increasingly popular in the United States. Supported by favorable federal and local policies, microgrid projects can provide greater energy stability and resilience within a project site or community. This paper reviews major federal, state, and utility-level policies driving microgrid development in the United States. Representative U.S. demonstration projects are selected and their technical characteristics and non-technical features are introduced. The paper discusses trends in the technology development of microgrid systems as well as microgrid control methods and interactions within the electricity market. Software tools for microgrid design, planning, and performance analysis are illustrated with each tool's core capability. Finally, the paper summarizes the successes and lessons learned during the recent expansion of the U.S. microgrid industry that may serve as a reference for other countries developing their own microgrid industries

Provision of secondary frequency regulation by coordinated dispatch of industrial loads and thermal power plants

Demand responsive industrial loads with high thermal inertia have potential to provide ancillary service for frequency regulation in the power market. To capture the benefit, this study proposes a new hierarchical framework to coordinate the demand responsive industrial loads with thermal power plants in an industrial park for secondary frequency control. In the proposed framework, demand responsive loads and generating resources are coordinated for optimal dispatch in two-time scales: (1) the regulation reserve of the industrial park is optimally scheduled in a day-ahead manner. The stochastic regulation signal is replaced by the specific extremely trajectories. Furthermore, the extremely trajectories are achieved by the day-ahead predicted regulation mileage. The resulting benefit is to transform the stochastic reserve scheduling problem into a deterministic optimization; (2) a model predictive control strategy is proposed to dispatch the industry park in real time with an objective to maximize the revenue. The proposed technology is tested using a real-world industrial electrolysis power system based upon Pennsylvania, Jersey, and Maryland (PJM) power market. Various scenarios are simulated to study the performance of the proposed approach to enable industry parks to provide ancillary service into the power market. The simulation results indicate that an industrial park with a capacity of 500 MW can provide up to 40 MW ancillary service for participation in the secondary frequency regulation. The proposed strategy is demonstrated to be capable of maintaining the economic and secure operation of the industrial park while satisfying performance requirements from the real world regulation market

Anomalous microwave response of high-temperature superconducting thin-film microstrip resonator in weak dc magnetic fields

We have studied an anomalous microwave (mw) response of superconducting YBa_{2}Cu_{3}O_{7-delta} (YBCO) microstrip resonators in the presence of a weak dc magnetic field, H_{dc}. The surface resistance (R_{s}) and reactance (X_{s}) show a correlated non-monotonic behaviour as a function of H_{dc}. R_{s} and X_{s} were found to initially decrease with elevated H_{dc} and then increase after H_{dc} reaches a crossover field, H_{c}, which is independent of the amplitude and frequency of the input mw signal within the measurements. The frequency dependence of R_{s} is almost linear at fixed H_{dc} with different magnitudes (H_{c}). The impedance plane analysis demonstrates that r_{H}, which is defined as the ratio of the change in R_{s}(H_{dc}) and that in X_{s}(H_{dc}), is about 0.6 at H_{dc}<H_{c} and 0.1 at H_{dc}>H_{c}. The H_{dc} dependence of the surface impedance is qualitatively independent of the orientation of H_{dc}.Comment: REVTex 3.1, 5 pages, 6 EPS figures, submitted to Physica

Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions

Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N_f=8 flavor system, thus verifying its QCD-like nature. With N_f=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free field value.Comment: 26 pages, 11 figure