Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2009/06/29). Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 2006. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 90-99). Also available for download via the World Wide Web; free to University of Oregon users.

Theories with a chemical potential are difficult to treat numerically because the action is complex and therefore methods based on a probability interpretation of the weight break down. This is an issue known as the sign problem. Complex Langevin dynamics was first proposed in the early 1980s and does not rely in a probability interpretation of the weight, so it can in principle l)e applied even where there is a severe sign problem. However, the combined problems of numerical instabilities and incorrect convergence impeded such early studies. In this work, the problem of runaway trajectories is cured l)y the use of a general adaptive stepsize procedure, which can be applied to both abelian and non-abelian theories. A study of the three-dimensional XY model at non-zero chemical potential follows, in which the problem of incorrect convergence is encountered. A formal justification of complex Langevin dynamics is given, from which a set of criteria are derived which can be used to test the validity of results. These ideas are applied to the SU(3) spin model, which is found to pass them all and therefore give correct results. An improved integration algorithm, which eliminates leading order step size corrections, is outlined and shown to give improved results.

Thesis (Ph.D.)--Tufts University, 2004. / Adviser: Larry H. Ford. Submitted to the Dept. of Physics. Includes bibliographical references (leaves 117-120). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

The generalized Langevin equation (GLE) has been used to describe the dynamics of particles in a stationary environment. To better understand the dynamics of polymerization, the GLE has been generalized to the irreversible generalized Langevin equation (iGLE) so as to incorporate the non-stationary response of the solvent. This non-stationary response is manifested in the friction kernel and the behavior of the projected (stochastic) force. A particular polymerizing system, such as living polymerization, is specified both through the parameters of the friction kernel and the potential of mean force (PMF). Equilibrium properties such as extent of polymerization have been obtained and are consistent with Flory-Huggin¡¯s theory. In addition, time-dependent non-equilibrium observables such as polymer length, the polymer length distribution, and polydispersity index (PDI) of living polymerization have been obtained. These have been compared to several experiments so as to validate the models, and to provide additional insight into the thermodynamic and kinetic properties of these systems. In addition to the iGLE, a stochastic model has been used to study the effect of nonequilibrium reactivity on living polymerization. This model can be used to determine whether the reaction is controlled by kinetics or diffusion. A combination of the iGLE and stochastic models may help us obtain more information about living polymerization.

Thesis (Ph. D.)--University of Chicago, Department of Chemistry, December 2002. / Includes bibliographical references. Also available on the Internet.

Thesis (M. Sc.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 111-114). Also available via the World Wide Web.

