A concise approach to the calculation of the polaron ground-state energy

Ward Huybrechts

François Maria Peeters, J. T. Devreese

Nikolay N. Bogolubov, Alexey N. Kireev, A. M. Kurbatov

Wang Kelin, Wang Yi, Wan Shaolong

A concise approach for static polarons is extended to study the dynamic polaron system having nonspherical symmetry. The general properties of moving polarons, such as the ground-state energy, the phonon number, the effective mass, and the density distribution of phonon momentum---studied as functions of the total polaron momentum and electron-phonon coupling strength---are calculated numerically in a wide range of intermediate coupling strengths. In particular, a modified Fr\"ohlich Hamiltonian is derived for the problem of polaron momentum Q\ensuremath{\geqslant}1. \textcopyright{} 1996 The American Physical Society.

Davor Juretić

L. F. Lemmens, J. DE SITTER, J. T. Devreese

A ground-state theorem for the Fr\"ohlich polaron is derived. We show that the zeroth moment of the current-current correlation function is proportional to the kinetic energy of the polaron. While the electron-phonon interaction does not depend on the electron mass, the coupling constant $\ensuremath{\alpha}$ does; this allows us to relate the kinetic energy with the ground-state energy using the Feynman-Helmann theorem. As an example we compare the polaron ground-state energy on variational grounds with the ground-state energy obtained from the function $\ensuremath{\chi}(\ensuremath{\omega})$ calculated by Feynman, Hellwarth, Iddings, and Platzman. For $\ensuremath{\alpha}<5$ both ground-state energies turn out to be identical, as can be concluded from numerical calculations.