Centre de Physique Théorique


February 2020

Wednesday 5 February 14:00-15:00, Amphi 5

Low-dimensional chaos in the self-consistent wave-particle interaction

J.V. Gomez, Federal University of Paraná, Brazil et AMU, Marseille

We analyze nonlinear aspects of the wave-particle interaction using Hamiltonian dynamics and considering a low-dimension realization of the single wave model. The wave-particle interaction plays an
important role in plasma dynamics, and the nonlinear processes resulting from this interaction are related
to the emergence of plasma instabilities and turbulence. This interaction can be represented in the (x, v)
space by regular and chaotic trajectories of particles. Regular trajectories may lead to coherent particle
acceleration while chaotic trajectories are responsible for particle heating and escape.
Often, low-dimensional approximations shed light on the dynamics of systems with many degrees of
freedom, as chaotic motion arises as one increases the number of degrees of freedom. We start with the
simple case where one particle (N = 1) is coupled to one wave (M = 1) [1]. This case is completely
integrable, so that all trajectories are regular and the nonlinear effects degenerate to particle trapping while
the wave potential pulsates. The bifurcation diagram of this simple system is already rich, with a saddlecentre coalescence and a special role of the trajectory for which the wave intensity goes through zero. On
increasing the number of particles (N = 2, M = 1), chaos arises due to the strong sensitivity in the initial
condition of relative velocity or relative position of the particles. Continuous time behaviours were also
analyzed through particle motion in the energy and wave comoving frame.
[1] J.C. Adam, G. Laval and I. Mendonça, Phys. Fluids 24, 260-267 (1981).

Friday 7 February 14:00-15:00, Amphi 5 du CPT

Paths, Groupoids and Quantization

Patrick Iglesias-Zemmour (HUJ, Israel)

I will show how, in the context of diffeology, one can find the prequatization framework for general diffeological spaces (finite or infinite dimensional, in presence of singularities or not) as a groupoid, quotient of the space of paths, equipped with a left-right invariant connectionlike-form. This construction suggests a variant of the program of geometric quantization which I will describe.

Wednesday 12 February 14:00-15:00, Amphi 5

Mesures indirectes d’un système quantique: les mesures, le système.

Yan Pautrat, Université Paris Sud

On s’intéresse aux mesures indirectes d’un système quantique, dans lesquelles la mesure est faite non pas sur le système qui nous intéresse, mais sur une ``sonde’’ interagissant avec ce système. Ceci permet de s’affranchir (partiellement) de la projection du paquet d’onde. En particulier, si l’on répète l’expérience (avec une sonde neuve), le deuxième résultat de mesure ne sera a priori pas identique au premier. On peut donc imaginer répéter un grand nombre de fois cette expérience, et de nombreuses questions se posent alors : quelles propriété a la suite de résultats de mesure ? quelle information peut-on tirer de ces résultats ? quel est le comportement du système ? Cet exposé abordera ces différentes questions.

Les travaux présentés dans cet exposé ont été obtenus en collaboration avec Tristan Benoist, Martin Fraas, Eric Hanson, Vojkan Jaksic, Alain Joye, Annalisa Panati, Clément Pellegrini, Claude-Alain Pillet et Renaud Raquépas.

Friday 21 February 14:00-15:00, Amphi 5 du CPT

General Relativity from Scattering Amplitudes

Poul Damgaard (Niels Bohr Institute)

A remarkable connection between the loop expansion of quantized gravity and classical general relativity allows for the computation of two-body dynamics in general relativity using a number of new amplitude tools developed in recent years. The resulting expansion is known as Post-Minkowskian (in contradistinction to Post-Newtonian) and the new method promises to overturn all previously used techniques for analytical calculations of gravitational wave signals of two merging black holes. I will outline the program and illustrate with examples of the calculation of classical gravitational scattering angles.