couplingparameter

Coupling parameter is a dimensionless quantity that measures the strength of interaction between components of a system or between terms in a model. It is typically defined as a ratio of characteristic interaction energy to a characteristic energy scale, or as the magnitude of a coupling constant normalized to appropriate units, so that its size indicates the regime of behavior and the validity of approximations.

In plasma physics, the coupling parameter Gamma is defined as Gamma = (q^2 / (4 pi epsilon0 a)) / (k_B T), where q is particle charge, a is a characteristic interparticle distance, and T is temperature. Gamma << 1 corresponds to weakly coupled plasmas, where kinetic theory applies; Gamma >> 1 indicates strongly coupled plasmas with non-ideal effects.

In condensed matter and molecular physics, coupling parameters such as the electron-phonon coupling strength lambda or the spin-phonon coupling g quantify the interaction between electrons or spins and lattice vibrations. These dimensionless parameters influence phenomena such as superconductivity, charge transport, and relaxation times.

In quantum field theory and statistical mechanics, coupling constants (often denoted g or α) act as multipliers of interaction terms. Their magnitude governs the convergence of perturbation expansions; small coupling allows perturbative calculations, while large coupling requires non-perturbative methods.

Determination and use: coupling parameters are estimated from experimental data or from ab initio calculations and then used to classify regimes, fit models, or determine system responses to external changes, such as temperature, density, or pressure. They also serve to scale variables and compare disparate systems via dimensionless analysis.

See also: coupling constant, dimensionless parameter, perturbation theory.