Towards a full ab initio theory of strong electronic correlations in nanoscale devices

In this paper I give a detailed account of an ab initio methodology for describing strong electronic correlations in nanoscale devices hosting transition metal atoms with open $d$- or $f$-shells. The method combines Kohn-Sham Density Functional Theory for treating the weakly interacting electrons on a static mean-field level with non-perturbative many-body methods for the strongly interacting electrons in the open $d$- and $f$-shells. An effective description of the strongly interacting electrons in terms of a multi-orbital Anderson impurity model is obtained by projection onto the strongly correlated subspace properly taking into account the non-orthogonality of the atomic basis set. A special focus lies on the ab initio calculation of the effective screened interaction matrix U for the Anderson model. Solution of the effective Anderson model with the One-Crossing approximation or other impurity solver techniques yields the dynamic correlations within the strongly correlated subspace giving rise e.g. to the Kondo effect. As an example the method is applied to the case of a Co adatom on the Cu(001) surface. The calculated low-bias tunnel spectra show Fano-Kondo lineshapes similar to those measured in experiments. The exact shape of the Fano-Kondo feature as well as its width depend quite strongly on the filling of the Co $3d$-shell. Although this somewhat hampers accurate quantitative predictions regarding lineshapes and Kondo temperatures, the overall physical situation can be predicted quite reliably.Comment: 30 pages, 6 figure

Holographic Bound from Second Law

The holographic bound that the entropy (log of number of quantum states) of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas is widely regarded a desideratum of any fundamental theory, but some exceptions occur. By suitable black hole gedanken experiments I show that the bound follows from the generalized second law for two broad classes of isolated systems: generic weakly gravitating systems composed of many elementary particles, and quiescent, nonrotating strongly gravitating configurations well above Planck mass. These justify an early claim by Susskind.Comment: Invited talk at Marcel Grossman IX meeting in Rome, July 2000; improved version of Phys. Lett. B 481, 339 (2000). 7 pages, LaTeX with included mprocl.st

An alternative to the dark matter paradigm: relativistic MOND gravitation

MOND, invented by Milgrom, is a phenomenological scheme whose basic premise is that the visible matter distribution in a galaxy or cluster of galaxies alone determines its dynamics. MOND fits many observations surprisingly well. Could it be that there is no dark matter in these systems and we witness rather a violation of Newton's universal gravity law ? If so, Einstein's general relativity would also be violated. For long conceptual problems have prevented construction of a consistent relativistic substitute which does not obviously run afoul of the facts. Here I sketch TeVeS, a tensor-vector-scalar field theory which seems to fit the bill: it has no obvious conceptual problems and has a MOND and Newtonian limits under the proper circumstances. It also passes the elementary solar system tests of gravity theory.Comment: 18 pages, invited talk at the 28th Johns Hopkins Workshop on Current Problems in Particle Theory, June 2004, Johns Hopkins University, Baltimore. Corrections to Sec.7 for error pointed out by D. Giannios. To appear online in JHEP Proceedings of Scienc

Do We Understand Black Hole Entropy ?

I review various proposals for the nature of black hole entropy and for the mechanism behind the operation of the generalized second law. I stress the merits of entanglement entropy {\tenit qua\/} black hole entropy, and point out that, from an operational viewpoint, entanglement entropy is perfectly finite. Problems with this identification such as the multispecies problem and the trivialization of the information puzzle are mentioned. This last leads me to associate black hole entropy rather with the multiplicity of density operators which describe a black hole according to exterior observers. I relate this identification to Sorkin's proof of the generalized second law. I discuss in some depth Frolov and Page's proof of the same law, finding it relevant only for scattering of microsystems by a black hole. Assuming that the law is generally valid I make evident the existence of the universal bound on entropy regardless of issues of acceleration buoyancy, and discuss the question of why macroscopic objects cannot emerge in the Hawking radiance.Comment: plain TeX, 18 pages, Plenary talk at Seventh Marcel Grossman meeting at Stanford University, gr-qc/9409015, revised to include a figur

