The Theory of Quantum Liquids

Philippe Nozières, David Pines

T. R. Kirkpatrick, D. Belitz

We develop a theory for a generic instability of a Fermi liquid in dimension d>1 against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase transition, which is driven by the effective interaction strength. A scaling theory in conjunction with an effective field theory for clean electrons is used to obtain the critical behavior of observables. In the Fermi-liquid phase the order-parameter susceptibility, which is measurable by tunneling, is predicted to diverge for 1<d<3.

David Pines

Vieri Mastropietro

In the context of the Anderson theory of high T c 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 T c predicted by the BCS equation for Luttinger liquids is quite higher than the usual T c for Fermi liquids. 1 The anomalous BCS equation The equivalent of BCS theory for a Luttinger liquid has not formally worked out, despite the relevance of such theory for the problem of superconductivity in the high-T c cuprates, see [1] or the discussion in the following section. Such theory should describe superconductors which in their normal state are Luttinger liquids. In this paper we develop such theory using constructive quantum field theory techniques, applied in many other Luttinger liquid problems, see [2], [3]. In particular, we compute in a rigorous way the BCS self-consistence equation for a spinni...

Fa Yueh Wu

Григорий Ефимович Воловик

Abstract There are two ways to study quantum liquids. One is the fully microscopic treatment, which can be realised either by numerical simulations of the many-body problem, or for some special ranges of the material parameters, analytically. The other is a phenomenological approach in terms of effective theories. The hierarchy of the effective theories corresponds to the low-frequency, long-wavelength dynamics of quantum liquids in different ranges of frequency. This chapter discusses the microscopic (atomic) physics of quantum liquids which is the analog of the Theory of Everything — the Planck scale physics, difference between microscopic particles and emerging quasiparticles, the interplay of microscopic and effective symmetries, the origin of fundamental constants and hierarchy of Planck energy scales in the ‘Theory of Everything’, vacuum pressure and vacuum energy and scenario of vanishing of cosmological constant. These are considered using the model of weakly interacting Bose gas, the model of quantum liquid, and the real liquid 4He.