Structures quantiques de certaines sous-variétés lagrangiennes non-monotones

Soit (M,ω) un variété symplectique fermée et connexe.On considère des sous-variétés lagrangiennes α : L → (M,ω). Si α est monotone, c.- à-d. s’il existe η > 0 tel que ημ = ω, Paul Biran et Octav Conea ont défini une version relative de l’homologie quantique. Dans ce contexte ils ont déformé l’opérateur de bord du complexe de Morse ainsi que le produit d’intersection à l’aide de disques pseudo-holomorphes. On note (QH(L), ∗), l’homologie quantique de L munie du produit quantique. Le principal objectif de cette dissertation est de généraliser leur construction à un classe plus large d’espaces. Plus précisément on considère soit des sous-variétés presque monotone, c.-à-d. α est C1-proche d’un plongement lagrangian monotone ; soit les fibres toriques de variétés toriques Fano. Dans ces cas non nécessairement monotones, QH(L) va dépendre de certains choix, mais cela sera irrelevant pour les applications présentées ici. Dans le cas presque monotone, on s’intéresse principalement à des questions de déplaçabilité, d’uniréglage et d’estimation d’énergie de difféomorphismes hamiltoniens. Enfin nous terminons par une application combinant les deux approches, concernant la dynamique d’un hamiltonien déplaçant toutes les fibres toriques non-monotones dans CPn.

Cobordismes lagrangiens et uniréglage

Ce mémoire traite de la question suivante: est-ce que les cobordismes lagrangiens préservent l'uniréglage? Dans les deux premiers chapitres, on présente en survol la théorie des courbes pseudo-holomorphes nécessaire. On examine d'abord en détail la preuve que les espaces de courbes $ J $-holomorphes simples est une variété de dimension finie. On présente ensuite les résultats nécessaires à la compactification de ces espaces pour arriver à la définition des invariants de Gromov-Witten. Le troisième chapitre traite ensuite de quelques résultats sur la propriété d'uniréglage, ce qu'elle entraine et comment elle peut être démontrée. Le quatrième chapitre est consacré à la définition et la description de l'homologie quantique, en particulier celle des cobordismes lagrangiens, ainsi que sa structure d'anneau et de module qui sont finalement utilisées dans le dernier chapitre pour présenter quelques cas ou la conjecture tient.

Quantum Dots As Biophotonics Tools.

This chapter provides a short review of quantum dots (QDs) physics, applications, and perspectives. The main advantage of QDs over bulk semiconductors is the fact that the size became a control parameter to tailor the optical properties of new materials. Size changes the confinement energy which alters the optical properties of the material, such as absorption, refractive index, and emission bands. Therefore, by using QDs one can make several kinds of optical devices. One of these devices transforms electrons into photons to apply them as active optical components in illumination and displays. Other devices enable the transformation of photons into electrons to produce QDs solar cells or photodetectors. At the biomedical interface, the application of QDs, which is the most important aspect in this book, is based on fluorescence, which essentially transforms photons into photons of different wavelengths. This chapter introduces important parameters for QDs' biophotonic applications such as photostability, excitation and emission profiles, and quantum efficiency. We also present the perspectives for the use of QDs in fluorescence lifetime imaging (FLIM) and Förster resonance energy transfer (FRET), so useful in modern microscopy, and how to take advantage of the usually unwanted blinking effect to perform super-resolution microscopy.

Measuring The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy.

Fluorescence Correlation Spectroscopy (FCS) is an optical technique that allows the measurement of the diffusion coefficient of molecules in a diluted sample. From the diffusion coefficient it is possible to calculate the hydrodynamic radius of the molecules. For colloidal quantum dots (QDs) the hydrodynamic radius is valuable information to study interactions with other molecules or other QDs. In this chapter we describe the main aspects of the technique and how to use it to calculate the hydrodynamic radius of quantum dots (QDs).

Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

Interplay Of Weak Interactions In The Atom-by-atom Condensation Of Xenon Within Quantum Boxes.

Condensation processes are of key importance in nature and play a fundamental role in chemistry and physics. Owing to size effects at the nanoscale, it is conceptually desired to experimentally probe the dependence of condensate structure on the number of constituents one by one. Here we present an approach to study a condensation process atom-by-atom with the scanning tunnelling microscope, which provides a direct real-space access with atomic precision to the aggregates formed in atomically defined 'quantum boxes'. Our analysis reveals the subtle interplay of competing directional and nondirectional interactions in the emergence of structure and provides unprecedented input for the structural comparison with quantum mechanical models. This approach focuses on-but is not limited to-the model case of xenon condensation and goes significantly beyond the well-established statistical size analysis of clusters in atomic or molecular beams by mass spectrometry.

Measurement Of The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy Excluding Blinking.

One of the most important properties of quantum dots (QDs) is their size. Their size will determine optical properties and in a colloidal medium their range of interaction. The most common techniques used to measure QD size are transmission electron microscopy (TEM) and X-ray diffraction. However, these techniques demand the sample to be dried and under a vacuum. This way any hydrodynamic information is excluded and the preparation process may alter even the size of the QDs. Fluorescence correlation spectroscopy (FCS) is an optical technique with single molecule sensitivity capable of extracting the hydrodynamic radius (HR) of the QDs. The main drawback of FCS is the blinking phenomenon that alters the correlation function implicating in a QD apparent size smaller than it really is. In this work, we developed a method to exclude blinking of the FCS and measured the HR of colloidal QDs. We compared our results with TEM images, and the HR obtained by FCS is higher than the radius measured by TEM. We attribute this difference to the cap layer of the QD that cannot be seen in the TEM images.

