Quantum Information Approach to Rotating Bose-Einstein Condensate

We investigate the 2D weakly interacting Bose-Einstein condensate in a rotating trap by the tools of quantum information theory. The critical exponents of the ground state fidelity susceptibility and the correlation length of the system are obtained for the quantum phase transition when the frst vortex is formed. We also find the single-particle entanglement can be an indicator of the angular momentums for some real ground states. The single-particle entanglement of fractional quantum Hall states such as Laughlin state and Pfaffian state is also studied.Comment: 4 pages, 6 figures, minimal changes are mad

An Augmented Lagrangian Method for the Optimal H

This paper treats the computational method of the optimal H∞ model order reduction (MOR) problem of linear time-invariant (LTI) systems. Optimal solution of MOR problem of LTI systems can be obtained by solving the LMIs feasibility coupling with a rank inequality constraint, which makes the solutions much harder to be obtained. In this paper, we show that the rank inequality constraint can be formulated as a linear rank function equality constraint. Properties of the linear rank function are discussed. We present an iterative algorithm based on augmented Lagrangian method by replacing the rank inequality with the linear rank function. Convergence analysis of the algorithm is given, which is distinct to the now available heuristic methods. Numerical experiments for the MOR problems of continuous LTI system illustrate the practicality of our method

Physics-Aware Reduced-Order Modeling of Nonautonomous Advection-Dominated Problems

We present a variant of dynamic mode decomposition (DMD) for constructing a reduced-order model (ROM) of advection-dominated problems with time-dependent coefficients. Existing DMD strategies, such as the physics-aware DMD and the time-varying DMD, struggle to tackle such problems due to their inherent assumptions of time-invariance and locality. To overcome the compounded difficulty, we propose to learn the evolution of characteristic lines as a nonautonomous system. A piecewise locally time-invariant approximation to the infinite-dimensional Koopman operator is then constructed. We test the accuracy of time-dependent DMD operator on 2d Navier-Stokes equations, and test the Lagrangian-based method on 1- and 2-dimensional advection-diffusion with variable coefficients. Finally, we provide predictive accuracy and perturbation error upper bounds to guide the selection of rank truncation and subinterval sizes.Comment: 27 pages, 21 figure

Carbon Sequestration in Agriculture: Value and Implementation

Examining the value of carbon sequestration in a dynamic model, the authors demonstrate that unless the sequestration is permanent, it is only a fraction of the value of emission abatement. The magnitude of the fraction increases in the duration of sequestration, the natural decay rate of carbon, and the discount rate. The authors also show that sinks should be used as early as possible in order to optimally reduce the carbon stock. Finally, the authors propose and assess three mechanisms for efficiently introducing sequestration into a carbon permit trading market: a pay-as-you-go system, a variable-length-contract system, and a carbon-annuity-account system. All are efficient, but all may not be equally feasible to implement

Research And Application On The Coupled Method Of Remote-Sensing And Ground-Monitoring Of Reservoir Storage Capacity

Reservoir storage capacity monitoring is the basis of reservoir operation. The relationship curves of reservoir water level-area and water level-capacity are the significant parameters of storage capacity calculation. With the long-term operation, both on the bottom and bank of the reservoir have erosion and deposition, causing the relationship of water level-area and level-storage changes, which leads to inaccuracy of reservoir storage capacity calculation with the original curves. It is costly to revise the curves of reservoir water level-area and water level-capacity by ground measurement termly. A coupled Method of Remote-sensing and Ground-monitoring of Reservoir Storage Capacity is proposed in this paper. Based on coupled data of satellite image of the reservoir water-area monitoring and the ground water-level monitoring on the same day, the relationship curves of reservoir water level-area and water level-capacity are updated, the calculation accuracy of reservoir storage capacity is improved. The Gangnan Reservoir is taken as an example for this research. 10 HJ-satellite images are used for revising the curve of reservoir water level-area and water level-capacity. The reservoir storage capacity differences between original and revised curves are analyzed and turned out to be reasonable

Quantum Information Approach to Bose-Einstein Condensate in a Tilted Double-Well System

We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitions are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.Comment: 5 pages, 5 figures, slightly different from the published versio