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Dispersion forces in a nondegenerate polaron gas
Using the Feynman path integral method and a theory of polarizable fluids, I evaluate properties of nondegenerate Fr¨ohlich polarons interacting in the strong coupling limit. At large enough densities and temperatures these properties are found to be mainly governed by the dispersion forces, i.e. attractive van-der-Waals interactions, which are no attributed to any permanent electric multipoles. Neglecting short-range correlations in the polaron gas, I have obtained an explicit expression for the dispersion contribution to the free energy of the system. The analysis of this contribution indicates that the dispersion effect is nonlinear and strongly cooperative at large enough densities of the polaron gas. The quasiparticles attract due to these forces leading to softening of the absorption peak, negativity of the dielectric function, and divergence of compressibility of the system. The main consequence of the dispersion forces is a quantum transition which results in a dielectric catastrophe considered as the onset of metallization. A possible excitonic phase consisting from quasiparticles with a nonzero dipole momentum is also examined. Comparing experimental data for metal-ammonia solutions, alkali-halide molten salts, and high-Tc superconducting cuprates, I find that dispersion forces may govern the behavior of self-trapped carries in these compounds.