Complex trajectory method in semiclassical propagation of wave packets

International audienceWe propose a semiclassical wave packet propagation method relying on classical trajectories in a complex phase space. It is based on the Schrödinger wave equation and the usual expansion with respect to ℏ, except that the amplitude of the wave packet is taken into account at the very zeroth order, unlike in the usual WKB method where it is treated as a corrective or first order term. Formally, it amounts to making both the wavelength and the width of the wave packet tend to zero with ℏ. The action and consequently the classical trajectories derived are complex. This method is tested successfully in many cases, analytically or numerically, including the bounce and even the splitting of the wave packet. Our method appears to be much more accurate than the WKB method while less computationally demanding than the Van-Vleck formula. Moreover, it has a particularly interesting property: the singularities (caustics) of the usual semiclassical theories do not appear in this formalism in all cases tested

Coupled modes semiclassical treatment of nonadiabatic transitions

International audienceWe analyse the Schrödinger wave equation of a two-level or spinorial Hamiltonian, from a classical point of view. An iterative scheme, the coupled mode semiclassical formalism, is proposed, allowing us to deal with the nonadiabatic transfer. As the WKB expansion, it allows the one-dimensional Schrödinger equation to be integrated by successive quadratures. Finally, we show that time-dependent information can be drawn from the previous, purely stationary, analysis by extending the notion of group velocity. The proposed formalism is thus coherent with an image of multiple trajectories, conforming more to physical behaviour than a single trajectory

An atomic Hong-Ou-Mandel experiment

The celebrated Hong, Ou and Mandel (HOM) effect is one of the simplest illustrations of two-particle interference, and is unique to the quantum realm. In the original experiment, two photons arriving simultaneously in the input channels of a beam-splitter were observed to always emerge together in one of the output channels. Here, we report on the realisation of a closely analogous experiment with atoms instead of photons. This opens the prospect of testing Bell's inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics, with an eye on theories of the quantum-to-classical transition. Our work also demonstrates a new way to produce and benchmark twin-atom pairs that may be of interest for quantum information processing and quantum simulation

Nonadiabatic effects in two-level systems: A classical analysis

International audienceOur aim in this paper is to study classical dynamics in two-level molecular systems. We first derive, through the Wigner phase-space transform, a classical limit that reduces unfortunately to the adiabatic approximation. This lead us to develop a one-center quantal approximation whose variables can be interpreted in a fully classical Hamiltonian scheme. As a prominent feature, this Hamiltonian couples polarization and spatial motion. We apply it successfully to the Rosenthal-Stückelberg oscillations. We analyze one-dimensional diffusion similar to a molecular reaction, it appears to exhibit chaotic behavior

The 2nd order coherence of superradiance from a Bose--Einstein condensate

We have measured the 2-particle correlation function of atoms from a Bose--Einstein condensate participating in a superradiance process, which directly reflects the 2nd order coherence of the emitted light. We compare this correlation function with that of atoms undergoing stimulated emission. Whereas the stimulated process produces correlations resembling those of a coherent state, we find that superradiance, even in the presence of strong gain, shows a correlation function close to that of a thermal state, just as for ordinary spontaneous emission

Upper crustal record of migmatites exhumation: the South Armorican Domain

The South Armorican Massif hosts a high-grade metamorphic domain mainly composed of medium to high-grade micaschists, migmatitic gneisses and anatectic granites [1]. At the end of the Carboniferous, these deep crustal units were exhumed rapidly during the extension associated with the collapse of the Hercynian chain [2]. To the North, this domain is limited by the listhospheric-scale South Armorican Shear Zone (SASZ). Giant quartz veins are associated with the SASZ and recorded important synmetamorphic fluid circulation [3]. Together with very low δ18O values for some euhedral quartz, down to -2‰, low-salinity fluid inclusions argue for a contribution from meteoric fluids [3]. Corresponding δ18Ofluid values estimated around -11‰ are probably related to the high palaeoelevation of meteoric precipitation. Scarce, but significant, CO2 fluid inclusions in euhedral quartz indicate also a metamorphic contribution. Metamorphic fluids were probably sourced from the exhumed metamorphic basement in the southern part of the Massif. Also, because of the synchronicity between the metamorphic event (exhumation) and the meteoric infiltration, it is proposed that the heat advected towards the surface by the exhumation of high-grade metamorphic rocks provided the driving force for meteoric fluid circulation on a regional scale. The meteoric infiltration is recorded regionally by the mylonites which actually define the SASZ and by the syn-kinematic granites which emplaced along the SASZ. Low δ18O values have been measured on some feldspar and zircon grains in the formers [4] while oxygen isotope disequilibirum was recorded by Qz-Fds pairs in the latters [5]. The muscovite Ar-Ar and monazite U-Th-Pb chronometers from these lithologies were highly disturbed [4,6]. In the Questembert granite, a classical example of a syn-kinematic granite, pervasive infiltration of oxydative meteoric water was facilitated by the penetrative character of the deformation (C/S planes are observed throughout the massif) and was probably responsible for the leaching of millions of tons of uranium while the granite was still at depth

