Chapter 5. Observables and perturbation theory

Lin Lin, Jianfeng Lu

Many properties of chemical or materials systems are characterized by how they respond to external perturbations. When the external perturbation is sufficiently small that only the leading-order perturbation is important, this is known as the linear response regime. It is in some sense analogous to the linear stability analysis of a dynamical system or that in fluid mechanics. This chapter will give an in-depth discussion of the linear response theory for both static and dynamic perturbations and their applications. The analysis will be from the perspective of the perturbation theory of Green's functions. Towards the end of the chapter, the perturbation theory of a many-body quantum system and its connection to DFT will also be briefly addressed.

Francisco Marcelo Fernández

S. Rajasekar, R. Velusamy

Approximation methods are developed for systems where the time dependence of the Hamiltonian is small, slowly varying or rapidly varying. These correspond to perturbation, adiabatic and sudden approximations respectively. In this chapter we consider the time-dependent perturbation theory applicable for small time-dependent perturbation. This is the case when we wish to investigate the response of systems to incident radiation. The incident electromagnetic wave makes the electric and magnetic potentials to oscillate and the perturbation is usually very small compared with the static Hamiltonian. The theory of time-dependent perturbation was developed by Dirac in 1927 [1]. In this chapter we discuss the theory for constant and harmonic perturbations applied during a finite time interval, adiabatic and sudden perturbations.

Victor Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract This chapter analyzes problems that deal with stationary perturbation theory (discrete spectrum); variational method; stationary perturbation theory (continuous spectrum); non-stationary perturbation theory (transitions in continuous spectrum); sudden perturbations; and adiabatic approximation.

C. Vargas‐Hernández