Nucleon Spin in QCD: Old Crisis and New Resolution

We discuss the shortfalls of existing resolutions of the long-standing gauge invariance problem of the canonical decomposition of the nucleon spin to the spin and angular momentum of quarks and gluons. We provide two logically flawless expressions of nucleon spin which have different physical meanings, using the gauge independent Abelian decomposition. The first one is based on the assumption that all gluons (binding and valence gluons) contribute to the nucleon spin, but the second one is based on the assumption that only the binding gluons (and the quarks) contribute to it. We propose the second expression to be the physically correct one

Strong 3p -T1u Hybridization in Ar@C60

Multilayers of fullerenes with and without endohedral Ar units, C60 and Ar@C60, were investigated by photoemission and density functional theory. The stoichiometry and the endohedral nature of Ar is checked by x-ray photoelectron spectroscopy and x-ray photoelectron diffraction. Valence band ultraviolet photoemission spectra show a strong hybridisation of the Ar 3p valence shell with the 6T1u molecular orbital of C60. A hybridisation gap of 1.6 +/- 0.2 eV is found. This is in agreement with density functional theory (DFT) that predicts 1.47 eV, and indicates Ar@C60 to be a noble gas compound with a strong coupling between Ar and the C60 cage. No giant Ar photoemission cross section as predicted for the gas phase in [Phys. Rev. Lett. 99, 243003 (2007)] was found

Reconfiguration on sparse graphs

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is possible to transform S into T by a sequence of vertex additions and deletions such that each intermediate set is also a feasible solution of size bounded by k. We study reconfiguration variants of two classical vertex-subset problems, namely Independent Set and Dominating Set. We denote the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete on graphs of bounded bandwidth and W[1]-hard parameterized by k on general graphs. We show that ISR is fixed-parameter tractable parameterized by k when the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we answer positively an open question concerning the parameterized complexity of the problem on graphs of bounded treewidth. Moreover, our techniques generalize recent results showing that ISR is fixed-parameter tractable on planar graphs and graphs of bounded degree. For DSR, we show the problem fixed-parameter tractable parameterized by k when the input graph does not contain large bicliques, a class of graphs which includes graphs of bounded degeneracy and nowhere-dense graphs

Power-law tails from multiplicative noise

We show that the well-known Langevin equation, modeling the Brownian motion and leading to a Gaussian stationary distribution of the corresponding Fokker-Planck equation, is changed by the smallest multiplicative noise. This leads to a power-law tail of the distribution at large enough momenta. At finite ratio of the correlation strength for the multiplicative and additive noise the stationary energy distribution becomes exactly the Tsallis distribution.Comment: 4 pages, LaTeX, revtex4 style, 2 figure