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The finite temperature QCD transition for physical quark masses is a crossover. For smaller quark masses a first-order phase transition is expected. Using Symanzik improved gauge and stout improved fermion action for 2+1 flavour staggered QCD we give estimates/bounds for the phase line separating the first-order region from the crossover one. The calculations are carried out on two different lattice spacings. Our conclusion for the critical mass is $m_0 \lesssim 0.07 \cdot m_{phys}$ for $N_T=4$ and $m_0 \lesssim 0.12 \cdot m_{phys}$ for $N_T=6$ lattices. Comment: Talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany. 7 pages, 6 figures

The quark gluon plasma is formed in heavy-ion collisions, and it can be described by solutions of relativistic hydrodynamics. In this paper we utilize perturbative hydrodynamics, where we study first order perturbations on top of a known solution. We investigate the perturbations on top of the Hubble flow. From this perturbative solution we can give the form of the particle emitting source and calculate observables of heavy-ion collisions. We describe the source function and the single-particle momentum spectra for a spherically symmetric solution. Comment: 7 pages, 3 figures

Ballistic electrons confined to a billiard and subject to spin--orbit coupling of the Rashba type are investigated, using both approximate semiclassical and exact quantum--mechanical methods. We focus on the low--energy part of the spectrum that has negative eigenvalues. When the spin precession length is smaller than the radius of the billiard, the low--lying energy eigenvalues turn out to be well described semiclassically. Corresponding eigenspinors are found to have a finite spin polarization in the direction perpendicular to the billiard plane. Comment: 5 pages, 2 figures

Using a tight binding model we calculate the conductance of monovalent atomic chains for different contact geometries. The leads connected to the chains are modelled as semi-infinite fcc lattices with different orientations and couplings. Our aim is twofold: To check the validity of a three-parametric conductance formula for differently oriented leads, and to investigate the geometry dependence of the conductance oscillations. We show that the character of these oscillations depends strongly on the geometry of the chain-lead coupling. Comment: 9 pages, 5 figures, 1 table

Suppose $${\Lambda}$$ is a discrete infinite set of nonnegative real numbers. We say that $${\Lambda}$$ is type 1 if the series $$s(x)=\sum\nolimits_{\lambda\in\Lambda}f(x+\lambda)$$ satisfies a “zero-one” law. This means that for any non-negative measurable $$f \colon \mathbb{R} \to [0,+ {\infty})$$ either the convergence set $$C(f, {\Lambda})=\{x: s(x)<+ {\infty} \}= \mathbb{R}$$ modulo sets of Lebesgue zero, or its complement the divergence set $$D(f, {\Lambda})=\{x: s(x)=+ {\infty} \}= \mathbb{R}$$ modulo sets of measure zero. If $${\Lambda}$$ is not type 1 we say that $${\Lambda}$$ is type 2. The exact characterization of type 1 and type 2 sets is not known. In this paper we continue our study of the properties of type 1 and 2 sets. We discuss sub and supersets of type 1 and 2 sets and give a complete and simple characterization of a subclass of dyadic type 1 sets. We discuss the existence of type 1 sets containing infinitely many elements independent over the rationals. Finally, we consider unions and Minkowski sums of type 1 and 2 sets.