Non-Abelian generalization of off-diagonal geometric phases

If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.Comment: Additional material, journal reference adde

Nodal free geometric phases: Concept and application to geometric quantum computation

Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well-defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates.Comment: Small typo corrected, journal reference adde

Monitoring Bear Creek nitrate-N flux and quantifying the impacts of concentrated flow on grass filters and riparian forest buffers

Hydrology and climate are critical factors controlling NO3--N flux. In order to understand the dynamics of stream water nitrate-N flux, a small agricultural 6900 ha watershed was monitored throughout the year, along a spatial gradient, and in response to specific storm events. Seven sampling locations along the Bear Creek watershed were monitored for nitrate-N concentration from January 2006 through June 2008. Two sampling locations were located along each of the two main tributaries, with three others distributed along the main channel of Bear Creek. Grab samples were taken on an approximately bi-weekly basis, with increased sampling intensity during the spring. Event based samples were taken at a site mid-watershed next to an instrumented weir in order to assess the NO3--N concentration response during a storm event. A stage-discharge rating curve was developed in order to quantify NO3--N flux. Nitrate-N concentrations were relatively high during the study period and would have exceeded the EPA\u27s maximum contaminant level (MCL) of 10 mg L-1 for drinking water at a majority of the sites throughout the year. The headwater of West Bear Creek (a tributary of Bear Creek) was over the MCL 89% of the time, which was the highest for any of the seven sites. The furthest downstream site, was over the MCL the least amount of time of any site, but was still higher than 10 mg L-1 47% of the time. There was a general trend of decreasing NO3--N concentration from the headwaters to the outlet of Bear Creek. A spatial gradient was more profound during the spring and fall months, which was attributed to the effects of subsurface drainage. Spring consistently had the highest NO3--N concentrations of all the seasons for each of the sampling sites. NO3--N concentrations were the lowest during the summer months when subsurface drainage was limited and conditions are ideal for in-stream processing. Event samples showed that there was a lag between peak NO3--N concentrations and the peak in the hydrograph. Sediment delivery models based on plot studies have been developed to predict watershed sediment yield. The modified universal soil loss equation (MUSLE) is a modification made to the original universal soil loss equation (USLE) in order to predict sediment yield applicable to individual storm events. A major limitation to the MUSLE is that it does not take into account the effects of concentrated flow leading to ephemeral gully (EG) erosion. The formation of an EG provides a direct link from the uplands to the streams which increases sediment delivered from sheet and rill flow by reducing the surface roughness. Two study sites were located on the Southern Iowa Drift Plain ecoregion to quantify the amount of sediment loss in small catchments with ephemeral gullies. The observed amount of sediment loss was then compared to the MUSLE predicted amount of sediment loss for each individual storm event. Monitoring began in April of 2007 and continued through mid-October 2007 at Dor 1 located within the Lake Darling Watershed. A total of 12 rainfall generated runoff events were monitored. Monitoring began in June of 2007 and continued through mid-October 2007 at Orr 3 located within the Lake Rathbun Watershed. A total of 7 rainfall generated runoff events were monitored. The MUSLE under-predicted sediment yield for all the events occurring at Dor 1, and all but 2 events at Orr 3. The disparity among the predicted and observed sediment yields increased with storm size. A general weakness with the MUSLE is that rainfall events are based on a 24 hour rainfall depth and not intensity which is a dominant factor in how much rainfall will result in runoff. Riparian buffers have been accepted as an edge of field best management practice to improve surface water quality by reducing the sediment and nutrients transported in surface runoff. Many plot scale studies under uniform flow conditions have assessed the effectiveness of various riparian buffers at mitigating the effects of concentrated flow. The purpose of this study was to examine, at the hillslope scale and natural rainfall conditions, the impact that concentrated flow has on edge of field practices. The study was conducted on two private farms located in the Lake Darling and Lake Rathbun watersheds located in the Southern Iowa Drift Plain physiographic region. The three sites located in the Lake Rathbun watershed consisted of one control, located at the crop field/buffer interface, and two sites with a 15.2 m wide grass filter treatment. The three sites located in the Lake Darling watershed consisted of one control, located at the crop field/buffer interface, and two sites with a 15.2 m wide natural riparian forest buffer. Monitoring at the Lake Darling watershed began in April of 2007 and lasted until late October 2007. Monitoring at the Lake Rathbun watershed began in June of 2007 and lasted until late October 2007. There were seven natural rain events monitored at the Lake Rathbun watershed, and twelve natural rain events monitored at the Lake Darling watershed. Potential pollutants monitored were total sediment, nitrate-N, ortho-P, total-N, and total-P. The grass filter strips reduced pollutant load relative to the control at the field edge in smaller rain events. However, one of the grass filter sites was not effective at reducing pollutant load during larger events. There appears to be a threshold that is dependent upon the amount and intensity of rain, and the contributing area to effective buffer ratio. The riparian forests were less predictable for which storm events they can be considered effective. This is because there is little to no resistance to concentrated flow within the riparian forest, as concentrated flow forms a classic gully within the buffer