Analyticity of The Ground State Energy For Massless Nelson Models

We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive an explicit expression for the ground state energy which is used to determine the effective mass.Comment: 33 pages, 1 figure, added a section on the calculation of the effective mas

Binding of Polarons and Atoms at Threshold

If the polaron coupling constant $\alpha$ is large enough, bipolarons or multi-polarons will form. When passing through the critical $\alpha_c$ from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explodes? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at $\alpha_c$. Similarly, we show that the same phenomenon occurs for atoms, e.g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schr\"odinger equation, and are very general. They use the fact that the Coulomb repulsion decays like $1/r$, while `uncertainty principle' localization energies decay more rapidly, as $1/r^2$.Comment: 19 page

Effect of screening of the electron-phonon interaction on the temperature of Bose-Einstein condensation of intersite bipolarons

Here we consider an interacting electron-phonon system within the framework of extended Holstein-Hubbard model at strong enough electron-phonon interaction limit in which (bi)polarons are the essential quasiparticles of the system. It is assumed that the electron-phonon interaction is screened and its potential has Yukawa-type analytical form. An effect of screening of the electron-phonon interaction on the temperature of Bose-Einstein condensation of the intersite bipolarons is studied for the first time. It is revealed that the temperature of Bose-Einstein condensation of intersite bipolarons is higher in the system with the more screened electron-phonon interaction.Comment: 6 pages, 4 figure