Langevin equations for interacting fermions and Cooper-like pairing in trapped one-dimensional fermions

Momentum correlations in a one-dimensional equilibrium ensemble of trapped fermions, with a point interaction between particles of opposite spin have been studied. In the degenerate regime correlations were observed between fermions with opposite spins and momenta, similar to Cooper pairing. These correlations appear as soon as the temperature is below the Fermi energy, which is a much less stringent condition than that of the BCS transition proper. Calculations are carried out in both perturbative and non-perturbative regimes. To achieve the latter. it is shown that interacting fermionic dynamics may be solved as a stochastic linear transformation of Grassmann algebra generators, much in the way random c-number paths are introduced in the conventional quantum stochastics of bosons. Importantly, the method thus emerging is inherently free of the sign problem

Understanding Volumetric Water Storage in Monsoonal Wetlands of Northeastern Bangladesh

The volume of water stored in seasonal wetlands is a fundamental but difficult to measure variable for developing a physical understanding of wetland behavior. For seasonal wetlands that are a major source of water for rice and fish production, this physical understanding is key to planning for water-food security and ecosystem services. This study quantified variations in volumetric storage for the numerous seasonal wetlands of northeastern Bangladesh, locally known as “haors.” These haors receive transboundary runoff from densely vegetated and mountainous terrain in India and face persistent monsoonal cloud cover as they become full. We estimated volumetric storage for 13 haors by using extensive remote sensing data on water surface extent and elevation that was complemented with citizen-contributed gauge data. Assuming a trapezoidal bathymetry, an area-volume relationship was developed for selected haors. This relationship was assumed to be valid for extrapolating volumetric estimations over all the haors in the region. Results suggested that as haors get filled with the onset of monsoon rains, total estimated storage relative to the lowest observable level varied from 6.5 (±0.4) km3 in May to 30.9 (±2.0) km3 in July (peak of monsoon). Choosing a rectangular bathymetry can lead to 47% higher estimates compared to trapezoidal cross section. Estimating this intra-annual/interannual increase in storage is important for the region to plan water management policies that balance the human and ecosystem needs. Our analytical approach has potential for application to wetlands worldwide in light of the upcoming Surface Water and Ocean Topography (SWOT) mission

Quantum feedback with weak measurements

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schr\"odinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.Comment: 11 pages, TeX, replaced to incorporate suggestions of Asher Pere

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature