trotterised

The term "trotterised" refers to a mathematical operation involving a specific type of discretization of differential equations, particularly partial differential equations. It is named after the American mathematician Hale Trotter. Trotterisation is a method for approximating solutions to evolution equations, which are equations describing how a system changes over time. This technique is fundamental in the study of functional analysis and operator theory.

In essence, Trotterisation approximates the exponential of an operator, which is often a key component in the solution of linear evolution equations. It involves breaking down a complex operator into a sum of simpler operators. The approximation is achieved by considering the product of the exponentials of these simpler operators over small time steps. The core idea is that the exponential of a sum of operators can be approximated by the product of the exponentials of the individual operators, especially when the time step is small.

This method is particularly useful in situations where the direct computation of the exponential of a large or complex operator is computationally intractable. The Trotter-Lie-Trotter theorem is a central result in this area, providing conditions under which the approximation converges to the true solution as the time step approaches zero. It has applications in various fields, including quantum mechanics, where it is used to simulate the time evolution of quantum systems. The accuracy of the Trotterisation method depends on the size of the time step, with smaller steps generally leading to better approximations but requiring more computational effort.