Exact derivation of the Langevin and master equations for harmonic quantum Brownian motion

A many particle Hamiltonian, where the interaction term conserves the number of particles, is considered. A master equation for the populations of the different levels is derived in an exact way. It results in a local equation with time-dependent coefficients, which can be identified with the transition probabilities in the golden rule approximation. A reinterpretation of the model as a set of coupled harmonic oscillators enables one to obtain for one of them an exact local Langevin equation, with time-dependent coefficients.Comment: 7 pages, Revtex, to be published in Physica

Minimal irreversible quantum mechanics. The decay of unstable states

Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution that is used to study the time evolution of the reduced density operator. It is derived in a closed form, in the one-particle sector of the model. The irreversible behavior of the Brownian particle is described by a reduced density matrix.Comment: 39 pages, 2 figure

Impacts of Greenhouse and Local Gases Mitigation Options on Air Pollution in the Buenos Aires Metropolitan Area: Valuation of Human Health Effects

The objective of this work is to assess through the "avoided health cost method" what would be the economic benefits of undertaking greenhouse (and local) gases mitigation policies in the Buenos Aires Metropolitan Area. To do so, we have developed six steps: Mitigation Scenarios (which policies to undertake), Emissions Inventory according to those, an Ambient Air Pollution Model to calculate the physical impacts, Health Effects Estimation to assess the health consequences of reducing air pollution, and Economic Valuation of those health impacts. The mitigation measures valued have to do with the transportation sector (greater penetration of compressed natural gas, consumption improvements, and some mode substitution) and the energy sector (the introduction of new dams and the rational use of energy by reducing energy consumption in residential, commercial and public buildings). There are three scenarios: a Baseline or Business-as-Usual scenario, a scenario that considers GHG mitigation options for Argentina with impacts in terms of local pollution, and an Integrated scenario which in addition to GHG mitigation includes policies related to local air quality and rational use of energy programs. All scenarios were built up to the year 2012. Particulate matter is the pollutant whose impact is valued.

Impacts of greenhouse and local gases mitigation options on air pollution in the Buenos Aires Metropolitan Area: Valuation of human health effects

The objective of this work is to assess through the avoided health cost method what would be the economic benefits of undertaking greenhouse (and local) gases mitigation policies in the Buenos Aires Metropolitan Area. To do so, we have developed six steps: Mitigation Scenarios (which policies to undertake), Emissions Inventory according to those, an Ambient Air Pollution Model to calculate the physical impacts, Health Effects Estimation to assess the health consequences of reducing air pollution, and Economic Valuation of those health impacts. The mitigation measures valued have to do with the transportation sector (greater penetration of compressed natural gas, consumption improvements, and some mode substitution) and the energy sector (the introduction of new dams and the rational use of energy by reducing energy consumption in residential, commercial and public buildings). There are three scenarios: a Baseline or Business-as-Usual scenario, a scenario that considers GHG mitigation options for Argentina with impacts in terms of local pollution, and an Integrated scenario which in addition to GHG mitigation includes policies related to local air quality and rational use of energy programs. All scenarios were built up to the year 2012. Particulate matter is the pollutant whose impact is valued

Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation

The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism.Comment: 6 pages, RevTex, no figures, submitted to Phys. Lett.

