This chapter is about the minimum time evolution between two quantum states considering the dynamics obeying either time-invariant Hamiltonians or time-varying ones. Merit figures are defined to help quantum control designers to define optimization parameters. The expressions are derived from the time-energy uncertainty relations and a practical case is studied as an example.
Part of the book: Research Advances in Quantum Dynamics
Information entropy concept is the base for many measures used to evaluate the complexity of complex environmental systems. Its application has great potential to evaluate landscape organization and dynamics, especially if we consider that there is a direct relation between their patterns and processes: the spatial arrangement (structure) of units within a mosaic reflects on system functions. Consequently, changes on structure reflects on functions and vice versa. Here, we exemplify how three measures based on information entropy – LMC and SDL complexity measures and He/Hmax variability measure – could be applied to evaluating the degree of complexity of a landscape and its components by associating their heterogeneity with the diversity of information acquired from the remote sensors’ images. For this, we developed two scripts for a Geographical Information System (QGIS): (1) CompPlex HeROI, that compares the complexity of a landscape patch with others and also with their transition areas; and (2) CompPlex Janus, which analyzes how complexity varies in the landscape over space and time, generating landscape complexity maps. We also use LMC and SDL complexity measures and He/Hmax variability measure to evaluate complexity time series of environmental variables, as rain and temperature, which allow to evaluate how their variations along time and space affects landscape dynamics. Therefore, application of such metrics in multi-temporal studies of landscape dynamics provides indicators of landscape resilience and the degree of conservation or degradation of its different fragments due to anthropic impacts related to land uses.
Part of the book: Theory of Complexity