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See detailChaotic Bohmian trajectories for stationary states
Cesa, Alexandre ULg; Martin, John ULg; Struyve, Ward

in Journal of Physics A: Mathematical and Theoretical (2016), 49

In Bohmian mechanics, the nodes of the wave function play an important role in the generation of chaos. However, so far, most of the attention has been on moving nodes; little is known about the ... [more ▼]

In Bohmian mechanics, the nodes of the wave function play an important role in the generation of chaos. However, so far, most of the attention has been on moving nodes; little is known about the possibility of chaos in the case of stationary nodes. We address this question by considering stationary states, which provide the simplest examples of wave functions with stationary nodes. We provide examples of stationary wave functions for which there is chaos, as demonstrated by numerical computations, for one particle moving in 3 spatial dimensions and for two and three entangled particles in two dimensions. Our conclusion is that the motion of the nodes is not necessary for the generation of chaos. What is important is the overall complexity of the wave function. That is, if the wave function, or rather its phase, has complex spatial variations, it will lead to complex Bohmian trajectories and hence to chaos. Another aspect of our work concerns the average Lyapunov exponent, which quantifies the overall amount of chaos. Since it is very hard to evaluate the average Lyapunov exponent analytically, which is often computed numerically, it is useful to have simple quantities that agree well with the average Lyapunov exponent. We investigate possible correlations with quantities such as the participation ratio and different measures of entanglement, for different systems and different families of stationary wave functions. We find that these quantities often tend to correlate to the amount of chaos. However, the correlation is not perfect, because, in particular, these measures do not depend on the form of the basis states used to expand the wave function, while the amount of chaos does. [less ▲]

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See detailChaotic Bohmian trajectories for stationary states
Cesa, Alexandre ULg; Martin, John ULg; Struyve, Ward

Poster (2016, May 18)

We study the possibility of chaos for the Bohmian dynamics when the wave function is stationary. Examples of stationary wave functions are given for which there is chaos, as demonstrated by numerical ... [more ▼]

We study the possibility of chaos for the Bohmian dynamics when the wave function is stationary. Examples of stationary wave functions are given for which there is chaos, as demonstrated by numerical computations, for one particle moving in 3 spatial dimensions and for two and three entangled particles in 2 dimensions. What is important for the amount of chaos is the overall complexity of the wave function. Some simple measures that partly capture the complexity of the wave function are considered: the participation ratio and different measures of entanglement. We find that these measures often tend to correlate to the amount of chaos. However, the correlation is not perfect, because the measures do not depend on the intrinsic complexity of the states of a given basis. [less ▲]

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See detailChaotic Bohmian trajectories for the hydrogen atom
Cesa, Alexandre ULg; Struyve, Ward ULg; Martin, John ULg

Poster (2015, May 13)

In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the ... [more ▼]

In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the guiding equation. This equation states that the velocity of the particle is proportional to the usual probability current associated with its wave function. In this work, we study the quantum trajectory of a single particle in a Coulomb potential whose eigenstates are the well known eigenstates of the hydrogen atom. More precisely, we focus on the relation between chaotic Bohmian trajectories and the motion of wave function nodes. At wave function nodes i.e., where the wave function vanishes, the velocity is not defined which generically induces vorticity. In order to probe chaos, we compute Poincaré map and we numerically evaluate Lyapounov exponents, which characterize the divergence of close trajectories as time increases. For the 2d Coulomb potential, although the superposition of two eigenstates with different energies can lead to an arbitrary high number of moving nodes of the wave function, the Bohmian trajectories display no trace of chaos. This absence of chaotic behaviour originates from the existence of a constant of motion. Therefore, the motion and the number of nodes do not constitute a sufficient condition for the emergence of chaos in Bohmian mechanics. For superpositions of more than two eigenstates, there is no constant of motion, there are moving nodes and we find that the Bohmian trajectories are chaotic. [less ▲]

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See detailChaotic bouncing of a droplet on a soap film
Gilet, Tristan ULg; Bush, John, W.M.

