T-matrix approach to the phonon-mediated Casimir interaction

Abstract

We develop a theory of the phonon mediated Casimir interaction between two point-like impurities, which is based on the single impurity scattering T-matrix approach. Within this, we show that the Casimir interaction at $T=0$ falls off as a power law with the distance between the impurities. We find that the power in the weak and in the unitary phonon-impurity scattering limits differs, and we relate the power law to the low-energy properties of the single impurity scattering T-matrix. In addition, we consider the Casimir interaction at finite temperature and show that at finite temperatures the Casimir interaction becomes exponential at large distances.

arXiv comment8 pages, 10 figures

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Cited by in corpus (6)

• Induced correlations between impurities in a one-dimensional quenched Bose gas
• Universal van der Waals Force Between Heavy Polarons in Superfluids
• Interactions mediated by atoms, photons, electrons, and excitons
• Magnonic Casimir Effect in Ferrimagnets
• Many-impurity phonon Casimir effect in atomic chains
• Phonon Casimir effect in polyatomic systems