Graduate Symplectic split of Hamiltonian with complex term

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The discussion centers on the feasibility of formulating a symplectic split integrator for Hamiltonian systems that include an imaginary term, specifically in the form H=T+V+iV_2. Participants explore the implications of incorporating the complex term V_2 and its potential effects on the integrator's properties. The conversation highlights the need for a clear definition of V_2 and its role within the Hamiltonian framework. There is an emphasis on understanding how the imaginary component interacts with traditional symplectic structures. Ultimately, the integration of complex terms in Hamiltonian systems raises significant questions about stability and accuracy in numerical simulations.
ematt
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Is it possible to express symplectic split integrator for Hamiltonian containing an extra imaginary term? For instance H=T+V+iV_2
 
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What is V_2 here?
 

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