in Physical Review Letters (2009), 102

We examine the complex dynamics arising when a water droplet bounces on a horizontal soap film suspended on a vertically oscillating circular frame. A variety of simple and complex periodic bouncing ... [more ▼]

We examine the complex dynamics arising when a water droplet bounces on a horizontal soap film suspended on a vertically oscillating circular frame. A variety of simple and complex periodic bouncing states are observed, in addition to multiperiodicity and period-doubling transitions to chaos. The system is simply and accurately modeled by a single ordinary differential equation, the numerical solution of which captures all the essential features of the observed behavior. Iterative maps and bifurcation diagrams indicate that the system exhibits all the features of a classic low-dimensional chaotic oscillator. [less ▲]

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See detailChaotic dynamics of a Bose-Einstein condensate coupled to a qubit
Martin, John ULg; Georgeot, B.; Shepelyansky, D. L.

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2009), 79

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice, using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than ... [more ▼]

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice, using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than the lattice period, the chaotic dynamics of the BEC is effectively controlled by the qubit state. The feedback effects of the nonlinear chaotic BEC dynamics preserve the coherence and purity of the qubit in the regime of strong BEC nonlinearity. This gives an example of an exponentially sensitive control over a macroscopic state by internal qubit states. At weak nonlinearity quantum chaos leads to rapid dynamical decoherence of the qubit. The realization of such coupled systems is within reach of current experimental techniques. [less ▲]

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See detailChap II : Mécanisme et étiopathologie des pneumopathies du sujet à haut risque
Bury, Thierry ULg

in Yernault; Demedts, M (Eds.) Infections respiratoires pour le spécialiste (1997)

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See detailChap. 14 : PET scan et cancer broncho-pulmonaire
Bury, Thierry ULg

in Le cancer bronchopulmonaire (1998)

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See detailChap.I : Epidemiologie
Bury, Thierry ULg

in Demedts, M; Vermeire, P; Yernault, JC (Eds.) Le cancer du poumon (1997)

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See detailLa chapelle Sainte-Pétronille (Bargème, France), témoin d’une apparition moustérienne dans les préalpes nord-varoises
Marzin, Sébastien; Purdue, Louise; Tomasso, Antonin ULg et al

in Bulletin du Musée d'Anthropologie Préhistorique de Monaco (in press)

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See detailUm chapéu amarelo e um capuz vermelho: uma leitura semiótica de Chapeuzinho Amarelo de Chico Buarque
Lindenberg Lemos, Carolina ULg

in CASA : Cadernos de Semiótica Aplicada (2008), 6(1), 1-12

In the 1970’s, Chico Buarque published the children's book Chapeuzinho Amarelo – a parody of the fairy tale The Little Red Riding Hood. This analysis tries to emphasize the intertextual structures ... [more ▼]

In the 1970’s, Chico Buarque published the children's book Chapeuzinho Amarelo – a parody of the fairy tale The Little Red Riding Hood. This analysis tries to emphasize the intertextual structures underlying the two stories, showing in what ways elements of the narrative, themes and figures are borrowed from the classical text. In the traditional version of the brothers Grimm, the central theme is that of transgression, but in the background we can also see the theme of maturation. This secondary theme is brought to the center in Chapeuzinho Amarelo. Linguistic, sound and visual resources of the expression plane will bring a symbolic aspect to the confrontation between Chapeuzinho Amarelo and the Wolf. To close the analysis, we investigate the pictures that compose the book. These pictures bring contributions to the meanings conveyed by the written text and reinforce the general interpretation given in this work. [less ▲]

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See detailChapiter 10: Identification of mechanosensitive genes in chondrocytes and osteoblasts and their role in OA pathogenesis
Henrotin, Yves ULg; Pesesse, Laurence ULg; Sanchez, Christelle ULg

in Kamklin, Andre; Kiseleva, Irina (Eds.) Mechanical stretch and cytokines (2012)

