Approximate solutions of the density matrix equation for a local average field

Виктор Павлович Маслов, O. Yu. Shvedov

James P. Stone

We consider the density matrix for weakly damped quantum oscillators. It is proved that the locally time-averaged density matrix derived from the full density matrix satisfies a closed set of equations, which reduce under specified conditions to population rate equations. Rate coefficients in these equations include contributions from collision-induced transitions and internal collisionless transitions explicitly arranged as sequential processes. We compare solutions of the new rate equations with the full density matrix for a four-level driven system. It is shown that despite some notable success in matching locally time-averaged quantities by extending the Wilcox-Lamb formalism to the weak-damping limit, the new equations are more naturally suited for this limit. In contrast with the Wilcox-Lamb formalism, we show that the new equations give a representation of the local time average whose accuracy is limited only by the degree of time-scale separation between collisions and internal dynamics.

Г. А. Варданян, G S Mkrtchyan

Karl Blum

Leon Freitag, Yingjin Ma, Alberto Baiardi +2 more

We present an approximate scheme for analytical gradients and nonadiabatic couplings for calculating state-average density matrix renormalization group self-consistent-field wave function. Our formalism follows closely the state-average complete active space self-consistent-field (SA-CASSCF) ansatz, which employs a Lagrangian, and the corresponding Lagrange multipliers are obtained from a solution of the coupled-perturbed CASSCF (CP-CASSCF) equations. We introduce a definition of the matrix product state (MPS) Lagrange multipliers based on a single-site tensor in a mixed-canonical form of the MPS, such that a sweep procedure is avoided in the solution of the CP-CASSCF equations. We apply our implementation to the optimization of a conical intersection in 1,2-dioxetanone, where we are able to fully reproduce the SA-CASSCF result up to arbitrary accuracy.

Bernd Esser