We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite size periodic cluster. The dynamical mean field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, Φ-derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a Quantum Monte Carlo and Exact Enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the CDW transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

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The gravitational field resulting from static scalar field configurations is investigated by means of coupled Einstein-scalar equations. Imposing plane symmetry, the author obtains a family of exact soliton-like stable solutions representing thick cosmic membranes in a spacetime which is flat at spatial infinity. The physical properties of the cosmic membrane (such as thickness, surface energy density, and interior gravitational field) are derived without detailed knowledge of the scalar field, and it is shown that test particles are repelled by the gravitational field of the membrane. Finally, they discuss an interesting possibility of generating a spacetime foliation due to superposition of soliton-like configurations of the scalar field.

We present a mathematical framework for generating thick domain wall solutions to the coupled Einstein-scalar field equations which are (locally) plane symmetric. This approach leads naturally to two broad classes of walllike solutions. The two classes include all previously known thick domain walls. Although one of these classes is static and the other dynamic, the corresponding Einstein-scalar equations share the same mathematical structure independent of the assumption of any reflection symmetry. We also exhibit a class of thick static domain wall spacetimes with different asymptotic vacua.Our analyses of particle motion in such spacetimes raises the interesting possibility that static domain walls will possess a unique experimental signature.

We consider SU (N ) symmetric one dimensional quantum chains at finite temperature. For such systems the correlation lengths, ground state energy, and excited state energies are investigated in the framework of conformal field theory. The possibility of different types of excited states are discussed. Logarithmic corrections to the ground state energy and different types of excited states in the presence of a marginal opeartor, are calculated. Known results for SU (2) and SU (4) symmetric systems follow from our general formula.