The evolution of classically chaotic quantum systems is analyzed within the formalism of Quantum Pseudo-Probability Distributions. Due to the deep connections that a quantum system shows with its classical correspondent in this representation, the Pseudo-Probability formalism appears to be a useful method of investigation in the field of "Quantum Chaos." In the first part of the thesis we generalize this formalism to quantum systems containing spin operators. It is shown that a classical-like equation of motion for the pseudo-probability distribution ρw can be constructed, dρw/dt = (L_CL + L_QGD)ρw, which is rigorously equivalent to the quantum von Neumann-Liouville equation. The operator L_CL is undistinguishable from the classical operator that generates the semiclassical equations of motion. In the case of the spin-boson system this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian the joint action of L_CL and L_QGD is illustrated. It is shown that the latter operator, L_QGD makes the spin system 'remember' its quantum nature, and competes with the irreversibility induced by the former operator. In the second part we test the idea of the enhancement of the quantum uncertainty triggered by the classical chaos by investigating the analogous effect of diffusive excitation in periodically kicked quantum systems. The classical correspondents of these quantum systems exhibit, in the chaotic region, diffusive behavior of the unperturbed energy. For the Quantum Kicked Harmonic Oscillator, in the case of quantum resonances, we provide an exact solution of the quantum evolution. This proves the existence of a deterministic drift in the energy increase over time of the system considered. More generally, this "superdiffusive" excitation of the energy is due to coherent quantum mechanical tunnelling between degenerate tori of the classical phase space. In conclusion we find that some of the quantum effects resulting from this fast increase do not have any classical counterpart, they are mainly tunnelling processes. This seems to be the first observation of an effect of this kind.

The quantum dynamics of minimum uncertainty wave packets in a system described by the surface-state-electron (SSE) Hamiltonian are studied herein.

Reproduction de : Thèse de doctorat : Histoire. Histoire des sciences et des techniques : Lyon 2 : 2004. / Titre provenant de l'écran-titre. Bibliogr. Index.

It has been customary practice in galactic dynamics to implicitly assume that the corresponding N-body problem is (near) integrable. After a review of some relevant ideas from non-linear dynamics, I discuss the evidence suggesting that the above assumption is not generally satisfied and the consequences of such a situation. Next, I discuss the characterization of such "chaotic" behaviour. A geometric method-which I argue is best suited for measuring the instability properties of N-body systems-is tested on systems of 231 particles integrated with high precision and displaying "obvious" instabilities like violent relaxation and collective processes. The predicted instability time-scales show good agreement with those inferred from the spatial evolution. As a further test I study closed systems which relax towards definite equilibrium states. The times of relaxation towards such states are then compared to the exponential instability time-scales in an attempt to identify the physical interpretation of the exponential instability that appears to be always present in N -body systems. As an application of the method, the variation of the exponential divergence time-scales in N -body Plummer models with particle number, rotation, softening, and central mass is studied. I also study the extent of chaotic behaviour in some non-axisymmetric but smooth potentials representing galaxies with triaxial halos. This is done with the aid of Liapunov exponents, Poincare maps, and stability analysis of resonant orbits. It is found that a significant amount of chaos is usually present and increases dramatically with the addition of rotating bar perturbations, or of central masses. The degree of instability may also depend on the presence of external noise. It is also shown that dissipative perturbations have the important effect of producing an inflow of matter to the central areas. The consequences of the above processes are then discussed and it is suggested that they may explain some aspects of the observed relative bulge-disk-halo contributions to galaxy rotation curves.

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