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See detailChapitre 1 : distinction des biens
Salvé, Arianne ULg

in Chroniques Notariales (2008), 48

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See detailChapitre 10 : L'aménagement des territoires
Merenne-Schoumaker, Bernadette ULg

in Pitte, Jean-Robert (Ed.) Géographie 2de. Les hommes et la terre (1996)

En 13 fiches de deux pages et deux modules d'activités, tour d'horizon sur les acteurs, les actions, les échelles, les politiques et les stratégies en aménagement du territoire

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See detailChapitre 10 : Les espaces industriels
Merenne-Schoumaker, Bernadette ULg

in Pitte, Jean-Robert (Ed.) Géographie 2de (1993)

Rapports des industries à l'espace; facteurs et théories de localisation; anciens et nouveaux espaces industriels

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See detailChapitre 115 : De l’Angleterre, et de ses malheurs après l’invasion de la France. De Marguerite d’Anjou femme de Henri VI, etc.
Tilkin, Françoise ULg

in Bernard, Bruno; Renwick, John; Cronk, Nicholas (Eds.) et al Voltaire, Essai sur les mœurs et l’esprit des nations (V), sous la direction de Bruno Bernard, John Renwick, Nicholas Cronk, Janet Godden, Texte et bibliographie établis par Henri Duranton (2012)

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See detailChapitre 116 : D’Edouard IV. De Marguerite d’Anjou et de la mort de Henri VI.
Tilkin, Françoise ULg

in Bernard, Bruno; Renwick, John; Cronk, Nicholas (Eds.) et al Voltaire, Essai sur les mœurs et l’esprit des nations (V), sous la direction de Bruno Bernard, John Renwick, Nicholas Cronk, Janet Godden, Texte et bibliographie établis par Henri Duranton (2012)

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See detailChapitre 117 : Suite des troubles d’Angleterre sous Edouard IV, sous le tyran Richard III, et jusqu’à la fin du règne de Henri VII
Tilkin, Françoise ULg

in Bernard, Bruno; Renwick, John; Cronk, Nicholas (Eds.) et al Voltaire, Essai sur les mœurs et l’esprit des nations (V), sous la direction de Bruno Bernard, John Renwick, Nicholas Cronk, Janet Godden, Texte et bibliographie établis par Henri Duranton (2012)

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See detailChapitre 12 : Les mares, petits terrains d’Histoire et d’histoires
Castiaux, Annick; Morelle, Kevin ULg

in Van Dam, Denise (Ed.) Agroécologie - entre pratiques et sciences sociales (2012)

Cet ouvrage nous conduit aux quatre coins du monde. On y découvre des expériences d’agroforesterie en Inde, le développement de l’agriculture biologique en Alsace, la mise en place de certi!cation ... [more ▼]

Cet ouvrage nous conduit aux quatre coins du monde. On y découvre des expériences d’agroforesterie en Inde, le développement de l’agriculture biologique en Alsace, la mise en place de certi!cation participative au Brésil, ou encore le fonctionnement de groupements d’achats alimentaires en Belgique… Ces expériences ont en commun de promouvoir une agriculture et une alimentation soucieuses des principes de l’écologie. Cet ouvrage est ainsi un des premiers en langue française à présenter les recherches qui se font dans le domaine de l’agroécologie, un courant qui se développe depuis une trentaine d’années, principalement aux États-Unis et en Amérique latine. Les multiples expériences sont analysées à travers le prisme des sciences sociales. On s’interroge sur le rôle des différents acteurs (paysans, consommateurs, …), sur la manière dont les initiatives s’inscrivent dans les territoires et sur les modes de régulation assurés par les pouvoirs publics. [less ▲]

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See detailChapitre 12. Littérature : entre insularité et activisme
Denis, Benoît ULg; Klinkenberg, Jean-Marie ULg

in Delhalle, Nancy; Dubois, Jacques (Eds.) Le tournant des années 1970. Liège en effervescence (2010)

Detailed reference viewed: 30 (4 ULg)