The Dirac point electron in zero-gravity Kerr--Newman spacetime

Dirac's wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr--Newman spacetime is studied in a zero-gravity limit; here, "zero-gravity" means $G\to 0$, where $G$ is Newton's constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint; the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. Some of our results extend to a generalization of the zero-$G$ Kerr--Newman spacetime with different electric-monopole-to-magnetic-dipole-moment ratio.Comment: 49 pages, 17 figures; referee's comments implemented; the endnotes in the published version appear as footnotes in this preprin

Coherence scale of the Kondo lattice

It is shown that the large-N approach yields two energy scales for the Kondo lattice model. The single-impurity Kondo temperature, $T_K$, signals the onset of local singlet formation, while Fermi liquid coherence sets in only below a lower scale, $T^{\star}$. At low conduction electron density $n_c$ ("exhaustion" limit), the ratio $T^{\star}/T_K$ is much smaller than unity, and is shown to depend only on $n_c$ and not on the Kondo coupling. The physical meaning of these two scales is demonstrated by computing several quantities as a function of $n_c$ and temperature.Comment: 4 pages, 4 eps figures. Minor changes. To appear in Phys. Rev. Let

"Exhaustion" Physics in the Periodic Anderson Model using Iterated Perturbation Theory

We discuss the "exhaustion" problem in the context of the Periodic Anderson Model using Iterated Perturbation Theory(IPT) within the Dynamical Mean Field Theory. We find that, despite its limitations, IPT captures the exhaustion physics, which manifests itself as a dramatic, strongly energy dependent suppression of the effective Anderson impurity problem. As a consequence, low energy scales in the lattice case are strongly suppressed compared to the "Kondo scale" in the single-impurity picture. The IPT results are in qualitative agreement with recent Quantum Monte Carlo results for the same problem.Comment: 13 preprint pages including 1 table and 4 eps figures, replaced by revised version, accepted for publication in Europhysics Letters, added references and conten

The low-energy scale of the periodic Anderson model

Wilson's Numerical Renormalization Group method is used to study the paramagnetic ground state of the periodic Anderson model within the dynamical mean-field approach. For the particle-hole symmetric model, which is a Kondo insulator, we find that the lattice Kondo scale T_0 is strongly enhanced over the impurity scale T_K; T_0/T_K ~ exp(1/3I), where I is the Schrieffer-Wolff exchange coupling. In the metallic regime, where the conduction band filling is reduced from one, we find characteristic signatures of Nozi\`eres exhaustion scenario, including a strongly reduced lattice Kondo scale, a significant suppression of the states available to screen the f-electron moment, and a Kondo resonance with a strongly enhanced height. However, in contrast to the quantitative predictions of Nozi\`eres, we find that the T_0 ~ T_K with a coefficient which depends strongly on conduction band filling.Comment: 11 pages, 9 figures, submitted to Phys. Rev.

Dynamic correlations in doped 1D Kondo insulator: Finite-T DMRG study

The finite-T DMRG method is applied to the one-dimensional Kondo lattice model to calculate dynamic correlation functions. Dynamic spin and charge correlations, S_f(omega), S_c(omega), and N_c(omega), and quasiparticle density of states rho(omega) are calculated in the paramagnetic metallic phase for various temperatures and hole densities. Near half filling, it is shown that a pseudogap grows in these dynamic correlation functions below the crossover temperature characterized by the spin gap at half filling. A sharp peak at omega=0 evolves at low temperatures in S_f(omega) and N_c(omega). This may be an evidence of the formation of the collective excitations, and this confirms that the metallic phase is a Tomonaga-Luttinger liquid in the low temperature limit.Comment: 5 pages, 6 Postscript figures, REVTe

Kondo screening and exhaustion in the periodic Anderson model

We investigate the paramagnetic periodic Anderson model using the dynamical mean-field theory in combination with the modified perturbation theory which interpolates between the weak and strong coupling limits. For the symmetric PAM, the ground state is always a singlet state. However, as function of the hybridization strength, a crossover from collective to local Kondo screening is found. Reducing the number of conduction electrons, the local Kondo singlets remain stable. The unpaired f-electrons dominate the physics of the system. For very low conduction electron densities, a large increase of the effective mass of the quasiparticles is visible, which is interpreted as the approach of the Mott-Hubbard transition.Comment: 10 pages, 8 figures, accepted by Phys. Rev.

Two energy scales and slow crossover in YbAl3

Experimental results for the susceptibility, specific heat, 4f occupation number, Hall effect and magnetoresistance for single crystals of YbAl$_{3}$ show that, in addition to the Kondo energy scale $k_{B}T_{K}$ $$ 670K, there is a low temperature scale $T_{coh}<50$K for the onset of coherence. Furthermore the crossover from the low temperature Fermi liquid regime to the high temperature local moment regime is slower than predicted by the Anderson impurity model. These effects may reflect the behavior of the Anderson Lattice in the limit of low conduction electron density.Comment: Ten pages, including three figure

Dynamics of Bianchi type I elastic spacetimes

We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotropic matter model that naturally generalizes perfect fluids. Based on our dynamical systems formulation of the equations we are able to prove that (i) toward the future all solutions isotropize; (ii) toward the initial singularity all solutions display oscillatory behavior; solutions do not converge to Kasner solutions but oscillate between different Kasner states. This behavior is associated with energy condition violation as the singularity is approached.Comment: 28 pages, 11 figure

Slow crossover in YbXCu4 intermediate valence compounds

We compare the results of measurements of the magnetic susceptibility Chi(T), the linear coefficient of specific heat Gamma(T)=C(T)/T and 4f occupation number nf(T) for the intermediate valence compounds YbXCu4 (X = Ag, Cd, In, Mg, Tl, Zn) to the predictions of the Anderson impurity model, calculated in the non-crossing approximation (NCA). The crossover from the low temperature Fermi liquid state to the high temperature local moment state is substantially slower in the compounds than predicted by the NCA; this corresponds to the ''protracted screening'' recently predicted for the Anderson Lattice. We present results for the dynamic susceptibility, measured through neutron scattering experiments, to show that the deviations between theory and experiment are not due to crystal field effects, and we present x-ray-absorption fine-structure (XAFS) results that show the local crystal structure around the X atoms is well ordered, so that the deviations probably do not arise from Kondo Disorder. The deviations may correlate with the background conduction electron density, as predicted for protracted screening.Comment: Submitted to Physical Review B on June 7, 2000, accepted for publication November 2, 2000. Changes to the original manuscript include: 1) a discussion of the relation of the slow crossover to the conduction electron density; 2) a discussion of the relation of the reported results to earlier photoemission results; and, 3) minor editorial change

Relativistic Elasticity

Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially frame-indifferent case and, on Minkowski space, reduces to the latter in the non-relativistic limit . The field equations are cast into a first -- order symmetric hyperbolic system. As a consequence one obtains local--in--time existence and uniqueness theorems under various circumstances.Comment: 23 page