Phonon displacement distribution at T=0

Frédéric van Wijland

Physica A: Statistical Mechanics and its Applications, 2004, vol. 332, issue C, 360-366

Abstract: We compute the probability distribution function of the displacement squared of linearly coupled quantum oscillators in their ground state. We find it to be one of the extreme-value distributions, the Fisher–Tippett–Gumbel distribution, in d=1, while it is a Gaussian in d=2,3 dimensions. We also discuss the crossover to non-Gaussian distributions (at d=2,3) at finite temperature T. We observe that the quantum effects remain important for sizes ℓ(T)∼aTD/T, where a is the lattice spacing and TD is the Debye temperature.

Keywords: Phonons; Ground-state fluctuations; Distribution fuctions (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:332:y:2004:i:c:p:360-366

DOI: 10.1016/j.physa.2003.10.027

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