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Collective excitations in many body systems

R. M. Dreizler

Published Jan 1, 1994• 0 citations
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The stability and collective excitation of Bose–Einstein condensates with both two- and three-body interactions in a two-dimensional anharmonic trap (i.e., harmonic plus quartic trap) are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability are discussed in detail. It is found that the anharmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.
Spectroscopic measurements in quantum systems are subject to selection rules, usually based on space-time symmetries, that allow or disallow transitions between states. In many-body systems, in addition to the single-particle states, there emerge new ones due to collective excitations of the system. Here we demonstrate the existence of a ``fragile'' selection rule that emerges as a manifestation of many-body effects and outlines the conditions for collective excitations to couple to a given spectroscopic probe beyond the usual symmetry considerations. As an example, we apply the rule to Raman spectroscopy of multiband superconductors and settle some unresolved features in experiments, one of them being the spectral weight distribution between the pair-breaking excitations and the collective modes.
We extend the recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin ± 1. In addition, we obtain new, spin-zero magnon-density-wave excitations, which have been missing in Anderson's spin-wave theory. Implications of these new collective modes are discussed.