Monotonicity of the polaron energy

Tadahiro Miyao

Published 2012-11-02, updated 2013-09-03Version 2

In condensed matter physics, the polaron has been fascinating subject. It is described by the Hamiltonian of H. Fr\"ohlich. In this paper, the Fr\"ohlich Hamiltonian is investigated from a viewpoint of the self-dual cone analysis proposed in Miyao (2011). This point of view clarifies the monotonicity of polaron energy, i.e., denoting the lowest energy of the Fr\"ohlich Hamiltonian with the ultraviolet cutoff $\Lambda$ by $E_{\Lambda}$, we prove $E_{\Lambda}>E_{\Lambda'}$ for $\Lambda<\Lambda'$.