Use of limit theorems in the theory of many-phonon processes

Yu. E. Perlin

Yu. E. Perlin

Nikolay V. Prokof'ev, Ilya Esterlis, Ar. Abanov +1 more

It is widely believed that in the adiabatic limit the Fermi liquid state of an electron-phonon system, described by Migdal-Eliashberg theory, remains stable until the dressed phonon softens. Our variational and analytic analysis of the prototypical Holstein model shows that, in a wide range of fillings both in 3D and 2D, a polaronic/bipolaronic state emerges before phonon softening; at small filling in 3D this happens already at weak coupling. We show that a polaronic/bipolaronic state emerges, upon increasing coupling, via an intermediate pseudogap-type mixed state, in which some fermions retain Fermi liquid behavior, yet Luttinger's theorem is violated. At even larger couplings the density of states gradually approaches its form in the atomic limit.

Nikolay V. Prokof'ev, Ilya Esterlis, Ar. Abanov +1 more

It is widely believed that in the adiabatic limit the Fermi liquid state of an electron-phonon system, described by Migdal-Eliashberg theory, remains stable until the dressed phonon softens. Our variational and analytic analysis of the prototypical Holstein model shows that, in a wide range of fillings both in 3D and 2D, a polaronic/bipolaronic state emerges before phonon softening; at small filling in 3D this happens already at weak coupling. We show that a polaronic/bipolaronic state emerges, upon increasing coupling, via an intermediate pseudogap-type mixed state, in which some fermions retain Fermi liquid behavior, yet Luttinger's theorem is violated. At even larger couplings the density of states gradually approaches its form in the atomic limit.

Fabio Bagarello

Tobias Lausch, Artur Widera, Michael Fleischhauer

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergences in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. This makes it necessary to include second-order phonon scattering above a crossover temperature ${T}_{2}\mathrm{ph}$. ${T}_{2}\mathrm{ph}$ scales inversely with the system size and is much smaller than currently experimentally accessible.