Is it possible to calculate and analytically solve 3dimensional polymer chain , modeled as elastic beads and springs, with harmonic interaction with the nearest neighbor ? Kindly suggest some reference to solve this problem. Is it possible to decouple hamiltonian of polymer chain in fourier space as we do in one dimensional linear chain with a periodic arrangement of particles and springs ?
It is very interested question
these links may help you Vingeshwaran
http://www.biosimu.org/publications/PDFs/gotlib-2D-Net-P1-mts00.pdf
http://power.itp.ac.cn/~suncp/papers/JCP/JCP97-2.PDF
http://padding.awardspace.com/polymerdynamics_Padding_part1.pdf
Yes you can, but the model would not be very realistic, since all particles would cluster around the center-of-mass of the entire polymer. Hence, the notion of nearest neighbor interaction becomes physically meaningless, since all particles are essentially equally close to each other.
Nevertheless, your model may be a starting point for more realistic ones. I will return to the solution you ask for; it is simple and mathematically beautiful.
If you want some references you should look up the work by Christos N. Likos.
He did a lot on knots of polymer chains.
Also Marisol Ripoll has done a lot of computer simulations concerning polymer chains.
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