Théorie de la perturbation (mécanique quantique)

En mécanique quantique, la théorie de la perturbation, ou théorie des perturbations, est un ensemble de schémas d'approximations liée à une perturbation mathématique utilisée pour décrire un système quantique complexe de façon simplifiée. L'idée est de partir d'un système simple et d'appliquer graduellement un hamiltonien « perturbant » qui représente un écart léger par rapport à l'équilibre du système (perturbation). Si la perturbation n'est pas trop importante, les différentes quantités physiques associées avec le système perturbé (comme ses niveaux d'énergie et états propres) seront générés de manière continue à partir de ceux du système simple. On peut donc étudier le premier à partir des connaissances sur le dernier. Description Si le système étudié peut être décrit par l'opérateur hamiltonien \mathcal{H}, la théorie de la perturbation s'applique lorsqu'il peut s'écrire sous la forme : : \mathcal{H} = H_0 + W

où H_0 est l'hamil

Apertureless SNOM

Rubén Esteban Llorente

This thesis studies apertureless Scanning Near Field Optical Microscopy, a technique that uses the apex of a very sharp tip to obtain local optical information with lateral resolution much beyond the diffraction limit. Both theoretical and experimental results are discussed. The theoretical work is a significant advance towards the quantitative convergence of experiments and theoretical predictions, and should be useful in aiding the interpretation of measured images. Extended tips and substrates are used, and the detector is also carefully modeled. A static tip in vacuum serves to study the influence of the tip and illumination geometry on the far fields and on the near fields in the proximity of the tip apex, the volume used to probe the sample. Including a gold substrate and the commonly used demodulation scheme allows to study the discrimination of the components carrying the local information. A very good discrimination is verified for silicon tips and small oscillation amplitudes, as far as the tip interacts closely with the substrate and the oscillation remains highly sinusoidal. The imaging process is studied by including patterned substrates. The obtained signal is mostly sensitive to a few nanometers of depth into the sample, and the influence of the scanning conditions on the level of signal, background suppression and lateral resolution is characterized. Further, a closer look into the behavior of the extended physical detector reveals the influence of the spatial inhomogeneities of the scattered fields and, for interferometric measurements, the large significance of the optical phase. Experimentally, different techniques are first described that can facilitate images with clear local information. A cross polarization scheme is introduced which is very useful for non-perturbative measurements. It is applied to the mapping of the the field distribution surrounding plasmonic structures, for both the phase and the amplitude. Beyond dipolar resonances, I also study coupled dipoles and quadrupole field distributions. When imaging artifacts are avoided, the obtained images closely resemble theoretical expectations.

EPFL2007

Predictors and predictands of linear response in spatially extended systems

Umberto Maria Tomasini

The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz '96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.

SPRINGER HEIDELBERG2021

Aspects of the energy transition and their effects on power systems

Laurent Vincent Pagnier

Most European countries are committed to an energy transition which consists in the substitution of conventional CO2 emitting energy sources by new renewable energy sources (RES), in particular wind and solar power. As opposed to conventional energy sources, new RES are distributed, non-dispatchable, fluctuating and inertialess and have negligible marginal costs. In this thesis, we investigate the impact of the energy transition on the electricity sector in Europe. In the first part of this thesis, we investigate the future electricity production and prices in Europe. We develop a dispatch algorithm on an aggregated model of the pan-European power grid with which we study the future European productions. We show that, as the penetration of new RES increases, the transmission grids are more strongly used and that more flexibility is required from conventional generators. The existing infrastructures seem to able to absorb, through increased international power exchanges and usage of the existing pumped-storage hydroelectricity, the variations of new RES productions even for high penetrations. Then we investigate the effects of new RES on electricity prices. We explain why, due to their negligible marginal cost and their lack of dispatchability, they tend to drag electricity prices down and can be considered as a reduction of the load in the electricity pricing. In particular, photovoltaics decreases the volatility of electricity prices. We show that, in most European countries, the day-ahead electricity price is strongly correlated with the residual load, which is obtained by subtracting the non-dispatchable productions, in particular those of the new RES, from the load. From this observation, we build an effective price model based solely on the residual load with which the revenues of different electricity producers are evaluated. The second part of this thesis deals with disturbances in large transmission grids. The substitution of conventional generators by inertialess RES reduces the amount of inertia connected to power systems which might affect their reliability. To examine the propagation of disturbances in large transmission grids, we develop a dynamical model of the continental European transmission grid. We observe that the magnitude of the disturbance following a power loss depends on the fault location. We show that when inertia and primary control are uniformly distributed, the faults exciting the slowest eigenmodes of the network Laplacian are followed by the strongest disturbances. Reducing inertia on those eigenmodes, which are mostly located in the periphery of the grid, affects more its resilience than when the reduction occurs in its center. Finally, we use perturbation theory to derive algorithms for optimal placement of inertia and primary control when some mild inhomogeneities are present in their distributions. We show that,when the vulnerability of the whole grid is taken into account, a uniform distribution of inertia is optimal and the primary control is best placed in the periphery of the grid.

EPFL2019