Symplectic properties of algorithms and simulation methods

Symplectic algorithms are investigated for their phase space conserving properties for thermo-statted Hamiltonians commonly used in equilibrium molecular dynamics. Corresponding algorithms can be generated for the dissipative Sllod equations of motion for Couette flow in two dimensions. This study focuses on the verification of the conjugate pairing rule (CPR) for such systems. For thermostatted Hamiltonian dynamics, adiabatic and thermostatted Dolls algorithms, the CPR is satisfied at each time step during a simulation unlike the Sllod case in which there are small yet finite deviations from the CPR.