Factorizing the time evolution operator

There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator Exp{-itH/h} on an initial wave function. That is to say, because the hamiltonian operator generally is the sum of two operators, then it is a difficult task to apply the time evolution operator on an initial wave function f(x,0), for it implies to apply terms operators like (a+b)^n. A possible solution of this problem is to factorize the time evolution operator and then apply successively the individual exponential operator on the initial wave function. However, the exponential operator does not directly factorize, i. e. Exp{a+b} is not equal to Exp{a}Exp{b}. In this work we present a useful procedure for factorizing the time evolution operator when the argument of the exponential is a sum of two operators, which obey specific commutation relations. Then, we apply the exponential operator as an evolution operator for the case of elementary unidimensional potentials, like the particle subject to a constant force and the harmonic oscillator. Also, we argue about an apparent paradox concerning the time evolution operator and non-spreading wave packets addressed previously in the literature.Comment: 24 pages; added references; one figure change

Modelling carbon stock and carbon sequestration ecosystem services for policy design: a comprehensive approach using a dynamic vegetation model.

Ecosystem service (ES) models can only inform policy design adequately if they incorporate ecological processes. We used the Lund-Potsdam-Jena managed Land (LPJmL) model, to address following questions for Mexico, Bolivia and Brazilian Amazon: (i) How different are C stocks and C sequestration quantifications under standard (when soil and litter C and heterotrophic respiration are not considered) and comprehensive (including all C stock and heterotrophic respiration) approach? and (ii) How does the valuation of C stock and C sequestration differ in national payments for ES and global C funds or markets when comparing both approach? We found that up to 65% of C stocks have not been taken into account by neglecting to include C stored in soil and litter, resulting in gross underpayments (up to 500 times lower). Since emissions from heterotrophic respiration of organic material offset a large proportion of C gained through growth of living matter, we found that markets and decision-makers are inadvertently overestimating up to 100 times C sequestrated. New approaches for modelling C services relevant ecological process-based can help accounting for C in soil, litter and heterotrophic respiration and become important for the operationalization of agreements on climate change mitigation following the COP21 in 2015

Impacts of climate change on plant diseases – opinions and trends

There has been a remarkable scientific output on the topic of how climate change is likely to affect plant diseases in the coming decades. This review addresses the need for review of this burgeoning literature by summarizing opinions of previous reviews and trends in recent studies on the impacts of climate change on plant health. Sudden Oak Death is used as an introductory case study: Californian forests could become even more susceptible to this emerging plant disease, if spring precipitations will be accompanied by warmer temperatures, although climate shifts may also affect the current synchronicity between host cambium activity and pathogen colonization rate. A summary of observed and predicted climate changes, as well as of direct effects of climate change on pathosystems, is provided. Prediction and management of climate change effects on plant health are complicated by indirect effects and the interactions with global change drivers. Uncertainty in models of plant disease development under climate change calls for a diversity of management strategies, from more participatory approaches to interdisciplinary science. Involvement of stakeholders and scientists from outside plant pathology shows the importance of trade-offs, for example in the land-sharing vs. sparing debate. Further research is needed on climate change and plant health in mountain, boreal, Mediterranean and tropical regions, with multiple climate change factors and scenarios (including our responses to it, e.g. the assisted migration of plants), in relation to endophytes, viruses and mycorrhiza, using long-term and large-scale datasets and considering various plant disease control methods

Plant diversity enhances provision of ecosystem services: A new synthesis

Biodiversity is known to play a fundamental role in ecosystem functioning and thus may positively influence the provision of ecosystem services with benefits to society. There is a need for further understanding of how specific components of biodiversity are affecting service provision. In this context, terrestrial plants are a particularly important component of biodiversity and one for which a wealth of information on biodiversity–ecosystem functioning relationships is available. In this paper, we consider terrestrial plants as providers of ecosystem services and analyze whether manipulating plant diversity has an effect on the magnitude of ecosystem service provision using a meta-analysis of 197 effect sizes and a vote-counting analysis of 361 significance tests. The results of these analyses are compared with those of a previous meta-analysis that included a wide diversity of service providers.We produce a synthesis table to explicitly link plants as service providers to indicators of ecosystem properties and these to ecosystem services. By focusing on only plants, we found a clear positive effect of biodiversity on six out of eight services analyzed (provisioning of plant products, erosion control, invasion resistance, pest regulation, pathogen regulation and soil fertility regulation). When controlling for pseudoreplication (repeated records from single studies), we found that four of the six positive effects remained significant; only pest regulation and soil fertility showed non-significant effects. Further expanding our basis for inference with the vote-counting analysis corroborated these results, demonstrating that quantitative meta-analysis and vote-counting methods are both useful methods to synthesize biodiversity–ecosystem service studies. Notwithstanding the restricted number of identified services, our results point to the importance of maintaining plant diversity to ensure and increased provision of ecosystem services which benefit human well-being

Population dynamics of Mammillaria magnimamma Harworth. (Cactaceae) in a lava-field in central Mexico

One of the habitats occupied by Mammillaria magnimamma is a 2000-year old lava-field, in Mexico City. The great ecological interest on this lava-field and the little knowledge there is regarding cacti population ecology have compelled us to analyse the demography of this species to evaluate its present conservation status at this site. We studied two populations of this species within the lava-field: one in a disturbed site (i.e., recently burned) and another one in a well preserved site. For each population we built two size-based population projection matrices (1996/97 and 1997/98). Demographic data were gathered directly from observations of plant fates from one year to the next. Additionally, seed germination and seedling establishment experiments were carried out in the field to estimate fecundity values and seedling survival probabilities. The four matrices built were used to perform numerical analyses simulating yearly stochastic demographic variation to project the overall population's long-term behaviour under these changing conditions. Three of the four matrices showed lambda values slightly below unity. In these cases elasticity values were highest for matrix entries corresponding to plants remaining in their same category. The matrix that showed a lambda value above unity (well preserved site, 1997/98) had higher elasticity values for entries referring to seedling survival and growth. The numerical simulations of demographic stochasticity showed that the population appears to be growing at a slow rate. According to the simulation results, the variation in overall population size over time may be accounted for by yearly variation in seed germination and seedling survival. Population persistence probability might decrease significantly if fire frequency increases

Biodiversity loss and its impact on humanity

The most unique feature of Earth is the existence of life, and the most extraordinary feature of life is its diversity. Approximately 9 million types of plants, animals, protists and fungi inhabit the earth. So, too, do 7 billion people. Two decades ago, at the first Earth Summit, the vast majority of the world's nations declared that human actions were dismantling Earth's ecosystems, eliminating genes, 30 species, and biological traits at an alarming rate. This observation led to a daunting question: How will loss of biological diversity alter the functioning of ecosystems and their ability to provide society with the goods and services needed to prosper