π+−π−\pi^+ - \pi^- Asymmetry and the Neutron Skin in Heavy Nuclei

In heavy nuclei the spatial distribution of protons and neutrons is different. At CERN SPS energies production of $\pi^+$ and $\pi^-$ differs for $pp$, $pn$, $np$ and $nn$ scattering. These two facts lead to an impact parameter dependence of the $\pi^+$ to $\pi^-$ ratio in $^{208}Pb + ^{208}Pb$ collisions. A recent experiment at CERN seems to confirm qualitatively these predictions. It may open a possibility for determination of neutron density distribution in nuclei.Comment: 6 pages and 2 figures, a talk by A.Szczurek at the international conference MESON2004, June 4-8, Cracow, Polan

Thermodynamics of Adiabatically Loaded Cold Bosons in the Mott Insulating Phase of One-Dimensional Optical Lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.Comment: 10 pages, 6 figure

Properties of noncommutative axionic electrodynamics

Using the gauge-invariant but path-dependent variables formalism, we compute the static quantum potential for noncommutative axionic electrodynamics, and find a radically different result than the corresponding commutative case. We explicitly show that the static potential profile is analogous to that encountered in both non-Abelian axionic electrodynamics and in Yang-Mills theory with spontaneous symmetry breaking of scale symmetry.Comment: 4 pages. To appear in PR

Zeno Dynamics in Quantum Statistical Mechanics

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Further, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium.Comment: 15 pages, AMSLaTeX; typos corrected, references updated and added, acknowledgements added, style polished; revised version contains corrections from published corrigend

FORTRAN optical lens design program

Computer program uses the principles of geometrical optics to design optical systems containing up to 100 planes, conic or polynomial aspheric surfaces, 7 object points, 6 colors, and 200 rays. This program can be used for the automatic design of optical systems or for the evaluation of existing optical systems

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

Bounding and approximating parabolas for the spectrum of Heisenberg spin systems

We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w.r.t. its neighbours is constant for all N spins. The coefficients of the bounding parabolas are given in terms of special eigenvalues of the N times N coupling matrix which are usually easily evaluated. In addition we show that the bounding parabolas, if properly shifted, provide very good approximations of the true boundaries of the spectrum. We present numerical examples of frustrated rings, a cube, and an icosahedron.Comment: 8 pages, 3 figures. Submitted to Europhysics Letter

Type Ia supernova counts at high z: signatures of cosmological models and progenitors

Determination of the rates at which supernovae of Type Ia (SNe Ia) occur in the early Universe can give signatures of the time spent by the binary progenitor systems to reach explosion and of the geometry of the Universe. Observations made within the Supernova Cosmology Project are already providing the first numbers. Here it is shown that, for any assumed SNe Ia progenitor, SNe Ia counts up to $m_{R}\simeq 23-26$ are useful tests of the SNe Ia progenitor systems and cosmological tracers of a possible non-zero value of the cosmological constant, $\Lambda$. The SNe Ia counts at high redshifts compare differently with those at lower redshifts depending on the cosmological model. Flat $\Omega_{\Lambda}$--dominated universes would show a more significant increase of the SNe Ia counts at $z \sim 1$ than a flat, $\Omega_{M} = 1$ universe. Here we consider three sorts of universes: a flat universe with $H_{0} = 65 km s^{-1} Mpc^{-1}$, $\Omega_{M} = 1.0$, $\Omega_{\Lambda} = 0.0$; an open universe with $H_{0} = 65 km s^{-1} Mpc^{-1}$, $\Omega_{M} = 0.3$, $\Omega_{\Lambda} = 0.0$; and a flat, $\Lambda$--dominated universe with $H_{0} = 65 km s^{-1} Mpc^{-1}$, $\Omega_{M} = 0.3$, $\Omega_{\Lambda} = 0.7$). On the other hand, the SNe Ia counts from one class of binary progenitors (double degenerate systems) should not increase steeply in the $z= 0$ to $z= 1$ range, contrary to what should be seen for other binary progenitors. A measurement of the SNe Ia counts up to $z \sim 1$ is within reach of ongoing SNe Ia searches at high redshifts.Comment: 16 pages, incl. 2 figures. To appear in ApJ (Letters