C. Meier et Dj. Tannor, Non-Markovian evolution of the density operator in the presence of strong laser fields, J CHEM PHYS, 111(8), 1999, pp. 3365-3376
We present an accurate, efficient, and flexible method for propagating spat
ially distributed density matrices in anharmonic potentials interacting wit
h solvent and strong fields. The method is based on the Nakajima-Zwanzig pr
ojection operator formalism with a correlated reference state of the bath t
hat takes memory effects and initial/final correlations to second order in
the system-bath interaction into account. A key feature of the method propo
sed is a special parametrization of the bath spectral density leading to a
set of coupled equations for primary and N auxiliary density matrices. Thes
e coupled master equations can be solved numerically by representing the de
nsity operator in eigenrepresentation or on a coordinate space grid, using
the Fourier method to calculate the action of the kinetic and potential ene
rgy operators, and a combination of split operator and Cayley implicit meth
od to compute the time evolution. The key advantages of the method are: (1)
The system potential may consist of any number of electronic states, eithe
r bound or dissociative. (2) The cost for arbitrarily long solvent memories
is equal to only N + 1 times that of propagating a Markovian density matri
x. (3) The method can treat explicitly time-dependent system Hamiltonians n
onperturbatively, making the method applicable to strong field spectroscopy
, photodissociation, and coherent control in a solvent surrounding. (4) The
method is not restricted to special forms of system-bath interactions. Cho
osing as an illustrative example the asymmetric two-level system, we compar
e our numerical results with full path-integral results and we show the imp
ortance of initial correlations and the effects of strong fields onto the r
elaxation. Contrary to a Markovian theory, our method incorporates memory e
ffects, correlations in the initial and final state, and effects of strong
fields onto the relaxation; and is yet much more effective than path integr
al calculations. It is thus well-suited to study chemical systems interacti
ng with femtosecond short laser pulses, where the conditions for a Markovia
n theory are often violated. (C) 1999 American Institute of Physics. [S0021
-9606(99)01631-1].