results that I'd like to share

The results from my PhD and later work on the coefficients of fractional parentage (CFPs) have been summarized in a paper published in the International Journal of Quantum Chemistry, © John Wiley & Sons, Inc., in 1994. I consider that the ideas by Julius Kaniauskas, when materialized, have appeared to be quite powerful in revealing the coherent picture of what the CFPs in the second quantization are. Unfortunately, the paper is not available on the Web yet (year 1994 isn't accessible from Int.J.Quant.Chem. ), and the published version contains quite many irritating misprints in the mathematical expressions (partly my fault: I haven't been able to correct the proofs, but to make matters worse, I haven't ever submitted an errata). To remedy this situation, I take a freedom as an author of the work to offer the double-checked version here: . The second quantization "CFPs", their properties and generalizations, the "CFPs"-like expansions of the many-fermion wave functions of coupled momenta in the second quantization representation are all there. Enjoy!

Since 1996 I have been guided by Professor John Hertz of NORDITA in modeling neural networks. I have collaborated with Thomas Z. Lauritzen, Andrea Fazzini and Sergio Solinas in Professor's laboratory during my several stays at NORDITA. The problem that we have investigated is the emergence of spontaneous asynchronous chaotic activity in neural networks comprising populations of excitatory and inhibitory neurons. And we have tried to model this activity via the computer simulations of networks consisting of "simple neurons" (with the key parameters chosen to be biologically plausible). Specifically, I have developed an ifnet C++ code for simulating the network of "integrate & fire" leaky neurons. Some of our results have been presented in the Society for Neuroscience (1999) meeting poster

In 2000, professor Romualdas Karazija sugggested to write a paper on the application of the particle-hole pair approach to explain some pecularities of spectra of free atoms and ions (original idea by J.Kaniauskas, again). The key idea is that the creation or annihilation of the "electric dipole"-coupled vacancy-electron pairs provide the main contribution to many observed emission, photoexcitation and Auger spectra. In other words, the eigenfunctions of the excited atoms are almost the eigenfunctions of the number of such vacancy-electron pairs, too. We succeeded in relating the experimentally known concentration of the strongest transitions on the high-energy side of some emission, photoexcitation and Auger spectra of atoms to the existence of a formal additional selection rule for the number of these vacancy-electron pairs. The paper "Additional selection rule for some emission, photoexcitation and Auger spectra" has appeared in J. Phys. B: At. Mol. Opt. Phys., 2001, V. 34, No. 23, L741-L747, and is available at

Andrius Bernotas
Institute of Theoretical Physics and Astronomy
A. Goštauto 12, 2600 Vilnius, Lithuania