Monotonicity of the polaron energy

Abstract

In condensed matter physics, the polaron has been fascinating subject. It is described by the Hamiltonian of H. Fröhlich. In this paper, the Fröhlich 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 Fröhlich Hamiltonian with the ultraviolet cutoff $\Lambda$ by $E_{\Lambda }$, we prove $E_{\Lambda }>E_{{\Lambda }^{\prime }}$ for $\Lambda <{\Lambda }^{\prime }$.

20 pages, Sec.1 rewritten

References in corpus (1)

• The translation invariant massive Nelson model: III. Asymptotic completeness below the two-boson threshold

Cited by in corpus (1)

• Monotonicity of the polaron energy II:General theory of operator monotonicity