Temporal coherence, anomalous moments, and pairing correlations in the classical-field description of a degenerate Bose gas

The coherence properties of degenerate Bose gases have usually been expressed in terms of spatial correlation functions, neglecting the rich information encoded in their temporal behavior. In this paper we show, using a Hamiltonian classical-field formalism, that temporal correlations can be used to characterize familiar properties of a finite-temperature degenerate Bose gas. The temporal coherence of a Bose-Einstein condensate is limited only by the slow diffusion of its phase, and thus the presence of a condensate is indicated by a sharp feature in the temporal power spectrum of the field. We show that the condensate mode can be obtained by averaging the field for a short time in an appropriate phase-rotating frame, and that for a wide range of temperatures, the condensate obtained in this approach agrees well with that defined by the Penrose-Onsager criterion based on one-body (spatial) correlations. For time periods long compared to the phase diffusion time, the field will average to zero, as we would expect from the overall U(1) symmetry of the Hamiltonian. We identify the emergence of the first moment on short time scales with the concept of U(1) symmetry breaking that is central to traditional mean-field theories of Bose condensation. We demonstrate that the short-time averaging procedure constitutes a general analog of the 'anomalous' averaging operation of symmetry-broken theories by calculating the anomalous thermal density of the field, which we find to have form and temperature dependence consistent with the results of mean-field theories.Comment: 11 pages, 6 figures. v3: Final version. Typos fixed, and other minor change

Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

We review various connections between condensed matter systems with the Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Resent findings of a duality between the Nambu-Jona Lasinio model and the nonlinear sigma model enables us to investigate various properties underlying both theories. In this review we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in the nonlinear sigma model owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.Comment: 24pages, 10 figures, Invited review paper commissioned by Symmetry. Comments warmly welcom

Magnetic dipole excitations in nuclei: elementary modes of nucleonic motion

The nucleus is one of the most multi-faceted many-body systems in the universe. It exhibits a multitude of responses depending on the way one 'probes' it. With increasing technical advancements of beams at the various accelerators and of detection systems the nucleus has, over and over again, surprised us by expressing always new ways of 'organized' structures and layers of complexity. Nuclear magnetism is one of those fascinating faces of the atomic nucleus we discuss in the present review. We shall not just limit ourselves to presenting the by now very large data set that has been obtained in the last two decades using various probes, electromagnetic and hadronic alike and that presents ample evidence for a low-lying orbital scissors mode around 3 MeV, albeit fragmented over an energy interval of the order of 1.5 MeV, and higher-lying spin-flip strength in the energy region 5 - 9 MeV in deformed nuclei, nor to the presently discovered evidence for low-lying proton-neutron isovector quadrupole excitations in spherical nuclei. To the contrary, we put the experimental evidence in the perspectives of understanding the atomic nucleus and its various structures of well-organized modes of motion and thus enlarge our discussion to more general fermion and bosonic many-body systems.Comment: 59 pages, 59 figures, accepted for publication in Rev. Mod. Phys