A plot of the Hamiltonian and potential energy surfaces overlaid withe the Hamiltonian vector field (Figure 2) was generated using:
PotentialField2(2,'steps',20,'startPoint',[1,1],'npoints',1000,'step_size',1e-3,'save',true)
A plot of a series of tranjectories tilted out of the plane, together with a top-down projection, (Figure 3) was generated using:
PotentialField8(2,'steps',5,'npoints',1000,'step_size',1e-3,'save',true)
and a plot of the series of three-dimensional surfaces for decreasing values of the inter-state separation distance c (Figure 4) was generated using:
PotentialField11(3,1,'steps',100,'npoints',3000,'step_size',1e-3,'save',true)
PotentialField11(3,0.5,'steps',100,'npoints',3000,'step_size',1e-3,'save',true)
PotentialField11(3,0.25,'steps',100,'npoints',3000,'step_size',1e-3,'save',true)
PotentialField11(3,0.2,'steps',100,'npoints',3000,'step_size',1e-3,'save',true)
PotentialField11(3,0.125,'steps',100,'npoints',3000,'step_size',1e-3,'save',true)
PotentialField11(3,0.063,'steps',100,'npoints',3000,'step_size',1e-3,'save',true)
Two views plots of the surface with either the endpoints fixed (Figure 5A) or the midpoint fixed (Figure 5B) were created using:
PotentialField4(2,'steps',10,'npoints',200,'step_size',5e-3,'save',true) # Figure 5A
PotentialField4_1(2,'steps',10,'npoints',200,'step_size',5e-3,'save',true) # Figure 5A
Calculation of the inverse of the combination matrix B was perfomed using
combination_matrix(3)
combination_matrix(4)
for use in the Wolfram Notebook Moment of inertia matrix.nb, wherein the n × n matrices for the three- and four-state systems are computed symbollically.