Preparing the State of a Black Hole

Measurements of the mass or angular momentum of a black hole are onerous, particularly if they have to be frequently repeated, as when one is required to transform a black hole to prescribed parameters. Irradiating a black hole of the Kerr-Newman family with scalar or electromagnetic waves provides a way to drive it to prescribed values of its mass, charge and angular momentum without the need to repeatedly measure mass or angular momentum throughout the process. I describe the mechanism, which is based on Zel'dovich-Misner superradiance and its analog for charged black holes. It represents a possible step in the development of preparation procedures for quantum black holes.Comment: Essay in honor of Mario Novello's sixtieth birthday. LaTeX 209, 12 pages, no figure

Disturbing the Black Hole

I describe some examples in support of the conjecture that the horizon area of a near equilibrium black hole is an adiabatic invariant. These include a Schwarzschild black hole perturbed by quasistatic scalar fields (which may be minimally or nonminimally coupled to curvature), a Kerr black under the influence of scalar radiation at the superradiance treshold, and a Reissner--Nordstr\"om black hole absorbing a charge marginally. These clarify somewhat the conditions under which the conjecture would be true. The desired ``adiabatic theorem'' provides an important motivation for a scheme for black hole quantization.Comment: 15 pages, LaTeX with crckapb style, to appear in ``The Black Hole Trail'', eds. B. Bhawal and B. Iyer (Kluwer, Dordrecht 1998

Optimizing entropy bounds for macroscopic systems

The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic energy has a unique maximum $(S/E)_\mathrm{max}$. A simple argument from quantum dynamics allows one to set a model--independent upper bound on $(S/E)_\mathrm{max}$ which is usually much tighter than the universal bound. We illustrate with two examples.Comment: 13 pages, 2 figures, LaTe

Statistics of black hole radiance and the horizon area spectrum

The statistical response of a Kerr black hole to incoming quantum radiation has heretofore been studied by the methods of maximum entropy or quantum field theory in curved spacetime. Neither approach pretends to take into account the quantum structure of the black hole itself. To address this last issue we calculate here the conditional probability distribution associated with the hole's response by assuming that the horizon area has a discrete quantum spectrum, and that its quantum evolution corresponds to jumps between adjacent area eigenvalues, possibly occurring in series, with consequent emission or absorption of quanta, possibly in the same mode. This "atomic" model of the black hole is implemented in two different ways and recovers the previously calculated radiation statistics in both cases. The corresponding conditional probably distribution is here expressed in closed form in terms of an hypergeometric function.Comment: RevTeX, 9 page

The Limits of Information

Black holes have their own thermodynamics including notions of entropy and temperature and versions of the three laws. After a light introduction to black hole physics, I recollect how black hole thermodynamics evolved in the 1970's, while at the same time stressing conceptual points which were given little thought at that time, such as why the entropy should be linear in the black hole's surface area. I also review a variety of attempts made over the years to provide a statistical mechanics for black hole thermodynamics. Finally, I discuss the origin of the information bounds for ordinary systems that have arisen as applications of black hole thermodynamics.Comment: LaTeX, 10 pages, Invited talk at International Conference on the Foundations of Statistical Mechanics, Jerusalem May 2000. To appear in the Dec. 2001 issue of Studies in the History and Philosophy of Modern Physics. Typos corrected and one reference adde

If vacuum energy can be negative, why is mass always positive?: Uses of the subdominant trace energy condition

Diverse calculations have shown that a relativistic field confined to a cavity by well defined boundary conditions can have a negative Casimir or vacuum energy. Why then can one not make a finite system with negative mass by confining the field in a some way? We recall, and justify in detail, the not so familiar subdominant trace energy condition for ordinary (baryon-electron nonrelativistic) matter. With its help we show, in two ways, that the mass-energy of the cavity structure necessary to enforce the boundary conditions must exceed the magnitude of the negative vacuum energy, so that all systems of the type envisaged necessarily have positive mass-energy.Comment: LaTeX, 19 pages, added references and some clarifying remarks. Conclusions unchange