The kernel of Dirac operators on §3\S^3 and R3\R^3

In this paper we describe an intrinsically geometric way of producing magnetic fields on $\S^3$ and $\R^3$ for which the corresponding Dirac operators have a non-trivial kernel. In many cases we are able to compute the dimension of the kernel. In particular we can give examples where the kernel has any given dimension. This generalizes the examples of Loss and Yau (Commun. Math. Phys. 104 (1986) 283-290).Comment: 51 page

Underscreened Kondo effect in quantum dots coupled to ferromagnetic leads

We analyze the equilibrium transport properties of underscreened Kondo effect in the case of a two-level quantum dot coupled to ferromagnetic leads. Using the numerical renormalization group (NRG) method, we have determined the gate voltage dependence of the dot's spin and level-resolved spectral functions. We have shown that the polarization of the dot is very susceptible to spin imbalance in the leads and changes sign in the middle of the S=1 Coulomb valley. Furthermore, we have also found that by fine-tuning an external magnetic field one can compensate for the presence of ferromagnetic leads and restore the Kondo effect in the case of $S=1/2$ Coulomb valley. However, the underscreened Kondo effect cannot be fully recovered due to its extreme sensitivity with respect to the magnetic field.Comment: 7 pages, 6 figure

Interior Structures and Tidal Heating in the TRAPPIST-1 Planets

With seven planets, the TRAPPIST-1 system has the largest number of exoplanets discovered in a single system so far. The system is of astrobiological interest, because three of its planets orbit in the habitable zone of the ultracool M dwarf. Assuming the planets are composed of non-compressible iron, rock, and H$_2$O, we determine possible interior structures for each planet. To determine how much tidal heat may be dissipated within each planet, we construct a tidal heat generation model using a single uniform viscosity and rigidity for each planet based on the planet's composition. With the exception of TRAPPIST-1c, all seven of the planets have densities low enough to indicate the presence of significant H$_2$O in some form. Planets b and c experience enough heating from planetary tides to maintain magma oceans in their rock mantles; planet c may have eruptions of silicate magma on its surface, which may be detectable with next-generation instrumentation. Tidal heat fluxes on planets d, e, and f are lower, but are still twenty times higher than Earth's mean heat flow. Planets d and e are the most likely to be habitable. Planet d avoids the runaway greenhouse state if its albedo is $\gtrsim$ 0.3. Determining the planet's masses within $\sim0.1$ to 0.5 Earth masses would confirm or rule out the presence of H$_2$O and/or iron in each planet, and permit detailed models of heat production and transport in each planet. Understanding the geodynamics of ice-rich planets f, g, and h requires more sophisticated modeling that can self-consistently balance heat production and transport in both rock and ice layers.Comment: 34 pages, 3 tables, 4 figures. Accepted for publication in Astronomy & Astrophysics -- final version including corrections made in proof stag

Kondo "underscreening" cloud: spin-spin correlations around a partially screened magnetic impurity

We consider the spatial spin correlations around a partially screened spin-1 magnetic moment in a metal exhibiting the underscreened Kondo effect. We find that the underscreening of the impurity spin results in spatial spin correlations that are more pronounced as compared to the fully screened Kondo effect; their power-law decay is weaker because of characteristic logarithmic corrections at large distances. The spin correlator also changes sign as a function of distance to the impurity allowing for ferromagnetic correlations between conduction electron spin density and the local moment. The numerical findings are shown to be in agreement with the predictions deriving from an effective ferromagnetic Kondo Hamiltonian.Comment: 4+ pages, 2 figures, submitted to Phys. Rev.

Kondo screening cloud in a one dimensional wire: Numerical renormalization group study

We study the Kondo model --a magnetic impurity coupled to a one dimensional wire via exchange coupling-- by using Wilson's numerical renormalization group (NRG) technique. By applying an approach similar to which was used to compute the two impurity problem we managed to improve the bad spatial resolution of the numerical renormalization group method. In this way we have calculated the impurity spin - conduction electron spin correlation function which is a measure of the Kondo compensation cloud whose existence has been a long standing problem in solid state physics. We also present results on the temperature dependence of the Kondo correlations.Comment: published versio

New results and perspectives on R_{AA} measurements below 20 GeV CM-energy at fixed target machines

Transverse momentum spectra of pi^{+/-} at midrapidity are measured at high p_T in p+p and p+Pb collisions at 158 GeV/nucleon beam energy by the NA49 experiment. This study is complementary to our previous results on the same spectra from Pb+Pb collisions. The nuclear modification factors R_{A+A/p+p}, R_{p+A/p+p} and R_{A+A/p+A} as a function of p_T are extracted and compared to RHIC measurements, thus providing insight into the energy dependence of nuclear modification. The modification factor R_{A+A/p+A} proved to be consistent with our previous results on the central to peripheral modification factor R_{CP}. The limitation of our current p_T range is discussed and planned future upgrades are outlined. Some aspects of the FAIR-CBM experiment are also presented as a natural future continuation of the measurements at very high p_T.Comment: Proceedings of Quark Matter 200

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure