Formulating an Integrator
Using the large-P approximation
To advance the system over the time interval T
- break Liouville operator into displacement parts iLx + iLp
- write
- apply the Trotter expansion, and interpret T/P as a discretized time dt
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- application of P times advances the system (approximately) through T
An integrator formulated this way will be both time-reversible and symplectic