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

Analysis of Latin America's Corporations as a Rational Response to the Economic Environment Present in the Region - Part I

This is the first of a series of working papers analyzing the basic characteristics of the economic environment in which Latin American Corporations live and the optimal design of incentive programs compatible with such environment. By economic environment we mean the technology that the organizations have access to, the legal framework present in these countries, the macro-economical characteristics, the markets in which they operate (competitors, monopolies, customers, reliability of suppliers, etc.), the nature of their capital markets and in general of the sources of financing for their companies, etc. We could broadly say that any key feature of the economy that has the potential to influence the way business is run in Latin America is part of its economic environment. The underlying unifying idea in this series is that, unless we have clear evidence to the contrary, corporate practices observed in Latin American firms are rational responses to the environment in which they operate. They are a sort of Darwinian adaptation to such environment. Therefore, much like in biological systems, these characteristics of corporations should be considered optimal in a relative sense. That is, in order to survive in the market, the observed corporate practices should be better that the ones from the competition for the given economic environment. This observation suggests that improvements to the observed practices are indeed possible. In fact, the present series of working papers is in part structured to explore possible improvements. These improvements, however, are not likely to be the simple copy of corporate practices that evolved as an optimal response to the environment of the developed world. In this first work we present some important empirical characteristics of the Latin American Corporations and the first key aspect of the economic environment prevailing in this region: the legal framework. We show how many of the empirical characteristics presented can be see as optimal responses to the legal framework.

Quantum-classical transition and quantum activation of ratchet currents in the parameter space

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed {based on quantum, semiclassical and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.Comment: 6 pages, 3 figure

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