Quantum Diagonalization Method in the Tavis-Cummings Model

To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.Comment: Latex files, 21 pages; minor changes. To appear in International Journal of Geometric Methods in Modern Physic

Synthesis of IB-01212 by multiple N-methylations of peptide bonds.

There are many natural peptides with multiple N-methylamino acids that exhibit potent attractive biological activities. N-methylation of a peptide bond(s) is also one of the standard approaches in medicinal chemistry of bioactive peptides, to improve the potency and physicochemical properties, especially membrane permeability. In this study, we investigated a facile synthesis process of N-methylated peptides via simultaneous N-methylation of several peptide bonds in the presence of peptide bonds that were not to be methylated. As a model study, we investigated the synthesis of the antiproliferative depsipeptide, IB-01212. We used a pseudoproline to protect the non-methylated peptide bond during a simultaneous N-methylation with MeI-Ag[2]O. Using further manipulations including a dimerization/cyclization process, IB-01212 and its derivatives were successfully synthesized. A preliminary structure-activity relationship study demonstrated that the symmetric structure contributed to the potent cytotoxic activity of IB-01212