Adiabatic Green's function technique and the transient behavior in time-dependent fermion-boson coupled models

TL;DR

This paper develops an adiabatic Green's function approach to analyze the transient spectral behavior in time-dependent fermion-boson models, revealing how sideband spectral weights diminish over time.

Contribution

It introduces a method to derive two-time Green's functions for time-dependent fermion-boson systems in the adiabatic limit, extending the Lang-Firsov model to dynamic couplings.

Findings

Sidebands lose spectral weight as coupling decreases over time

Adiabatic Green's function effectively describes transient spectral changes

Method applicable to related spin-boson models and quantum systems

Abstract

The Lang-Firsov Hamiltonian, a well-known solvable model of interacting fermion-boson system with sideband features in the fermion spectral weight, is generalized to have the time-dependent fermion-boson coupling constant. We show how to derive the two-time Green's function for the time-dependent problem in the adiabatic limit, defined as the slow temporal variation of the coupling over the characteristic oscillator period. The idea we use in deriving the Green's function is akin to the use of instantaneous basis states in solving the adiabatic evolution problem in quantum mechanics. With such "adiabatic Green's function" at hand we analyze the transient behavior of the spectral weight as the coupling is gradually tuned to zero. Time-dependent generalization of a related model, the spin-boson Hamiltonian, is analyzed in the same way. In both cases the sidebands arising from the fermion-boson coupling can be seen to gradually lose their spectral weights over time. Connections of our solution to the two-dimensional Dirac electrons coupled to quantized photons are discussed.