Symplectic split of Hamiltonian with complex term

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SUMMARY

The discussion centers on the feasibility of implementing 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 the additional imaginary component, V_2, and its role within the Hamiltonian framework. The consensus indicates that while traditional symplectic integrators handle real-valued Hamiltonians effectively, the introduction of complex terms necessitates a reevaluation of existing methodologies to maintain symplectic properties.

PREREQUISITES
  • Understanding of symplectic geometry and its applications in Hamiltonian mechanics.
  • Familiarity with symplectic integrators and their implementation in numerical simulations.
  • Knowledge of complex analysis, particularly in the context of Hamiltonian systems.
  • Experience with computational tools for simulating dynamical systems, such as MATLAB or Python libraries.
NEXT STEPS
  • Research the implementation of complex Hamiltonians in numerical simulations.
  • Explore advanced symplectic integrators that accommodate complex terms.
  • Study the effects of imaginary components on the stability of dynamical systems.
  • Investigate existing literature on symplectic methods in quantum mechanics.
USEFUL FOR

Researchers in mathematical physics, computational physicists, and anyone involved in the numerical analysis of Hamiltonian systems with complex terms.

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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