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We describe mean field calculations of the properties of the dilute t J model for high T c superconductors. We first discuss a physical motivation for the model in terms of the effects of oxygen vacancies and the appropriate parametrization for a qualitative description of high T c superconductors. We present results on the local carrier density, the transition temperature as a function of carrier concentration, oxygen vacancy concentration and elastic scattering impurity concentration. These are compared with experiment on high T c materials. We conclude that the model is a promising framework for understanding high T c materials microscopically.

Experimental high T c systems are intrinsically strongly disordered by point defects. Here we consider two possible consequences of this fact: 1) The magnetic phases of prominent models for high T c are strongly affected. We present numerical calculations of the phase diagram of the Hubbard model as a function of the concentration of point defects and of the band filling in the Hartree Fock approximation. The results may explain the failure to experimentally observe a spin density wave phase predicted by Hartree Fock calculations without defects. 2) The superconductivity of the system may be strongly affected. We consider a model in which the pairing interactions are generated by point defects. We present numerical data on the density of states, T c and local charge density in the BCS approximation, while taking full account of the disorder. The stability of the BCS state was also checked using a variational Monte Carlo calculation.

Halley began the discussion of the theory of excitations in Bulk 4He with some remarks about the nature of the theoretical problem of describing liquid 4He. The main point is that the helium-helium potentiate has a hard core, e.g. V(r) ∝ (σ/r)12. This means that its Fourier transform V(Q) is extremely large (essentially infinite) at all wavelengths. A theory which expands in powers of V(Q) (as in the formulation of the Glyde-Griffin theory presented this morning) is unlikely to be reliable. The hard core problem is what stimulated Feynman and later Feenberg and others including Krotschek, Campbell, Pandharipande and Manousakis to take a different approach. The variational ground state and excited states which they find take full account of the hard core problem, so they can use microscopic atomic potentials. They then can do a convergent pertubation theory in the interactions of the approximate variational quasiparticle states. The achievements of this approach are impressive and numerous: correct ground state energy, correct phonon-roton spectrum, multiparticle terms S(q,ω), and a condensate fraction ≈ 10%. A weakness is that the theory has not been fully extended to finite temperatures.

We describe calculations of the inelastic light scattering spectrum for frequencies of the order of up to several times the roton frequency. The calculations are based on the two body approximation in a theoretical description of the fluid due to Pandiharipande and Manousakis. We use the results to determine the role of two mechanisms for the development of multiquasiparticle structure in the spectrum which we proposed earlier. We find that the mechanism arising from quasiparticle anharmonicities plays a much larger role in producing these structures in the spectrum than does the mechanism arising from nonlinearities in the relation between the density and quasiparticle operators. We find that the three quasiparticle couplings on which the theory rests depend strongly on the magnitudes and directions of the quasiparticles in a way which strongly favors processes involving colinear momenta. This has striking qualitative effects on the details of the predicted spectra.

The chapter by Dr. Stinchcombe has established connections between functions defined as $$\begin{gathered} G_r (t,t') = > _r \hfill \\ = - i\theta (t - t') \hfill \\ \end{gathered}$$ and scattering cross-sections and susceptibilities observed directly in experiments on condensed matter.

We consider a model with two metals (modeled for the present as jellium) separated by a barrier described by a potential V(x). We show that the current density j can be fixed by adding a term H’ to the energy which is of the form: $$H' = - m\int_{ - \infty }^\infty {v(x)j(x)d^3 x}$$ where v(x) is a Lagrange multiplier function which depends on the position x. We show that v(x) may be interpreted as the hydrodynamic velocity of the electrons in the junction so that v(x) depends on the electron density n(x) as j = v(x). The expectation value of j(x) is independent of x by current conservation. The computational part of the tunneling problem is thus reduced to the self-consistent solution of the Schroedinger equation with one additional term: $$\left( {H_o - mv(x)^2 /2} \right)\varphi _p (x) = E_p \varphi _p (x)$$ This equation is solved self-consistently with boundary conditions appropriate to waves incident from the left and right (which form an orthonormal complete set when appropriately normalized). The result shows that, within this model, a finite current can pass through the barrier with no electrostatic potential drop. We will argue that this result does not depend on the local density approximation (which is the only computational approximation in the model) but is to be expected because there is no dissipative mechanism in the model.