expmv22kT

expmv22kT refers to a specialized numerical operation used in linear algebra and computational physics: it denotes the action of the matrix exponential exp(tA) on a vector v with the scalar t taken as 22kT, where k is Boltzmann's constant and T is temperature. The shorthand expmv describes computing exp(tA) v without forming exp(tA) explicitly, a technique favored for large sparse matrices.

Mathematically, given a square matrix A and a vector v, expmv22kT computes y = exp(tA) v with t = 22 k_B T. This avoids computing the full matrix exponential, which would be costly for large systems. The result y is the propagated state after time t under the linear dynamical system x'(t) = A x(t) with initial condition x(0)=v. The use of a temperature-scaled time parameter is common in simulations where thermal effects influence system evolution.

Computational methods commonly used for expmv-like tasks include Krylov subspace methods (such as Arnoldi or Lanczos processes) to approximate exp(tA) v, and scaling-and-squaring techniques combined with Padé approximants when forming or approximating exp(tA) is feasible. The Expokit library by Ruey S. Sidje is a foundational reference for expmv-style algorithms. Modern implementations tailor these approaches to handle sparse or structured matrices and complex time parameters.

Context and usage: expressing t as 22 k_B T appears in simulations of thermally activated processes, diffusion, or quantum dynamics where Boltzmann factors influence the evolution operator. The exact interpretation depends on units and model specifics; in many workflows, t becomes a dimensionless time through appropriate normalization.

In practice, expmv22kT is a code-specific label or convention rather than a universal standard, and its availability depends on the software package used.