Exact solution for low energy quantum anharmonic vibrations in a long polymer chain
Abstract
We propose the algorithm for determining vibrational quantum eigenstates of periodic linear chain of atoms coupled by harmonic and third order anharmonic interactions (Fermi-Ulam-Pasta problem) in the long wavelength limit within the resonant approach. Eigenstates can be encoded by the sequence of integer numbers determining their energies and wavefunctions. Using these eigenstates we described a single phonon state time evolution showing coherent oscillations. The applications of theory to vibrational energy transport and quantum informatics are discussed.
Cite
@article{arxiv.1508.07069,
title = {Exact solution for low energy quantum anharmonic vibrations in a long polymer chain},
author = {Alexander L. Burin},
journal= {arXiv preprint arXiv:1508.07069},
year = {2016}
}
Comments
This manuscript need improvement because of the significant match of the results to the Luttinger liquid problem (Thanks to Dmitry Gutman for pointing that out). This match needs to be described and it can be used for the rigorous proof of the solutions found in the manuscript. The updated version will be posted as soon as the author will complete the revision