Approximation of excitonic absorption in disordered systems using a compositional component weighted CPA

Employing a recently developed technique of component weighted two particle Green's functions in the CPA of a binary substitutional alloy $A_cB_{1-c}$ we extend the existing theory of excitons in such media using a contact potential model for the interaction between electrons and holes to an approximation which interpolates correctly between the limits of weak and strong disorder. With our approach we are also able to treat the case where the contact interaction between carriers varies between sites of different types, thus introducing further disorder into the system. Based on this approach we study numerically how the formation of exciton bound states changes as the strengths of the contact potentials associated with either of the two site types are varied through a large range of parameter values.Comment: 27 pages RevTeX (preprint format), 13 Postscript figure file

alpha'-exact entropies for BPS and non-BPS extremal dyonic black holes in heterotic string theory from ten-dimensional supersymmetry

We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the alpha'-exact statistical entropies obtained from microstate counting (D=4) and AdS/CFT correspondence (D=5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R^2-truncated (four-derivative) actions (D-dimensional N=2 off-shell supersymmetric or Gauss-Bonnet) were used, which give the entropies agreeing (at best) just for BPS black holes. The key property of the solutions, which enabled us to tackle the action containing infinite number of terms, is vanishing of the Riemann tensor \bar{R}_{MNPQ} obtained from torsional connection defined with \bar{\Gamma} = \Gamma - H/2. Morover, if every monomial of the remaining part of the effective action would contain at least two Riemanns \bar{R}_{MNPQ}, it would trivially follow that our solutions are exact solutions of the full heterotic effective action in D=10. The above conjecture, which appeared (in this or stronger form) from time to time in the literature, has controversial status, but is supported by the most recent calculations of Richards (arXiv:0807.3453 [hep-th]). Agreement of our results for the entropies with the microscopic ones supports the conjecture. As for small black holes, our solutions in D=5 still have singular horizons.Comment: 28 pages; v2: minor changes, references added; v3: extended discussion on small black holes in sec. 5.4, more references added, accepted in JHE

Extremal black holes in D=5: SUSY vs. Gauss-Bonnet corrections

We analyse near-horizon solutions and compare the results for the black hole entropy of five-dimensional spherically symmetric extremal black holes when the N=2 SUGRA actions are supplied with two different types of higher-order corrections: (1) supersymmetric completion of gravitational Chern-Simons term, and (2) Gauss-Bonnet term. We show that for large BPS black holes lowest order \alpha' corrections to the entropy are the same, but for non-BPS are generally different. We pay special attention to the class of prepotentials connected with K3\times T^2 and T^6 compactifications. For supersymmetric correction we find beside BPS also a set of non-BPS solutions. In the particular case of T^6 compactification (equivalent to the heterotic string on $T^4\times S^1$) we find the (almost) complete set of solutions (with exception of some non-BPS small black holes), and show that entropy of small black holes is different from statistical entropy obtained by counting of microstates of heterotic string theory. We also find complete set of solutions for K3\times T^2 and T^6 case when correction is given by Gauss-Bonnet term. Contrary to four-dimensional case, obtained entropy is different from the one with supersymmetric correction. We show that in Gauss-Bonnet case entropy of small ``BPS'' black holes agrees with microscopic entropy in the known cases.Comment: 28 pages; minor changes, version to appear in JHE

Nonequilibrium critical dynamics of the relaxational models C and D

We investigate the critical dynamics of the $n$-component relaxational models C and D which incorporate the coupling of a nonconserved and conserved order parameter S, respectively, to the conserved energy density rho, under nonequilibrium conditions by means of the dynamical renormalization group. Detailed balance violations can be implemented isotropically by allowing for different effective temperatures for the heat baths coupling to the slow modes. In the case of model D with conserved order parameter, the energy density fluctuations can be integrated out. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of model C with n = 1 thus follows the behavior of other systems with nonconserved order parameter wherein detailed balance becomes effectively restored at the phase transition. For n >= 4, the energy density decouples from the order parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime (z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying critical exponents. Similarly, the nonequilibrium model C with spatially anisotropic noise and n < 4 allows for continuously varying exponents, yet with strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium perturbations leads to genuinely different critical behavior with softening only in subsectors of momentum space and correspondingly anisotropic scaling exponents. Similar to the two-temperature model B the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar type.Comment: Revtex, 23 pages, 5 eps figures included (minor additions), to appear in Phys. Rev.

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction