We study Nielsen's circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. In a multiple quench scenario, it is shown that the complexity shows remarkably different behaviour compared to the other information theoretic measures, such as the entanglement entropy. In particular, after two successive quenches, when the frequency returns to its initial value, there is a lower limit of complexity, which cannot be made to approach zero. Further, we show that by applying a large number of successive quenches, the complexity of the time evolved state can be increased to a high value, which is not possible by applying a single quench. This model also exhibits the interesting phenomenon of crossover of complexities between two successive quenches performed at different times.

Mapping the spatial variability of soil fertility by employing Geographic Information System (GIS) provides an elicit information for current and future use. To know the fertility status of the research farm, sixty four surface soil samples were collected to evaluate the spatial distribution of nutrients. The soils of the study area were sandy loam to sandy clay loam in texture and slightly alkaline to moderately alkaline (7.40-8.20) in reaction and non-saline (0.19-0.86 dS m-1) in nature. Organic carbon was recorded high to low and varied from 0.22-0.82 percent. The soils of the research farm were low in available nitrogen (112-161 kg ha-1), high to medium in available phosphorus  (10-22 kg ha-1) and high to medium in available potassium (170-538 kg ha-1). The diethylenetriaminepentaacetic acid (DTPA) extractable micronutrients (Zinc, Copper and Manganese) status was found moderate to sufficient except Iron, which was found in moderate to deficient category (4.30-12.56 mg kg-1). Available nitrogen, phosphorus and potassium showed high variation as indicated by coefficient of variance values (142.58, 16.63 and 10380.04, respectively). Organic carbon (0.02), zinc (0.07), iron (6.28), copper (0.19) and manganese (2.25) showed small variation as indicated by low variance. Organic carbon was significantly correlated with nitrogen and potassium suggesting synergistic effect. All the soils were low in available nitrogen that’s why application of nitrogenous fertilizers is necessary to ameliorate nutrient deficiency and enhance crop production. The spatial variability maps of nutrients provide an insight of fertility status of the area and this will help in easy monitoring of precision fertilizer management.

We study Nielsen’s circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. This simple system is amenable to analytical computations and yet offers considerable insight into the dynamics of quantum information. For a single quench scenario, we highlight some important differences between our results that explicitly use the wavefunction, as compared to the recently proposed covariance matrix method and point out the consequences. In a multiple quench scenario, the complexity shows remarkably different behaviour compared to the other information theoretic measures, such as the entanglement entropy and the out of time ordered correlator. In particular, the latter is known to show signs of chaos in this integrable system, but our results indicate the contrary. We further show the presence of a ‘residual complexity,’ i.e. after two successive quenches, when the frequency returns to its initial value, the complexity has a non-zero lower limit. Further, applying a large number of successive quenches, the complexity of the time evolved state can be increased to a high value, which is not possible by applying a single quench. Finally, we show that this simplistic model exhibits the interesting phenomenon of ‘complexity crossover’ between two successive quenches performed at different times.

We study information theoretic quantities in models with three and four spin interactions. These models show distinctive characteristics compared to their nearest neighbour (NN) counterparts. Here, we quantify these in terms of the Nielsen complexity (NC) in static and quench scenarios, the Fubini–Study complexity (FSC), and the entanglement entropy (EE). The models that we study have a rich phase structure, and we show how the difference in the nature of phase transitions in these, compared to ones with NN interactions, result in different behaviour of information theoretic quantities, from ones known in the literature. For example, the derivative of the NC does not diverge but shows a discontinuity near continuous phase transitions, and the FSC may be regular and continuous across such transitions. We also study multiple quench scenarios in these models and contrast these with quenches in the transverse XY model. The EE shows a novel discontinuity both at first and second order quantum phase transitions.

Assessment of different soil attributes provides an insight into the soil-related constraints and potentials for sustainable agricultural planning. In the present investigation, 37 tea gardens were selected at random from tea growing areas of Himachal Pradesh during 2017-19 to evaluate the status of different soil attributes in surface (0-0.30 m) and sub-surface (0.30-0.60 m) soils. All the collected soil samples were analyzed for particle density, porosity, water stable aggregates, electrical conductivity, exchangeable Ca and Mg and microbial count as per standard procedures. The particle density, porosity and water stable aggregates in soils of tea gardens varied from 2.58 to 2.64 Mg m3, 39 to 57% and 26 to 58%. The electrical conductivity, exchangeable Ca and Mg were in the range of 85 to 210 dS m-1, 1.2 to 4.0 cmol (p+) kg-1 and 0.6 to 2.3 cmol (p+) kg-1 with a mean value of 134±35.8, 2.7±0.8 and 1.4±0.4, respectively. With regards to microbial count, the bacterial population ranged from 49 to 71 x 106 CFU, fungal population ranged from 36 to 69 x 104 CFU and actinomycetes population varied from 31 to 58 x 104 CFU.