Higher Dimensional SUSY Quantum Mechanics

Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic supersymmetry algebra.Comment: 8 pages, Late

Sleeping Beauty on Monty Hall

Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful

Recurrent deficit irrigation and fruit harvest affect tree water relations and fruitlet growth in ‘Valencia’ orange

Background. Partial rootzone drying is an irrigation strategy known for increasing water use efficiency without significantly affecting tree water status. ‘Valencia’ oranges have a very long development period and nearly mature fruit and new fruitlets may be present at the same time on the tree, competing for water and assimilates. Objectives. The present study investigates the effect of recurrent deficit irrigation and fruit harvest on tree water status and fruitlet growth of ‘Valencia’ orange. Methods. Forty-eight adult trees were exposed to three irrigation treatments for seven years (2007-2013): irrigation with 100% of ETc (CI), continuous deficit irrigation (DI, 50% of CI) and partial root-zone drying (PRD, 50% of CI on alternated sides of the root-zone). In spring 2014, stem water potential (Ψstem) and continuous measurements of sap flow and fruitlet growth were recorded before (May) and after (June) the harvest of mature fruit. Results. No differences in Ψstem were found among irrigation treatments, while Ψstem was lower in June than in May at midday. In both May and June, sap flow density (not sap flow per tree) was higher in DI than in CI and PRD trees suggesting more efficient water uptake/transport in the former. In May, DI and PRD fruit showed lower daily relative growth rate (RGR) than CI fruit due to a possible shortage of carbon and nutrients. After removing mature fruits, differences among irrigation treatments were canceled. Sap flow was directly related to fruit RGR at low sap flow rates, but inversely related to RGR at high sap flow rates. Conclusions. Our data show that the presence of maturing fruit does not impact the water status of ‘Valencia’ trees, while it may transiently limit fruitlet growth (by source limitation) in deficit irrigated trees

On the Divergence of Perturbation Theory: Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism

Diamond electro-optomechanical resonators integrated in nanophotonic circuits

Diamond integrated photonic devices are promising candidates for emerging applications in nanophotonics and quantum optics. Here we demonstrate active modulation of diamond nanophotonic circuits by exploiting mechanical degrees of freedom in free-standing diamond electro-optomechanical resonators. We obtain high quality factors up to 9600, allowing us to read out the driven nanomechanical response with integrated optical interferometers with high sensitivity. We are able to excite higher order mechanical modes up to 115 MHz and observe the nanomechanical response also under ambient conditions.Comment: 15 pages, 4 figure