On the Spectral properties of Multi-branes, M2 and M5 branes

In this note we summarize some of the properties found in several papers. We characterize spectral properties of the quantum mechanical hamiltonian of theories with fermionic degrees of freedom beyond semiclassical approximation. We obtain a general class of bosonic polynomial potentials for which the Schr\"oedinger operator has a discrete spectrum. This class includes all the scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and ABJM theories. We also give a sufficient condition for discreteness of the spectrum for supersymmmetric and non supersymmetric theories with a fermionic contribution. We characterize then the spectral properties of different theories: the BMN matrix model, the supermembrane with central charges and a bound state of $N$ D2 with $m$ D0. We show that, while the first two models have a purely discrete spectrum with finite multiplicity, the latter has a continuous spectrum starting from a constant given in terms of the monopole charge.Comment: 10pg, Latex, Contributions to the Conference XVI European Workshop on String Theory 2010, Madrid June 14-18, 201

Magnetic behavior of lamellar mnps3 and cdps3 composites with a paramagnetic manganese(iii) macrocyclic guest

Indexación: ScieloSix new composites derived from the intercalation of the MPS3 phases (M = MnII, CdIII) with the macrocyclic manganese(III) complex [MnL(H2O)2].NO3(H2O) (LH2 = Schiff base macrocyclic ligand derived from the condensation of 2-hydroxy-5-methy1-1,3-benzene-dicarbaldehyde and 1,2-diamine-benzene) were obtained by two different synthetic procedures: a conventional and a microwave assisted method. The composites [MnL]0.25K0.15Mn0.80 PS3(H2O)~1.0 (1), and [MnL]0.25K0.15Cd 0. 80PS3(H2O)~0.5 (2) were obtained by the conventional method, after stirring a suspension of the corresponding potassium precursor and the macrocyclic complex for two weeks, while [MnL]0.35K0.15Mn0.80 PS3(H2O)~1.0 (3) and [MnL]0.25K0.15Cd 0. 80PS3(H2O)~0.5 (4) after stirring for four weeks at room temperature. Using a microwave assisted reaction permitted to obtain in a shorter period of time as compared with the conventional method, composites [MnL]0.20K0.15Mn0.80 PS3(H2O)~1.0 (5) and [MnL]0.15K0.15Cd 0. 80PS3(H2O)~0.5 (6). All the M = MnII, MnIII composites show a bulk antiferromagnetic behavior. However, the spontaneous magnetization present at low temperature in the potassium precursor K0.40Mn0.80 PS3(H2O)~1.0 is observable in composite [MnL]0.20K0.15Mn0.80 PS3(H2O)~1.0 (5), while it is completely absent in composites [MnL]0.25K0.15Mn0.80 PS3(H2O)~1.0 (1) and [MnL]0.35K0.15Mn0.80 PS3(H2O)~1.0 (3). Keywords: Intercalation; MPS3 phases; MnIII macrocyclic complex; microwave assisted synthesis; magnetic properties