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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 D2 with 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
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