Avec les progrès de la technologie, il est désormais devenu possible de manipuler des faibles quantités d’objets nanométriques, voire des objets uniques. Observer une réaction chimique de quelques centaines de molécules sur des catalyseurs, étudier le travail exercé lors du déploiement d’un brin d’ADN unique ou mesurer la chaleur émise par un unique électron dans un circuit électrique constituent aujourd’hui des actes expérimentaux courants. Cependant, à cette échelle, le caractère aléatoire des processus physiques étudiés se fait plus fortement ressentir. Développer une théorie thermodynamique à ces échelles nécessite d'y inclure de manière exhaustive ces fluctuations.Ces préoccupations et les résultats expérimentaux et théoriques associés ont mené à l’émergence de ce que l’on appelle aujourd’hui la thermodynamique stochastique. Cette thèse se propose de développer une approche originale à la thermodynamique stochastique, basée sur une extension de l'hypothèse d'équilibre local aux variables fluctuantes d'un système. Cette théorie offre de nouvelles définitions des grandeurs thermodynamiques stochastiques, dont l'évolution est donnée par des équations différentielles stochastiques (EDS).Nous avons choisi d'étudier cette théorie à travers des modèles simplifiés de phénomènes physiques variés; transport (diffusif) de chaleur ou de masse, transport couplé (comme la thermodiffusion), ainsi que des modèles de réactions chimiques linéaires et non-linéaires. A travers ces exemples, nous avons proposé des versions stochastiques de plusieurs grandeurs thermodynamiques d'intérêt. Une large part de cette thèse est dévolue à l'entropie et aux différents termes apparaissant dans son bilan (flux d'entropie, production d'entropie ou dissipation). D'autres exemples incluent l'énergie libre d'Helmholtz, la production d'entropie d'excès, ou encore les efficacités thermodynamiques dans le transport couplé.A l'aide de cette théorie, nous avons étudié les propriétés statistiques de ces différentes grandeurs, et plus particulièrement l'effet des contraintes thermodynamiques ainsi que les propriétés cinétiques du modèle sur celles-là. Dans un premier temps, nous montrons comment l'état thermodynamique d'un système (à l' équilibre ou hors d'équilibre) contraint la forme de la distribution de la production d'entropie. Au-delà de la production d'entropie, cette contrainte apparaît également pour d'autres quantités, comme l'énergie libre d'Helmholtz ou la production d'entropie d'excès. Nous montrons ensuite comment des paramètres de contrôle extérieurs peuvent induire des bimodalités dans les distributions d'efficacités stochastiques.Les non-linéarités de la cinétique peuvent également se répercuter sur la thermodynamique stochastique. En utilisant un modèle non-linéaire de réaction chimique, le modèle de Schlögl, nous avons calculé la dissipation moyenne, non-nulle, engendrée par les fluctuations du système. Les non-linéarités offrent aussi la possibilité de produire des bifurcations dans le système. Les différentes propriétés statistiques (moments et distributions) de la production d'entropie ont été étudiées à différents points avant, pendant et après la bifurcation dans le modèle de Schlögl.Ces nombreuses propriétés ont été étudiées via des développements analytiques supportés par des simulations numériques des EDS du système. Nous avons ainsi pu montrer la fine connexion existant entre les équations cinétiques du système, les contraintes thermodynamiques et les propriétés statistiques des fluctuations de différentes grandeurs thermodynamiques stochastiques. / Over the last decades, nanotechnology has experienced great steps forwards, opening new ways to manipulate micro- and nanosystems. These advances motivated the development of a thermodynamic theory for such systems, taking fully into account the unavoidable fluctuations appearing at that scale. This ultimately leads to an ensemble of experimental and theoretical results forming the emergent field of stochastic thermodynamics. In this thesis, we propose an original theoretical approach to stochastic thermodynamics, based on the extension of the local equilibrium hypothesis (LEH) to fluctuating variables in small systems. The approach provides new definitions of stochastic thermodynamic quantities, whose evolution is given by stochastic differential equations (SDEs).We applied this new formalism to a diverse range of systems: heat or mass diffusive transport, coupled transport phenomena (thermodiffusion), and linear or non-linear chemical systems. In each model, we used our theory to define key stochastic thermodynamic quantities. A great emphasis has been put on entropy and the different contributions to its evolution (entropy flux and entropy production) throughout this thesis. Other examples include also the stochastic Helmholtz energy, stochastic excess entropy production and stochastic efficiencies in coupled transport. We investigated how the statistical properties of these quantities are affected by external thermodynamic constraints and by the kinetics of the system. We first studied how the thermodynamic state of the system (equilibrium \textit{vs.} non-equilibrium) strongly impacts the distribution of entropy production. We then extended those findings to other related quantities, such as the Helmholtz free energy and excess entropy production. We also analysed how some external control parameters could lead to bimodality in stochastic efficiencies distributions.In addition, non-linearities affect stochastic thermodynamics quantities in different ways. Using the example of the Schlögl chemical model, we computed the average dissipation of the fluctuations in a non-linear system. Such systems can also undergo a bifurcation, and we studied how the moments and the distribution of entropy production change while crossing the critical point.All these properties were investigated with theoretical analyses and supported by numerical simulations of the SDEs describing the system. It allows us to show that properties of the evolution equations and external constraints could strongly reflect in the statistical properties of stochastic thermodynamic quantities. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Este trabalho apresenta uma contribuição ao estudo das flutuações quânticas dos feixes sonda e de bombeio na condição de transparência induzida por laser. Com esse estudo conseguimos observar nas flutuações dos campos uma manifestação do caráter coerente da interação dos átomos com os feixes. Para alcançar nosso objetivo, derivamos a teoria do fenômeno da transparência induzida tratando ambos feixes dentro do formalismo quântico. Com tal formulação, encontramos que a condição de transparência induzida corresponde a um estado de equilíbrio dinâmico do sistema átomo - campo de bombeio - campo sonda onde, os átomos redistribuem os fótons entre os campos, correlacionando os mesmos e alterando, ao mesmo tempo, as propriedades estatísticas desses feixes. Utilizando dois critérios diferentes, mostrando que a correlação entre os feixes sonda e de bombeio é de natureza quântica, o que possibilita a aplicação desse sistema, por exemplo, na informação e computação quânticas. Os resultados experimentais obtidos confirmaram as previsões teóricas em relação às flutuações quânticas dos campos, e a existência de uma correlação entre eles. Trata-se da primeira investigação experimental de propriedades estatísticas dos campos em transparência induzida. A correlação de intensidade medida é o primeiro passo para a observação de emaranhamento entre feixes sonda e de bombeio na condiçào de transparência induzida. / In this work we presente a contribution to the study of quantum fluctuations of pump and probe filds in the Electromagnetically Induced Transparency (EIT) condition. We observed in the fields fluctuations evidence of the coherent character of the interaction between the atoms and the fields. To reach our purpose, the fields were treated quantum-mechanically in deriving the theory of the EIT phenomenon. Using this formulation, we concluded that the EIT condition corresponds to a state of dynamical equilibrium of the system atom pump field probe field, where the atoms redistribute the photons between both fields, correlating them and, at the same time, affecting their statistical properties. By means of two different criteria we showed that such a correlation is of quantum nature, making possible the application of this system in, for example, quantum information and quantum computation. The theoretical predictions were corroborated by our experimental results regarding the quantum fluctuations and the existence of a correlation between the pump and probe fields. This is the first experiment to investigate statistical properties of the fields in EIT. The intensity correlation measured is the first step towards the observation of entanglement between the fields.

