Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids

Abstract

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as $1/r^3$, much slower than the van der Waals interaction $\sim 1/r^6$, where $r$ is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.

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• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Induced correlations between impurities in a one-dimensional quenched Bose gas
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• Magnonic Casimir Effect in Ferrimagnets
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• Phonon-mediated Casimir interaction between finite mass impurities
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• Long range mediated interactions in a mixed dimensional system
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• Nucleus--nucleus interactions in the inner crust of neutron stars
• Analytic thermodynamic properties of the Lieb-Liniger gas
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• Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons
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• The density of a one-dimensional Bose gas far from an impurity