Quantum chaos and 1/f noise

It is shown that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for different systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.     

Enantioselective 1,3-Dipolar Cycloaddition Using (Z)-α-Amidonitroalkenes as a Key Step to the Access to Chiral cis-3,4-Diaminopyrrolidines

The enantioselective 1,3-dipolar cycloaddition between imino esters and (Z)-nitroalkenes bearing a masked amino group in the β-position was studied using several chiral ligands and silver salts. The optimized reaction conditions were directly applied to the study of the scope of the reaction. The determination of the absolute configuration was evaluated using NMR experiments and electronic circular dichroism (ECD). The reduction and hydrolysis of both groups was performed to generate in an excellent enantiomeric ratio the corresponding cis-2,3-diaminoprolinate.     

Power spectrum of nuclear spectra with missing levels and mixed symmetries

Sequences of energy levels in nuclei are often plagued with missing levels whose number and position are unknown. It is also quite usual that all the quantum numbers of certain levels cannot be experimentally determined, and thus levels of different symmetries are mixed in the same sequence. The analysis of these imperfect spectra (from the point of view of spectral statistics) is unavoidable if one wants to extract some statistical information. The power spectrum of the δq${\delta }_q$ statistic has emerged in recent years as an important tool for the study of quantum chaos and spectral statistics. We derive analytical expressions for the observed power spectrum in terms of the fraction of observed levels and the number of mixed sequences. These expressions are tested with large shell model spectra simulating realistic experimental situations. A good estimation of the number of mixed symmetries and the fraction of missing levels is obtained by means of a least-squares fit in a wide set of different situations.     

Recoverable (R)- and (S)-binap-Ag(I) complexes for the enantioselective 1,3-dipolar cycloaddition reaction of azomethine ylides

The first enantioselective 1,3-dipolar cycloaddition reaction of amino acid derived azomethine ylides and maleimides catalyzed by very stable and recyclable chiral (R)- or (S)-binap-AgClO(4) complexes is described. The reactions are performed at room temperature, in good yields, with high endo diastereoselectivity and enantioselectivity, the complex being recovered by simple filtration.     

1/f alpha noise in spectral fluctuations of quantum systems

The power law 1/f(alpha) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1/f(alpha) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.     

Study of neutron rich neon isotopes

The half-lives andP _n -values of the neutron rich isotopes^26–29Ne have been determined. The results are compared to shell-model calculations and good agreement is found except for²⁹Ne, where the half-life exceeds the predictions by more than an order of magnitude. This unexpectedly long half-life can be explained as due to a fp intruder configuration.