Linear response theory

Linear response theory calculates how a system changes under a weak external disturbance, relating its response to equilibrium properties and correlation functions.

Susceptibility: A measure of how strongly a system responds to an applied perturbation. It quantifies the response that linear response theory predicts.
Statistical mechanics: The framework connecting microscopic states to macroscopic properties through probability and statistical averages. Linear response often derives predictions from equilibrium statistical ensembles.
Electrical conductivity: A material property measuring the current produced by an applied electric field. The Kubo formula calculates conductivity from equilibrium current correlations.
Nonlinear response theory: A framework for calculating higher-order changes caused by disturbances beyond first order. It retains terms that linear response discards when the disturbance is not sufficiently weak.
Kubo formula: A relation expressing linear response coefficients through equilibrium correlation functions. It gives the standard quantum-mechanical expression for response coefficients.
Perturbation theory: Methods for approximating a problem by expanding around a simpler reference system. A weak disturbance permits expansion to first order in its strength.
Optical conductivity: A frequency-dependent measure of a material’s electrical response to electromagnetic fields. It describes absorption and charge transport under oscillating fields.
Kinetic theory: A description of matter based on the statistical motion and collisions of its constituent particles. It often derives transport from distribution dynamics rather than equilibrium response correlations.
Retarded Green's function: A causal propagator that vanishes when its effect would precede its cause. Its causal structure encodes how disturbances influence later observables.
Correlation function: A quantity measuring statistical dependence between values of physical observables. Equilibrium correlations encode the fluctuations used to calculate response.

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