Invariant manifolds and collective motion in many-body systems

Collective modes of interacting many-body systems can be related to the motion on classically invariant manifolds. We introduce suitable coordinate systems. These coordinates are Cartesian in position and momentum space. They are collective since several components vanish for motion on the invariant manifold. We make a connection to Zickendraht's collective coordinates and also obtain shear modes. The importance of collective configurations depends on the stability of the manifold. We present an example of quantum collective motion on the manifoldComment: 8 pages, PDF, published in AIP Conference Proceedings 597 (2001

Single qubit decoherence under a separable coupling to a random matrix environment

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude than the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects and symmetry breaking equilibrium states.Comment: 13 pages, 7 figure