Este trabalho apresenta uma contribuição ao estudo das flutuações quânticas dos feixes sonda e de bombeio na condição de transparência induzida por laser. Com esse estudo conseguimos observar nas flutuações dos campos uma manifestação do caráter coerente da interação dos átomos com os feixes. Para alcançar nosso objetivo, derivamos a teoria do fenômeno da transparência induzida tratando ambos feixes dentro do formalismo quântico. Com tal formulação, encontramos que a condição de transparência induzida corresponde a um estado de equilíbrio dinâmico do sistema átomo - campo de bombeio - campo sonda onde, os átomos redistribuem os fótons entre os campos, correlacionando os mesmos e alterando, ao mesmo tempo, as propriedades estatísticas desses feixes. Utilizando dois critérios diferentes, mostrando que a correlação entre os feixes sonda e de bombeio é de natureza quântica, o que possibilita a aplicação desse sistema, por exemplo, na informação e computação quânticas. Os resultados experimentais obtidos confirmaram as previsões teóricas em relação às flutuações quânticas dos campos, e a existência de uma correlação entre eles. Trata-se da primeira investigação experimental de propriedades estatísticas dos campos em transparência induzida. A correlação de intensidade medida é o primeiro passo para a observação de emaranhamento entre feixes sonda e de bombeio na condiçào de transparência induzida. / In this work we presente a contribution to the study of quantum fluctuations of pump and probe filds in the Electromagnetically Induced Transparency (EIT) condition. We observed in the fields fluctuations evidence of the coherent character of the interaction between the atoms and the fields. To reach our purpose, the fields were treated quantum-mechanically in deriving the theory of the EIT phenomenon. Using this formulation, we concluded that the EIT condition corresponds to a state of dynamical equilibrium of the system atom pump field probe field, where the atoms redistribute the photons between both fields, correlating them and, at the same time, affecting their statistical properties. By means of two different criteria we showed that such a correlation is of quantum nature, making possible the application of this system in, for example, quantum information and quantum computation. The theoretical predictions were corroborated by our experimental results regarding the quantum fluctuations and the existence of a correlation between the pump and probe fields. This is the first experiment to investigate statistical properties of the fields in EIT. The intensity correlation measured is the first step towards the observation of entanglement between the fields.