Theoretical Studies of Dilute Alkali Gases and Amorphous Materials

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This grant addresses theoretical questions in two challenging problems in emerging areas in condensed matter physics: properties of dilute alkali Bose and Fermi gases and the "universal" properties of amorphous materials.In the first area, several questions are addressed: (a) the behavior of a recently discovered state in which not one, but two, orbital single-particle states are macroscopically occupied; (b) the conditions under which the degree of Bose-Einstein condensation (BEC) may be inferred from Ramsey-fringe type experiments; (c) the detailed dynamics of the process by which a Bose gas trapped in an optical lattice in a "Mott-insulator" state converts into a superfluid (phase-coherent) state when the optical barriers are lowered or removed; (d) the behavior of a dilute Bose gas in the limit that the s-wave scattering length tends to infinity; (e) in a dilute two-species Fermi alkali-gas system having attractive inter-species interactions, to possible limits on the transition temperature to the BCS state, and/or on the pairing amplitudes.The second major thrust is more speculative in nature; an attempt is being made to implement quantitatively a proposal made several years ago concerning the "universal" behavior of amorphous materials (glasses), namely that this behavior has nothing to do with the ubiquitous presence in these materials of "tunneling-two-level systems," which is required by the currently established model, but rather is a quite generic consequence of the presence at short length scales of any kind of excitations that are not harmonic and that can be coupled by the elastic medium.In addition to these major two projects, work is ongoing on quenching in very degenerate Fermi systems and on cuprate superconductivity.The proposed projects are at the intellectual core of modern condensed matter physics and success will be of fundamental consequence. Likewise, successful completion of this research will affect many other fields of study. Students will be trained and the principal investigator is also writing a textbook on quantum liquids for beginning graduate students.%%%This grant addresses theoretical questions in two challenging problems in emerging areas in condensed matter physics - that branch of physics that deals with matter in its solid or liquid phases. The first area is theoretical studies of the properties of dilute, ultra-cold gases that condense into a unique quantum phase. Discovery of this unique phase, predicted many years ago, has earned recent Nobel Prizes. Much research has yet to be done. The second research area is the strange and "universal" behavior of amorphous materials (glasses). At very low temperatures diverse materials exhibit common properties indicating a common mechanism. A possible model for these common properties will be explored.The proposed projects are at the intellectual core of modern condensed matter physics and success will be of fundamental consequence. Likewise, successful completion of this research will affect many other fields of study. Students will be trained and the principal investigator is also writing a textbook on quantum liquids for beginning graduate students.***