Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Effect of irrigation amounts applied with subsurface drip irrigation on corn evapotranspiration, yield, water use efficiency, and dry matter production in a semiarid climate

Quantifying the local crop response to irrigation is important for establishing adequate irrigation management strategies. This study evaluated the effect of irrigation applied with subsurface drip irrigation on field corn (Zea mays L.) evapotranspiration (ETc), yield, water use efficiencies (WUE = yield/ETc, and IWUE = yield/irrigation), and dry matter production in the semiarid climate of west central Nebraska. Eight treatments were imposed with irrigation amounts ranging from 53 to 356 mm in 2005 and from 22 to 226 mm in 2006. A soil water balance approach (based on FAO-56) was used to estimate daily soil water and ETc. Treatments resulted in seasonal ETc of 580-663 mm and 466-656 mm in 2005 and 2006, respectively. Yields among treatments differed by as much as 22% in 2005 and 52% in 2006. In both seasons, irrigation significantly affected yields, which increased with irrigation up to a point where irrigation became excessive. Distinct relationships were obtained each season. Yields increased linearly with seasonal ETc (R 2 = 0.89) and ETc/ETp (R 2 = 0.87) (ETp = ETc with no water stress). The yield response factor (ky), which indicates the relative reduction in yield to relative reduction in ETc, averaged 1.58 over the two seasons. WUE increased non-linearly with seasonal ETc and with yield. WUE was more sensitive to irrigation during the drier 2006 season, compared with 2005. Both seasons, IWUE decreased sharply with irrigation. Irrigation significantly affected dry matter production and partitioning into the different plant components (grain, cob, and stover). On average, the grain accounted for the majority of the above-ground plant dry mass (≈59%), followed by the stover (≈33%) and the cob (≈8%). The dry mass of the plant and that of each plant component tended to increase with seasonal ETc. The good relationships obtained in the study between crop performance indicators and seasonal ETc demonstrate that accurate estimates of ETc on a daily and seasonal basis can be valuable for making tactical in-season irrigation management decisions and for strategic irrigation planning and management.