Quantum properties of the electron field in Kerr-Newman black hole manifolds

We study some spectral features of the one-particle electron Hamiltonian obtained by separating the Dirac equation in a Kerr-Newman black hole background. We find that the essential spectrum includes the whole real line. As a consequence, there is no gap in the spectrum and discrete eigenvalues are not allowed for any value of the black hole charge $Q$ and angular momentum $J$. Our spectral analysis will be also related to the dissipation of the black hole angular momentum and charge.Comment: 9 pages, uses revte

Electronic States of Graphene Grain Boundaries

We introduce a model for amorphous grain boundaries in graphene, and find that stable structures can exist along the boundary that are responsible for local density of states enhancements both at zero and finite (~0.5 eV) energies. Such zero energy peaks in particular were identified in STS measurements [J. \v{C}ervenka, M. I. Katsnelson, and C. F. J. Flipse, Nature Physics 5, 840 (2009)], but are not present in the simplest pentagon-heptagon dislocation array model [O. V. Yazyev and S. G. Louie, Physical Review B 81, 195420 (2010)]. We consider the low energy continuum theory of arrays of dislocations in graphene and show that it predicts localized zero energy states. Since the continuum theory is based on an idealized lattice scale physics it is a priori not literally applicable. However, we identify stable dislocation cores, different from the pentagon-heptagon pairs, that do carry zero energy states. These might be responsible for the enhanced magnetism seen experimentally at graphite grain boundaries.Comment: 10 pages, 4 figures, submitted to Physical Review

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

Massive Dirac particles on the background of charged de-Sitter black hole manifolds

We consider the behavior of massive Dirac fields on the background of a charged de-Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordstr\"{o}m-de-Sitter one, the Nariai case and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the non-existence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and it is shown to hold true even for extremal cases. Furthermore, we shift our attention on the very interesting problem of the quantum discharge of the black holes. Following Damour-Deruelle-Ruffini approach, we show that the existence of level-crossing between positive and negative continuous energy states is a signal of the quantum instability leading to the discharge of the black hole, and in the cases of the Nariai geometry and of the ultracold geometries we also calculate in WKB approximation the transmission coefficient related to the discharge process.Comment: 19 pages, 11 figures. Macro package: Revtex4. Changes concern mainly the introduction and the final discussion in section VI; moreover, Appendix D on the evaluation of the Nariai transmission integral has been added. References adde

Rhodium metalloinsertor binding generates a lesion with selective cytotoxicity for mismatch repair-deficient cells

The DNA mismatch repair (MMR) pathway recognizes and repairs errors in base pairing and acts to maintain genome stability. Cancers that have lost MMR function are common and comprise an important clinical subtype that is resistant to many standard of care chemotherapeutics such as cisplatin. We have identified a family of rhodium metalloinsertors that bind DNA mismatches with high specificity and are preferentially cytotoxic to MMR-deficient cells. Here, we characterize the cellular mechanism of action of the most potent and selective complex in this family, [Rh(chrysi)(phen)(PPO)]^(2+) (Rh-PPO). We find that Rh-PPO binding induces a lesion that triggers the DNA damage response (DDR). DDR activation results in cell-cycle blockade and inhibition of DNA replication and transcription. Significantly, the lesion induced by Rh-PPO is not repaired in MMR-deficient cells, resulting in selective cytotoxicity. The Rh-PPO mechanism is reminiscent of DNA repair enzymes that displace mismatched bases, and is differentiated from other DNA-targeted chemotherapeutics such as cisplatin by its potency, cellular mechanism, and selectivity for MMR-deficient cells

Quantum properties of the Dirac field on BTZ black hole backgrounds

We consider a Dirac field on a $(1 + 2)$-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\infty}(r_+,\infty)^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $\mu$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\infty$ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the $(1 + 2)$-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.Comment: 19 pages; IOP styl

Perturbation Theory of Schr\"odinger Operators in Infinitely Many Coupling Parameters

In this paper we study the behavior of Hamilton operators and their spectra which depend on infinitely many coupling parameters or, more generally, parameters taking values in some Banach space. One of the physical models which motivate this framework is a quantum particle moving in a more or less disordered medium. One may however also envisage other scenarios where operators are allowed to depend on interaction terms in a manner we are going to discuss below. The central idea is to vary the occurring infinitely many perturbing potentials independently. As a side aspect this then leads naturally to the analysis of a couple of interesting questions of a more or less purely mathematical flavor which belong to the field of infinite dimensional holomorphy or holomorphy in Banach spaces. In this general setting we study in particular the stability of selfadjointness of the operators under discussion and the analyticity of eigenvalues under the condition that the perturbing potentials belong to certain classes.Comment: 25 pages, Late

Green's function for a Schroedinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.Comment: 14 page

The standards of practice for delivery of polypharmacy and chronic disease medication reviews by general practice clinical pharmacists: a consensus study.

Background: General practice in the UK is experiencing a crisis. Greater multidisciplinary working is a potential solution. The new general practice contract in Scotland encourages this and includes a new pharmacotherapy service to be delivered by General Practice Clinical Pharmacists (GPCPs). Consensus is lacking for the standards of practice for delivery of pharmacotherapy medication reviews (which are polypharmacy and chronic medication reviews) as part of this service. Aim: To identify and validate standards of practice for polypharmacy and chronic disease medication (pharmacotherapy level 3) reviews conducted by GPCPs. Method: A two-phased mixed-methods consensus methodology was used. Phase 1: An expert group of GPCPs (n = 4) and clinical pharmacist managers (n = 2) responsible for delivering the pharmacotherapy service used a Modified Nominal Group Technique to generate potential standards. Phase 2: Two-round Delphi survey involving GPCPs with ≥ 1 year of experience of working in general practice (n = 159). Results: The expert group identified 44 potential standards of practice for polypharmacy and chronic disease reviews. Practicing GPCPs indicated during the Delphi phase that the 44 standards were applicable to practice. The standards of practice covered seven main categories: skills, environment, qualifications, qualities and behaviours, knowledge, process and experience. Conclusion: Practicing GPCPs indicated that the standards identified by the expert group are acceptable and valid for current practice and the delivery of polypharmacy and chronic medication reviews. The application of these standards to practice may help GPCPs and general practices to ensure equitable delivery of patient care