Chaos induit par transition non-adiabatique dans les molécules

Afin d'étudier le chaos vibrationnel observé dans les molécules dans les régions d'énergie où les interactions vibroniques sont importantes, nous avons déterminé une limite classique permettant de traiter simultanément les degrés de liberté spatiaux et les degrés d'échange de probabilité quantiques entre les deux surfaces d'énergie électronique mises en jeu. Ce modèle classique permet de retrouver le phénomène d'oscillation de Rosenthal et exhibe clairement un caractère chaotique en diffusion

Modélisation phénoménologique de systèmes complexes non-linéaires à partir de séries chronologiques scalaires

Ces travaux de thèse visent à développer une méthode originale de modélisation du comportement des systèmes complexes. L'objectif est de construire un modèle phénoménologique d'évolution d'un système en régime chaotique, sous la forme d'équations différentielles ordinaires, à partir de la donnée d'une variable scalaire régulièrement échantillonnée. La technique de modélisation mise en place s'appuie sur l'utilisation d'une bibliothèque exhaustive de modèles, bibliothèque construite mathématiquement de façon formelle et rigoureuse. La méthode théorique d'identification a été intégrée au sein d'une méthode numérique générale pour laquelle la série chronologique analysée est la seule donnée d'entrée et qui permet de construire des modèles d'approximation du comportement dynamique du système étudié. Elle se décompose en trois modules. Dans un premier temps, la série scalaire est débruitée et ses séries dérivées, requises pour la reconstruction, sont calculées. Ensuite, la construction des équations est effectuée à l'aide de la bibliothèque de modèles ce qui permet d'identifier un ensemble de systèmes différentiels, dont la compatibilité avec la série chronologique initiale est ensuite vérifiée. Dans le cas positif, les systèmes reconstruits sont validés comme modèles phénoménologiques du système complexe étudié. La méthode de modélisation développée a été validée en traitant des séries scalaires générées par des systèmes différentiels numériques. L'analyse de séries numériques non bruitées a tout d'abord permis de vérifier les performances de la méthode mise en place par comparaison directe des équations identifiées avec les équations originales. La modélisation à partir de séries numériques bruitées a ensuite montré que la dynamique inscrite dans la série scalaire initiale était retrouvée au sein du système reconstruit. Enfin, nous avons appliqué cette technique de modélisation globale à des séries expérimentales de deux types. Les premières sont des tensions enregistrées en régime chaotique sur des circuits électroniques réalisés dans le cadre de cette thèse ; quant aux secondes, il s'agit de l'intensité générée par une réaction d'électrolyse et fournie par une équipe américaine. Dans tous les cas, des modèles phénoménologiques ont été établis et validésLYON1-BU.Sciences (692662101) / SudocNANCY/VANDOEUVRE-INPL (545472102) / SudocSudocFranceF

Optimizing territorial resources to support agroecological transitions: which levers to adapt to climate change in livestock systems in South of France?

International audienceAgroecological transitions require to foster frameworks and strategies to optimize the identification, access to and activation of territorial resources. Climate change threatens the durability of natural resources and the stability of favorable socioeconomic conditions for transitions. In this paper, we propose a framework to analyze the degree of agroecological transition in farming systems and the sets of territorial resources already available or required to support this transition. We implement this framework on a case study in South Western France, in the Basque region where PDO cheese are produced. After describing ten types of farming systems, we characterize their proximity to agroecology and their potential resilience and adaptation to climate change. The analysis of territorial resources shows that agroecological transition in this territory is possible and would enhance adaptation to climate change, but require further development of territorial resources which depends on economic and political dynamics at local level. This work contributes to the understanding of agroecological transition at territory level, and proposes a framework to bridge existing methods for their analysis

Stable isotope composition of quartz-calcite veins in the Witwatersrand basin

International audienc