We obtain the ground-state energy level and associated geometric phase in the Dicke model analytically by means of the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field is derived with the time-dependent unitary transformation. It is shown that the quantum phase transition characterized by the nonanalyticity of the geometric phase is remarkably of the first order. We also investigate the scaling behavior of the geometric phase at the critical point, which can be measured in a practical experiment to detect the quantum phase transition.

To determine the effect of different types of manure without or with inorganic P fertiliser on soil P pools and P uptake by plants, two experiments were conducted. In experiment 1, sheep or cow manure (P concentration sheep > cow manure) were added at 1.0, 2.0 and 3.5 g kg −1 , additional treatments were unamended control and soil with inorganic N and P equivalent to 3.5 g kg −1 cow manure. After 4 weeks compared to the unamended control, P pools were similar with cow manure P pools. But with sheep manure, citric acid P, HCl P and resin P with sheep manure were higher and increased with addition rates. Shoot P uptake with 3.5 g kg −1 manure was higher than the unamended control but lower than with inorganic fertiliser. In experiment 2, the amount of P and N added was as in 3.5 g kg −1 cow manure applied either as manure (C) and inorganic P (F) alone and combinations (75C25F, 50C50F, 25C75F). After 4 weeks of wheat growth, citric acid P and resin P increased with the proportion of inorganic P. Shoot P uptake in manure/fertiliser treatments was higher than in manure alone and unamended control but lower than with inorganic fertilisers alone.

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Compost application can increase plant nutrient availability. But the effect of compost on nutrient availability may depend on a number of factors. In this study, the effect of application method (mulch layer or mixed into the soil) and combination with inorganic fertiliser on soil P pools and available N was investigated. Soil was filled in microcosm with six treatments, including control, vermicompost layer with or without fertilisers (CL, CL/F), bulk soil mixed with inorganic fertiliser alone (F), vermicompost alone (CM) and both of inorganic fertiliser and vermicompost (CM/F). The microcosms were incubated in the dark for 3 weeks. Citrate P, HCl P and resin P were the highest in F, but MBP was higher in CM and CM/F. Citrate P and HCl P were about three-and six-fold higher in CM and CM/F than in CL and CL/F. Available N was the highest in CL/F and 20% higher in CL than in CM. Vermicompost mixed into soil slightly increased soil nutrient availability compared to unamended soil but had little effect when placed on the soil surface. Vermicompost mixed into soil with inorganic N and P could be used to minimise loss of N and P after inorganic fertiliser addition and thereby provide a longer-lasting nutrient supply for plants.