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

Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry

We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry arguments alone relate the spectra of systems with different particle numbers. For systems with non-spherical intrinsic ground states such as atomic nuclei or molecules, symmetry arguments alone yield the universal features of the low-lying excitations as vibrations that are the heads of rotational bands. The low-lying excitations in deformed nuclei differ from those in molecules because of symmetry properties caused by pairing.Comment: 9 pages; considerably expanded presentation; example of emergent U(1) breaking adde

Random Matrices and Chaos in Nuclear Spectra

We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. We approach the question by using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. We show that chaos is a generic feature of the ensemble and display some of its properties, emphasizing those which differ from standard random-matrix theory. In particular, we display the existence of correlations among spectra carrying different quantum numbers. These are subject to experimental verification.Comment: 17 pages, 20 figures, colloquium article, submitted to Reviews of Modern Physic