Response theory extended system applications

This part introduces variational principles relevant to the quantum mechanics of bound stationary states. Chapter 4 covers well-known variational theory that underlies modern computational methodology for electronic states of atoms and molecules. Extension to condensed matter is deferred until Part III, since continuum theory is part of the formal basis of the multiple scattering theory that has been developed for applications in this subfield. Chapter 5 develops the variational theory that underlies independent-electron models, now widely used to transcend the practical limitations of direct variational methods for large systems. This is extended in Chapter 6 to time-dependent variational theory in the context of independent-electron models, including linear-response theory and its relationship to excitation energies. 

Equilibrium statistical mechanics is a first principle theory whose fundamental statements are general and independent of the details associated with individual systems. No such general theory exists for nonequilibrium systems and for this reason we often have to resort to ad hoc descriptions, often of phenomenological nature, as demonstrated by several examples in Chapters 1 and 8. Equilibrium statistical mechanics can however be extended to describe small deviations from equilibrium in a way that preserves its general nature. The result is Linear Response Theory, a statistical mechanical perturbative expansion about equilibrium. In a standard application we start with a system in thermal equilibrium and attempt to quantify its response to an applied (static- or time-dependent) perturbation. The latter is assumed small, allowing us to keep only linear terms in a perturbative expansion. This leads to a linear relationship between this perturbation and the resulting response. 

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