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Understanding energy transfer at the molecular scale is both essential for the design of novel molecular level devices and vital for uncovering the fundamental properties of non-equilibrium open quantum systems. In this thesis, we first establish the connection between molecular scale devices -- molecular electronics and phononics -- and open quantum system models. We then develop theoretical tools to study various properties of these models. We extend the standard master equation method to calculate the steady state thermal current and conductance coefficients. We then study the scaling laws of the thermal current with molecular chain size and energy, and apply this tool to investigate the onset of nonlinear thermal current - temperature characteristics, thermal rectification and negative differential conductance. Our master equation technique is valid in the ``on-resonance" regime, referring to the situation in which bath modes in resonance with the subsystem modes are thermally populated. In the opposite ``off-resonance" limit, we develop the Energy Transfer Born-Oppenheimer method to obtain the thermal current scaling without the need to solve for the subsystem dynamics. Finally, we develop a mapping scheme that allows the dynamics of a class of open quantum systems containing coupled subsystems to be treated by considering the separate dynamics in different subsections of the Hilbert space. We combine this mapping scheme with path integral numerical simulations to explore the rich phenomenon of entanglement dynamics within a dissipative two-qubit model. The formalisms developed in this thesis could be applied for the study of energy transfer in different realizations, including molecular electronic junctions, donor-acceptor molecules, artificial solid state qubits and cold-atom lattices.

Understanding energy transfer at the molecular scale is both essential for the design of novel molecular level devices and vital for uncovering the fundamental properties of non-equilibrium open quantum systems. In this thesis, we first establish the connection between molecular scale devices -- molecular electronics and phononics -- and open quantum system models. We then develop theoretical tools to study various properties of these models. We extend the standard master equation method to calculate the steady state thermal current and conductance coefficients. We then study the scaling laws of the thermal current with molecular chain size and energy, and apply this tool to investigate the onset of nonlinear thermal current - temperature characteristics, thermal rectification and negative differential conductance. Our master equation technique is valid in the ``on-resonance" regime, referring to the situation in which bath modes in resonance with the subsystem modes are thermally populated. In the opposite ``off-resonance" limit, we develop the Energy Transfer Born-Oppenheimer method to obtain the thermal current scaling without the need to solve for the subsystem dynamics. Finally, we develop a mapping scheme that allows the dynamics of a class of open quantum systems containing coupled subsystems to be treated by considering the separate dynamics in different subsections of the Hilbert space. We combine this mapping scheme with path integral numerical simulations to explore the rich phenomenon of entanglement dynamics within a dissipative two-qubit model. The formalisms developed in this thesis could be applied for the study of energy transfer in different realizations, including molecular electronic junctions, donor-acceptor molecules, artificial solid state qubits and cold-atom lattices.

[pt] Consideramos o oscilador harmônico com amortecimento aleatório em presença de ruído externo. Os ruídos, representando perturbações externas e internas, são modelados pelo processo de Ornstein-Uhlenbeck ou ruído branco e pelo processo dicotômico ou ruído branco, respectivamente. Usando técnicas de sistemas dinâmicos, analisamos o valor médio e a dispersão da posição e da velocidade do oscilador harmônico estocástico, apresentando resultados analíticos e numéricos. Em particular, obtemos expressões para a expansão de baixa-ordem em relação ao tempo de correlação da perturbação interna, no caso da atuação do ruído dicotômico. Finalmente, usando o modelo de oscilador harmônico com amortecimento aleatório como referência, investigamos a série intradiária de preços do mercado brasileiro. / [en] We consider the random damping harmonic oscillator in presence of external noise. The noises, representing external and internal perturbations, are modeled as an Ornstein-Uhlenbeck process or a white noise and as a dichotomous process or a white noise, respectively. Using dynamical systems tools, we analyze the expected value as well as the dispersion of the stochastic harmonic oscillator s position and velocity, presenting analytical and numerical results. In particular, we also provide expressions for the low-order expansion in the correlation time of the internal perturbation, in the case the dichotomous noise is at play. Using random damped harmonic oscillator model as a reference, we conclude by investigating the intra-day Brazilian stock price series.

Le changement structurel en agriculture suscite beaucoup d’intérêt de la part des économistes agricoles ainsi que des décideurs politiques. Pour prendre en compte l’hétérogénéité du comportement des agriculteurs, une approche par les modèles de mélange de chaînes de Markov est appliquée pour la première fois en économie agricole pour analyser ce processus. La performance de cette approche est d’abord testée en utilisant une forme simplifiée du modèle, puis sa forme générale est appliquée pour étudier l’impact de certaines mesures de politique agricole. Pour identifier les principaux canaux d’interdépendance entre exploitations voisines dans les processus du changement structurel, une approche de mélange non-Markovienne a été appliquée pour modéliser la survie et l’agrandissement des exploitations agricolesTrois principales conclusions découlent de cette thèse. Tout d’abord, la prise en compte de l’hétérogénéité dans les processus de transition des exploitations agricoles permet de mieux représenter le changement structurel et conduit à des prédictions plus précises de la distribution des exploitations, comparé aux modèles généralement utilisés jusqu’ici. Deuxièmement, l’impact des principaux facteurs du changement structurel dépend lui aussi des types non-observables d’exploitations mis en évidence. Enfin, le cadre du modèle de mélange permet également de révéler différents types de relations inobservées entre exploitations voisines qui contribuent au changement structurel observé à un niveau global ou régional. / Structural change in farming has long been the subject of considerable interest among agricultural economists and policy makers. To account for heterogeneity in farmers’ behaviours, a mixture Markov modelling framework is applied to analyse this process for the first time in agricultural economics. The performance of this approach is first investigated using a restrictive form of the model, and its general form is then applied to study the impact of some drivers of structural change, including agricultural policy measures. To identify channels through which interdependency between neighbouring farms arises in this process, the mixture modelling approach is applied to analyse both farm survival and farm growth. The main conclusions of this thesis are threefoldFirstly, accounting for the generally unobserved heterogeneity in the transition process of farms allows better representing structural change in farming and leads to more accurate predictions of farm-size distributions than the models usually used so far. Secondly, the impacts of the main drivers of structural change themselves depend on the specific unobservable farm types which are revealed by the model. Lastly, the mixture modelling approach enables identifying different unobserved relationships between neighbouring farms that contributes to the structural change observed at an aggregate or regional level.