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arXiv:1508.07069

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

Alexander L. Burin

Published Aug 28, 2015• 0 citations
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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 $α$ 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.

DOI
10.48550/arxiv.1508.07069

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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 ααα 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.
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Abstract. We consider a quantum mechanical system consisting of a linear chain of harmonic oscillators coupled by a nearest neighbor interaction. The system configuration can be closed (periodic boundary conditions) or open (non-periodic case). We show that such systems can be considered as Wigner Quantum Systems (WQS), thus yielding extra solutions apart from the canonical solution. In particular, a class of WQS-solutions is given in terms of unitary representations of the Lie superalgebra gl(1|n). In order to determine physical properties of the new solutions, one needs to solve a number of interesting but difficult representation theoretical problems. We present these problems and their solution, and show how the new results yield attractive properties for the quantum system (energy spectrum, position probabilities, spacial properties). 1.
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