Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at $T=0$ K

TL;DR

This paper derives an exact analytical expression for the energy spectrum of a quasiparticle interacting with two phonon modes at zero temperature, within a limited state model, revealing how interaction strength affects phonon populations.

Contribution

It provides the first exact analytical solution for the renormalized quasiparticle spectrum with two-mode phonon interaction in a limited state system at zero temperature.

Findings

Exact energy spectrum obtained

Analytical expressions for phonon numbers derived

Dependence on interaction strength analyzed

Abstract

Within unitary transformed Hamiltonian of Fr\"ohlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at $T=0$ K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.