Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities

An optical semiconductor micrcavity consisting of two distributed bragg reflectors (DBRs) and a quantum well between, can be modeled using a transfer matrix approach, which solves the propagation through the DBR mirrors and the cavity segment in between the mirrors. Such an approach is easy to use if the interband polarization of the quantum well PQW is a given function of time or frequency, which includes the case of linear optical response, where PQW is given in terms of the linear susceptibility and the electric field at the position of the quantum well, EQW. In many cases of practical interest, the quantum well response is a nonlinear function of EQW, in which case the transfer matrix approach becomes impractical. In such cases, a time differential equation for PQW, which is of the form i¯ h dPQW(t) dt= F[PQW(t),EQW(t)] where F is a nonlinear function of PQW, is solved via time-stepping from earlier to later times. To obtain the electric field EQW needed as input to the PQW solution, a commonly used phenomenological approach utilizes the single-mode equation i¯ h dEQW(t) dt= hωcEQW(t)−ΩPQW(t) + S(t) with the source term S(t) being defined by S(t) = ¯ htcE+ inp(t) and corresponding constants that are defined in section 5 of this thesis. However, apart from containing phenomenological parameters, the simple source term entering the single-mode equation does not account for propagation, retardation, and pulse filtering effects of the incident light field traversing the DBR mirror. In this thesis, an alternate approach is presented along with evidence of its validity using a bounded convolution integral instead. The integral is used to determine the electric field as a function of time and therefore can be used to determine the time derivative of the polarization. The integral being EQW(t) =Z t −∞ [A(t−t0)E+ inp(t0) + B(t−t0)PQW(t0)]dt0. We show in the final sections that it is adequate to use this bounded integral to resolve pulses in the time domain. Evidence of that is done using a gaussian pulse and linear response. This method could then be used in conjunction with a time stepping algorithm to resolve nonlinear responses

Los fundamentos matemáticos: teoría de las finanzas

Para incluir modelos relativos a las decisiones financieras en condiciones de incertidumbre, necesitamos extender la teoría básica incorporando los entes adecuados.Un primer paso en este proceso es una aproximación a la Teoría de laUtilidad. En ella, los objetos básicos son las loterías que representan situaciones de elección en condiciones de riesgo. Se presenta un conjunto de axiomas para una teoría de la elección en condiciones de riesgo. Los resultados de la teoría se pueden entender fácilmente a partir de su interpretación geométrica.Las aplicaciones a las finanzas requieren de una generalización de esateoría y de unos supuestos adicionales. Aquellas se presentan de dosmaneras: intuitiva y semi-formal.Se presenta un modelo sencillo pero poderoso que incluye las principales características de otros modelos más avanzados.Riesgo, incertidumbre, interpretación geometrica, finanzas,

Un curso rápido de cálculo estocástico para aplicaciones a modelos económicos (primera parte)

La importancia de las ecuaciones diferenciales estocásticas y, en general elcálculo estocástico, en las ciencias económicas no ha sido resaltada suficientemente en nuestro medio. A diferencia de las aplicaciones financieras, que han sido ampliamente difundidas, las aplicaciones de otras áreas de la economía son prácticamente desconocidas en nuestro entorno académico. Este curso elemental es una invitación a conformar grupos interdisciplinarios de estudiosos de la matemática y las ciencias económicas para abordar tales aplicaciones.Palabras clave: ecuaciones diferenciales estocásticas, procesosestocásticos, modelo neoclásico de crecimiento, producción factores capita y trabajo.

Un curso rápido de cálculo estocástico para aplicaciones a modelos económicos (segunda parte)

El curso continúa. Acá presentamos la fórmula de Ito extendida a n dimensiones y el concepto de Ecuación Diferencial Estocástica, en forma Matricial-vectorial. Se resuelve el caso lineal como caso especial y se aplica a la solución del modelo de Solow. Se añade un apéndice sobre la teoríade los sistemas de ecuaciones lineales con el fin de ayudar a entender la última parteEcuaciones diferenciales determinísticas, fórmula de Ito, modelo de Solow, modelos de dinámicaeconómica.

The food system in Latin America: Between dispossession and non-capitalist provision

This thesis examines the system of food provision in Latin America in the context of hunger and environmental crises which have been brought about through capital accumulation. In analysing this crisis, I focus on the role of capital represented by agribusiness and the Latin American campesino. I ground my conceptual understanding of the food system through a Marxist approach that considers critical knowledge and practice specific to Latin America. My conceptual framework derives from a critical understanding of Harvey’s concept of accumulation by dispossession, and the mode of production approach. Accumulation by dispossession accounts for a dual character of capital accumulation prevalent in the food system. The first characteristic consists of the systemic features of ‘extra economic’ surplus extraction and the second characteristic considers the resistance to capital penetration and experiences of non-capitalist food provision. The mode of production approach links the systemic features of dispossession to the coexistence of capitalist and non-capitalist modes of production in capitalism. The concept of modes of production is combined with the metabolic rift perspective to account for the interaction of human and extra-human nature. This thesis demonstrates that the food system is a contested space between agribusiness and the campesino. I analyse how this contested dynamic has destructive consequences for human nature through the persistence of hunger, and on extra-human nature through the deepening of the metabolic rift. The thesis establishes that capital accumulation is destroying the social and natural foundation of production and reproduction. In this context, I argue that the campesino economy encompasses alternatives to the capital dominated food system, which has the potential to simultaneously feed the population and mitigate the degradation of nature