Photophysical properties and quantum chemical studies of poly(2,7-9,9'-dihexylfluorene-dyil)

This work reports the photophysical properties (excitation and fluorescence spectra, fluorescence quantum yield, fluorescence lifetimes) of the poly(2,7-9,9'-dihexylfluorene-dyil) in dilute solutions of four solvents (toluene, tetrahydrofuran, chloroform and ethyl acetate) as well as the properties in solid state. Photoluminescence showed spectra characteristic of disordered α-backbone chain conformation. Simulation of the electronic absorption spectra of oligomers containing 1 to 11 mers showed that the critical conjugation length is between 6 and 7 mers. We also estimated the theoretical dipole moments which indicated that a coil conformation is formed with 8 repeating units per turn. We also showed that some energy transfer process appears in solid state which decreases the emission lifetime. Furthermore, based on luminescent response of the systems herein studied and electroluminescent behavior reported on literature, both photo and electroluminescence emissions arise from the same emissive units.

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing the interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to the previously established classical limit with a classical field behavior, showing that the limit h -> 0 of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.

Phylogenetic position of the acariform mites: sensitivity to homology assessment under total evidence

Background: Mites (Acari) have traditionally been treated as monophyletic, albeit composed of two major lineages: Acariformes and Parasitiformes. Yet recent studies based on morphology, molecular data, or combinations thereof, have increasingly drawn their monophyly into question. Furthermore, the usually basal (molecular) position of one or both mite lineages among the chelicerates is in conflict to their morphology, and to the widely accepted view that mites are close relatives of Ricinulei. Results: The phylogenetic position of the acariform mites is examined through employing SSU, partial LSU sequences, and morphology from 91 chelicerate extant terminals (forty Acariformes). In a static homology framework, molecular sequences were aligned using their secondary structure as guide, whereby regions of ambiguous alignment were discarded, and pre-aligned sequences analyzed under parsimony and different mixed models in a Bayesian inference. Parsimony and Bayesian analyses led to trees largely congruent concerning infraordinal, well-supported branches, but with low support for inter-ordinal relationships. An exception is Solifugae + Acariformes (P. P = 100%, J. = 0.91). In a dynamic homology framework, two analyses were run: a standard POY analysis and an analysis constrained by secondary structure. Both analyses led to largely congruent trees; supporting a (Palpigradi (Solifugae Acariformes)) clade and Ricinulei as sister group of Tetrapulmonata with the topology (Ricinulei (Amblypygi (Uropygi Araneae))). Combined analysis with two different morphological data matrices were run in order to evaluate the impact of constraining the analysis on the recovered topology when employing secondary structure as a guide for homology establishment. The constrained combined analysis yielded two topologies similar to the exclusively molecular analysis for both morphological matrices, except for the recovery of Pedipalpi instead of the (Uropygi Araneae) clade. The standard (direct optimization) POY analysis, however, led to the recovery of trees differing in the absence of the otherwise well-supported group Solifugae + Acariformes. Conclusions: Previous studies combining ribosomal sequences and morphology often recovered topologies similar to purely morphological analyses of Chelicerata. The apparent stability of certain clades not recovered here, like Haplocnemata and Acari, is regarded as a byproduct of the way the molecular homology was previously established using the instrumentalist approach implemented in POY. Constraining the analysis by a priori homology assessment is defended here as a way of maintaining the severity of the test when adding new data to the analysis. Although the strength of the method advocated here is keeping phylogenetic information from regions usually discarded in an exclusively static homology framework; it still has the inconvenience of being uninformative on the effect of alignment ambiguity on resampling methods of clade support estimation. Finally, putative morphological apomorphies of Solifugae + Acariformes are the reduction of the proximal cheliceral podomere, medial abutting of the leg coxae, loss of sperm nuclear membrane, and presence of differentiated germinative and secretory regions in the testis delivering their products into a common lumen.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

Study of the influence of indium segregation on the optical properties of InGaAs/GaAs quantum wells via split-operator method

In the case of quantum wells, the indium segregation leads to complex potential profiles that are hardly considered in the majority of the theoretical models. The authors demonstrated that the split-operator method is useful tool for obtaining the electronic properties in these cases. Particularly, they studied the influence of the indium surface segregation in optical properties of InGaAs/GaAs quantum wells. Photoluminescence measurements were carried out for a set of InGaAs/GaAs quantum wells and compared to the results obtained theoretically via split-operator method, showing a good agreement.

Growth and capping of InAs/GaAs quantum dots investigated by x-ray Bragg-surface diffraction

An x-ray diffraction method, based on the excitation of a surface diffracted wave, is described to investigate the capping process of InAs/GaAs (001) quantum dots (QDs). It is sensitive to the tiny misorientation of (111) planes at the surface of the buffer layer on samples with exposed QDs. After capping, the misorientation occurs in the cap-layer lattice faceting the QDs and its magnitude can be as large as 10 degrees depending on the QDs growth rates, probably due to changes in the size and shape of the QDs. A slow strain release process taking place at room temperature has also been observed by monitoring the misorientation angle of the (111) planes.

Electron dephasing scattering rate in two-dimensional GaAs/InGaAs heterostructures with embedded InAs quantum dots

We report a comprehensive study of weak-localization and electron-electron interaction effects in a GaAs/InGaAs two-dimensional electron system with nearby InAs quantum dots, using measurements of the electrical conductivity with and without magnetic field. Although both the effects introduce temperature dependent corrections to the zero magnetic field conductivity at low temperatures, the magnetic field dependence of conductivity is dominated by the weak-localization correction. We observed that the electron dephasing scattering rate tau(-1)(phi), obtained from the magnetoconductivity data, is enhanced by introducing quantum dots in the structure, as expected, and obeys a linear dependence on the temperature and elastic mean free path, which is against the Fermi-liquid model. (c) 2008 American Institute of Physics. [DOI: 10.1063/1.2996034]

Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.