What present theory of superconductivity needs from many-body physicists

Alexandre M. Zagoskin

H. Forehlich

Alexandre M. Zagoskin

Paul W. Ayers, Dimitri Van Neck, Patrick Bultinck +2 more

Because the molecular Hamiltonian contains only one-body and two-body operators, the two-electron reduced density matrix contains all the information needed to evaluate the energy, as well as most of the other properties of interest to chemists and molecular physicists. A straightforward minimization of the energy is confounded by the N-representability problem, which can only be addressed approximately. The resulting theory has both advantages and disadvantages compared to more-traditional wavefunction-based approaches. The biggest advantage is that it performs well even when the molecule of interest has strong multireference character and the “Hartree-Fock plus correction” wavefunction paradigms fail. Also, as a lower-bound method, it provides a complementary tool to variational wavefunction approaches. The biggest disadvantages are the computational cost (which may yet be surmounted) and problems with dissociation and degeneracy that seem to afflict all approaches based on a “reduced” description of the system.

Kathryn Levin, Qijin Chen

The study of ultracold trapped fermionic gases is a rapidly exploding subject [1-10] which is defining new directions in condensed matter and atomic physics. It has also captured the attention of physicists who study color superconducting quark matter as well as nuclear matter [11-13]. Indeed, it is hard, in recent times, to find a subfield of physics which appeals this broadly to the research community. As we come to understand the gases, experimentalists will move to address fermionic atoms in optical lattices; this will provide important insight to condensed matter physicists as analogue systems for “solving ” intractable many body problems. What makes these gases (and lattices) so important is their remarkable tunability and controllability. Using a Feshbach resonance, one can tune the attractive two-body interaction from weak to strong, and thereby make a smooth crossover from a BCS superfluid to a Bose-Einstein condensation (BEC) [14, 15]. Not only does this allow high transition temperatures Tc (relative to the Fermi energy EF) but it may also provide insights into the high temperature cuprate superconductivity [16-19]. Furthermore, one can tune the population of the two spin states, essentially at will, in this way, allowing exploration [20-22] of exotic polarized phases such as the FFLO [23-25] superfluids, of interest to condensed matter, nuclear and particle physicists. One will be able to tune the lattice parameters such as bandwidth, on-site repulsion, even random disorder, etc and thereby study the famous, and as yet, unsolved Hubbard model Hamiltonian. This paper will concentrate on those issues relating to the effects which are of current interest to experimentalists. In particular, we will study BCS-BEC crossover in atomic Fermi gases, looking at a wide range of different experiments. Our group has been principally interested in the effects of finite temperature [26, 17, 18] and in this review, we will discuss how temperature T enters into the standard crossover theory, and how temperature can be measured, and how temc○

Godfrey Ejiroghene Akpojotor, Alexander O.E. Animalu