44 research outputs found
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 is large enough, bipolarons or
multi-polarons will form. When passing through the critical 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
. 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
, while `uncertainty principle' localization energies decay more rapidly,
as .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