In the context of the Anderson theory of high Tc cuprates, we develop a BCS theory for Luttinger liquids. If the Luttinger interaction is much stronger than the BCS potential we find that the BCS equation is quite modified compared to usual BCS equation for Fermi liquids. In particular Tc predicted by the BCS equation for Luttinger liquids is quite higher than the usual Tc for Fermi liquids. 1 ...

Density-functional theory is applied to compute the groundstate energies of quantum hard-sphere solids. The modified weighteddensity approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis, combined with an enhanced hy...

We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action’s interaction function. The classic derivation...

We develop and describe new approaches to the problem of interacting Fermions in spatial dimensions greater than one. These approaches are based on generalizations of powerful tools previously applied to problems in one spatial dimension. We begin with a review of one-dimensional interacting Fermions. We then introduce a simplified model in two spatial dimensions to study the role that spin and...

In this paper, we present new estimates for the entropy dissipation of Landau-Fermi-Dirac equation (with hard or moderately soft potentials) in terms a weighted relative Fisher information adapted to equation. Such are used studying large time behaviour equation, as well providing priori (in potential case). An important feature such is that they uniform with respect quantum parameter. Conseque...

Solvable models have greatly contributed to our understanding of the dynamics of quantum field theories. Two such (1 + 1)–dimensional models solvable in the large N limit which are “classics” in this regard, are the ’t Hooft model [1], gauge theory with fermionic matter, and the Gross–Neveu model [2], a model with a four fermi coupling. (For reviews on the subject, see, for instance, [3].) Both...

The understanding of thermal conductance in both classical and quantum mechanical systems is one of the fundamental problems of non-equilibrium statistical mechanics. A particular aspect that has attracted much interest is the observation that autonomous translation invariant systems in dimensions one and two exhibit anomalously large conductivity. The canonical example here is a chain of anhar...