Multi-dimensional spectroscopy represents a particularly insightful tool for
investigating the interplay of nuclear and electronic dynamics, which plays an
important role in a number of photophysical processes and photochemical
reactions. Here we present a coherent state representation of the vibronic
dynamics and of the resulting response functions. Analytical expressions are
initially derived for the case of third-order response functions in an N-level
system, with ground state initialization of the oscillator (zero-temperature
limit). The results are then generalized to the case of M-th order response
functions, with arbitrary M. The formal derivation is translated into a simple
recipe, whereby the explicit analytical expressions of the response functions
can be derived directly from the Feynman diagrams. We further generalize to the
whole set of initial coherent states, which form an overcomplete basis. This
allows one in principle to derive the dependence of the response functions on
arbitrary initial states of the vibrational modes and is here applied to the
case of thermal states. Finally, a non-Hermitian Hamiltonian approach is used
to include in the above expressions the effect of vibrational relaxation.Comment: 21 pages, 3 figure