Dissipation in quantum Brownian motion

En esta tesis discutimos el problema de la disipación y la evolución al equilibrio en el movimiento Browniano cuántico en el marco del formalismo de la segunda cuantización. Consideramos un modelo cuyo Hamiltoniano es bilineal en los operadores de creación y aniquilación, que puede reinterpretarse como el correspondiente a un conjunto de osciladores acoplados. Derivamos una ecuación exacta, completamente equivalente a las ecuaciones de Heisenberg, para los valores medios de los operadores número de ocupación, que tiene el aspecto de una ecuación maestra. En general, los coeficientes de dicha ecuación no son simétricos y dependen del tiempo, pero pueden ser interpretados como las probabilidades de transición por unidad de tiempo en la aproximación de segundo orden en la constante de acoplamiento. Los gráficos correspondientes a una solución numérica exacta permiten visualizar el rango de validez de dicha aproximación. Identificando uno de los osciladores como la partícula Browniana, lo que luego cobrará sentido mediante una elección adecuada de los parámetros del modelo, obtenemos una ecuación exacta, completamente equivalente a la ecuación de Heisenberg, para el operador posición. Dicha ecuación tiene la forma de la ecuación de Langevin pero nuevamente sus coeficientes dependen explícitamente del tiempo. Sin embargo, los mismos pueden identificarse con la frecuencia renormalizada y el factor de amortiguamiento luego de efectuada la aproximación de segundo orden. Para el caso particular en el que los osciladores que componen el reservorio no interactúan entre sí, resolvemos exactamente el modelo para un tipo de acoplamiento conocido como aproximación de onda rotante, diagonalizando el Hamiltoniano en el sector de un cuanto. Estudiamos primero el caso de un baño finito, que luego llevamos a un conjunto denso efecutando el límite continuo del modelo discreto. Para el modelo finito obtenemos un comportamiento “prácticamente” irreversible como consecuencia de las escalas temporales involucradas, en las cuales se manifiestan la presencia de fluctuaciones, el proceso de relajación y los períodos de recurrencia. En el caso continuo establecemos una relación entre el comportamiento termodinámico del conjunto de osciladores y la teoría del estado cuántico inestable. Relacionamos los efectos de bajas temperaturas para la población media del oscilador Browniano con el apartamiento de la ley de decaimiento puramente exponencial para largos tiempos (efecto Khalfin). Finalmente mostramos como un comportamiento de tipo estocástico puede ser asociado con la evolución asintótica del sistema, analizando las funciones de autocorrelación y obteniendo la relación de fluctuación-disipación.In this thesis we discuss the dissipation problem and the evolution towards equilibrium in quantum Brownian motion, in the framework of a second quantized formalism. We will consider a model in which the Hamiltonian is bilinear in the creation and annihilation operators so that it can be reinterpreted as a set of linearly coupled harmonic oscillators. We derive an exact equation, completely equivalent to the Heisenberg equations, for the mean values of the occupation number operators, which looks like a master equation. In general, the coefficients are non-symmetric and time-dependent. However, they can be interpreted as transition probabilities per unit time when the second order approximation in the coupling constant is taken. The figures corresponding to an exact solution allow us to visualize the range in which the second order solution fits the former. We identify one of the oscillators as a Brownian particle (it will later make sense through the adequate choice of parameters of the model) in order to obtain an exact equation for the position operator. Such an equation, equivalent to the Heisenberg one, has the form of the Langevin equation with time-dependent coefficients. These coefficients can be identified with the renormalized frequency and the damping factor once the second order approximation is made. For the particular case where the oscillators, which make up the reservoir, do not interact among themselves, we solve exactly the model for a kind of coupling known as rotating wave approximation, diagonalizing the Hamiltonian in the one-quantum sector. First, we study the case of a finite bath and then we put it into a dense set, taking the continuous limit of the discrete model. For the finite model we obtain “in practice” an irreversible behavior as a consequence of the time scales involved, in which we have fluctuations, a relaxation process, and recurrence periods. In the continuous case, we establish a relation between the thermodynamic behavior of the set of oscillators and the theory of an unstable quantum state. We relate the low-temperature effects for the mean population of the Brownian oscillator with the deviations of the purely exponential decay law for long times (Khalfin effect). Finally, we show how to associate a behavior of an stochastic type with the asymptotic evolution of the system, by analyzing the autocorrelation functions and by obtaining the fluctuation-dissipation relation.Fil:Gaioli, Fabián Horacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Bremsstrahlung atómico en colisiones ion-átomo (stripping)

Se estudia el Bremsstrahlung atómico (AB) producido en colisiones ion-átomo a altas energías (no relativistas) de colisión inclu-yendo efectos de retardación. Los estados mecánicos del sistema se describen con la aproximación eikonal simétrica y funciones de onda electrónicas de Hartree-Fock para el cálculo del factor de formac de cada átomo. Se presentan espectros en energía del fotón para colisiones de protones contra gases nobles, Ne, Ar, Kr y Xe. Se estudia la contribución de cada capa del átomo de estos espectros, correspondiendo la capa mas baja (1s) a la región de rayos -X duros, y las capas superiores a ener-gías del fotón menoresFil: Gaioli, Fabián Horacio. Universidad de Buenos Aires - CONICET. Instituto de Astronomía y Física del Espacio (IAFE). Buenos Aires. ArgentinaFil: Pacher, M.. Universidad de Buenos Aires - CONICET. Instituto de Astronomía y Física del Espacio (IAFE). Buenos Aires. ArgentinaFil: Miraglia, Jorge Esteban. Universidad de Buenos Aires - CONICET. Instituto de Astronomía y Física del Espacio (IAFE). Buenos Aires. Argentin