  Photoisomerization in a system with multiple electronic states and anharmonic
potential surfaces in a dissipative environment is investigated using a
rigorous numerical method employing quantum hierarchical Fokker-Planck
equations (QHFPE) for multi-state systems. We have developed a computer code
incorporating QHFPE for general-purpose computing on graphics processing units
(GPGPU) that can treat multi-state systems in phase space with any strength of
diabatic coupling of electronic states under non-perturbative and non-Markovian
system-bath interactions. This approach facilitates the calculation of both
linear and nonlinear spectra. We computed Wigner distributions for excited,
ground, and coherent states. We then investigated excited state dynamics
involving transitions among these states by analyzing linear absorption and
transient absorption processes and multi-dimensional electronic spectra with
various values of the heat bath parameters. Our results provide predictions for
spectroscopic measurements of photoisomerization dynamics. The motion of
excitation and ground state wavepackets and their coherence involved in the
photoisomerization were observed as the profiles of positive and negative peaks
of two-dimensional spectra.
