Dynamics MOC

Time evolution operator

A time evolution operator on some smooth manifold is a (not necessarily linear) operator describing the evolution of some point of a dynamical system. #m/def/dynamics In the case where time evolution is governed by a differential equation

where is a time-dependent vector field, then is the vector flow along so given any initial condition a solution is . In general has the semigroup property and thus .

Properties

• In the case where is given by a linear operator with , time evolution is given by the matrix exponential . See Quantum time evolution operator.

#state/develop | #lang/en | #SemBr