Magnetic Field Effects on Neutron Diffraction in the Antiferromagnetic Phase of UPt3UPt_3

We discuss possible magnetic structures in UPt$_3$ based on our analysis of elastic neutron-scattering experiments in high magnetic fields at temperatures $T<T_N$. The existing experimental data can be explained by a single-{\bf q} antiferromagnetic structure with three independent domains. For modest in-plane spin-orbit interactions, the Zeeman coupling between the antiferromagnetic order parameter and the magnetic field induces a rotation of the magnetic moments, but not an adjustment of the propagation vector of the magnetic order. A triple-{\bf q} magnetic structure is also consistent with neutron experiments, but in general leads to a non-uniform magnetization in the crystal. New experiments could decide between these structures.Comment: 5 figures included in the tex

Multiplicative structure of 2x2 tropical matrices

We study the algebraic structure of the semigroup of all $2 \times 2$ tropical matrices under multiplication. Using ideas from tropical geometry, we give a complete description of Green's relations and the idempotents and maximal subgroups of this semigroup.Comment: 21 pages, 5 figure

Holographic Duals of Flavored N=1 Super Yang-Mills: Beyond the Probe Approximation

We construct backreacted D3/D7 supergravity backgrounds which are dual to four-dimensional N=1 and N=2 supersymmetric Yang-Mills at large N_c with flavor quarks in the fundamental representation of SU(N_c). We take into account the backreaction of D7-branes on either AdS(5) x S(5) or AdS(5) x T^{1,1}, or more generically on backgrounds where the space transverse to the D3-branes is Kaehler. The construction of the backreacted geometry splits into two stages. First we determine the modification of the six-dimensional space transverse to the D3 due to the D7, and then we compute the warp factor due to the D3. The N=2 background corresponds to placing a single stack of N_f D7-branes in AdS(5) x S(5). Here the Kaehler potential is known exactly, while the warp factor is obtained in certain limits as a perturbative expansion. By placing another D7'probe in the backreacted D3/D7 background, we derive the effect of the D7-branes on the spectrum of the scalar fluctuations to first order in N_f. The two systems with N=1 supersymmetry that we discuss are D3/D7/D7' and D3/D7 on the conifold. In both cases, the Kaehler potential is obtained perturbatively in the number of D7-branes. We provide all the ingredients necessary for the computation of each term in the expansion, and in each case give the first few terms explicitly. Finally, we comment on some aspects of the dual gauge theories.Comment: 39 pp, no figures; v.2 section 2.2 modified, singularities clarifie

Numerical propagation of high energy cosmic rays in the Galaxy I: technical issues

We present the results of a numerical simulation of propagation of cosmic rays with energy above $10^{15}$ eV in a complex magnetic field, made in general of a large scale component and a turbulent component. Several configurations are investigated that may represent specific aspects of a realistic magnetic field of the Galaxy, though the main purpose of this investigation is not to achieve a realistic description of the propagation in the Galaxy, but rather to assess the role of several effects that define the complex problem of propagation. Our simulations of Cosmic Rays in the Galaxy will be presented in Paper II. We identified several effects that are difficult to interpret in a purely diffusive approach and that play a crucial role in the propagation of cosmic rays in the complex magnetic field of the Galaxy. We discuss at length the problem of the extrapolation of our results to much lower energies where data are available on the confinement time of cosmic rays in the Galaxy. The confinement time and its dependence on particles' rigidity are crucial ingredients for 1) relating the source spectrum to the observed cosmic ray spectrum; 2) quantifying the production of light elements by spallation; 3) predicting the anisotropy as a function of energy.Comment: 29 pages, 12 figures, submitted to JCA