Phonon-mediated Casimir interaction between finite mass impurities

Abstract

The Casimir effect, a two-body interaction via vacuum fluctuations, is a fundamental property of quantum systems. In solid state physics it emerges as a long-range interaction between two impurity atoms via virtual phonons. In the classical limit for the impurity atoms in $D$ dimensions the interaction is known to follow the universal power-law $U(r)\sim r^{-D}$. However, for finite masses of the impurity atoms on a lattice, it was predicted to be $U(r)\sim r^{-2D-1}$ at large distances. We examine how one power-law can change into another with increase of the impurity mass and in presence of an external potential. We provide the exact solution for the system in one-dimension. At large distances indeed $U(r)\sim r^{-3}$ for finite impurity masses, while for the infinite impurity masses or in an external potential it crosses over to $U(r)\sim r^{-1}$ . At short distances the Casimir interaction is not universal and depends on the impurity mass and the external potential.

arXiv comment5+7 pages, 5+6 figures

References in corpus (16)

• New Developments in the Casimir Effect
• Stiction, Adhesion Energy and the Casimir Effect in Micromechanical Systems
• Confinement induced molecules in a 1D Fermi gas
• High-precision calculations of dispersion coefficients, static dipole polarizabilities, and atom-wall interaction constants for alkali-metal atoms
• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Casimir interaction between a perfect conductor and graphene described by the Dirac model
• Casimir Effect Between World-Branes in Heterotic M-Theory
• Casimir effect in de Sitter and Anti-de Sitter braneworlds
• Casimir forces between defects in one-dimensional quantum liquids
• Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
• Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance
• Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids
• Oscillating Casimir force between impurities in one-dimensional Fermi liquids
• Matching the observational value of the cosmological constant
• Indirect forces between impurities in one-dimensional quantum liquids
• Mesoscopic Casimir forces from effects of discrete particle number in the quantum vacuum

Cited by in corpus (16)

• Induced correlations between impurities in a one-dimensional quenched Bose gas
• The Casimir-like effect in a one-dimensional Bose gas
• Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas
• Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas
• Impurities in a one-dimensional Bose gas: the flow equation approach
• Universal van der Waals Force Between Heavy Polarons in Superfluids
• Magnonic Casimir Effect in Ferrimagnets
• In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas
• Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas
• Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons
• Classical Casimir force from a quasi-condensate of light
• Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity
• T-matrix approach to the phonon-mediated Casimir interaction
• Many-impurity phonon Casimir effect in atomic chains
• Phonon Casimir effect in polyatomic systems
• Effective approaches to the dynamical properties of two distinguishable Bose polarons