Various dynamical aspects of a non-trivial theory of gravitation in (1+1) dimensions are investigated. It is shown that many features of Einstein's general relativity for (3+1) dimensions are qualitatively and to some extent quantitatively duplicated in this theory, including gravitational collapse, cosmological solutions and gravitational waves. Contact with Newton's theory is made and post-Newtonian expansions of the theory give relativistic corrections, similar to those of general relativity. Therefore this theory is presented as viable for both pedagogical purposes as well as a laboratory for the testing of new theoretical ideas.
We show that the Kondo chain away from half-filling has a spin gap upon the
introduction of an additional direct Heisenberg coupling between localized
spins. This is understood in the weak-Kondo-coupling limit of the
Heisenberg-Kondo lattice model by bosonization and in the strong-coupling limit
by a mapping to a modified t-J model. Only for certain ranges of filling and
Heisenberg coupling does the spin gap phase extend from weak to strong
coupling.Comment: 4 pages RevTeX including 4 eps figures; minor corrections and
clarification
We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possible model for the weak-moment heavy-fermion compound URu 2 Si 2 , in terms of two low-lying f singlets in which the uranium moment is coupled by on-site exchange to the conduction electron spins. In the mean-field approximation for an extended range of parameters, we show that the conduction electron magnetization responds logarithmically to f -moment formation, that the ordered moment in the antiferromagnetic state is anomalously small, and that the Néel temperature is of the order observed. The model gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat. The majority of the specific heat jump at the Néel temperature arises from the formation of a spin gap in the conduction electron spectrum. We also discuss the single-impurity version of the model and speculate on ways to increase the specific heat coefficient. In the limits of small bandwidth and of small Ising-Kondo coupling, we find that the model corresponds to anisotropic Heisenberg and Hubbard models respectively. PACS numbers: 71.10. Fd, 71.27.+a, 71.70.Ch, 75.30.Mb Γ t1 1 higher singlets doublets and t2 J J J -+ z Γ FIG. 5. Spectrum of the crystal-field Hamiltonian, showing states related to the low-lying singlets by application of the operator J.
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