Exact solution for low energy quantum anharmonic vibrations in a long polymer chain

TL;DR

This paper presents an exact algorithm for calculating quantum vibrational eigenstates in a long polymer chain with anharmonic interactions, enabling detailed analysis of vibrational dynamics relevant to energy transport and quantum information.

Contribution

It introduces a novel resonant approach to determine vibrational eigenstates in anharmonic chains, extending understanding of quantum vibrational behavior in polymers.

Findings

Eigenstates are encoded by integer sequences.

Single phonon states exhibit coherent oscillations.

Applications to vibrational energy transport and quantum informatics are discussed.

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 $\alpha$ 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.