Wave function for dissipative harmonically confined electrons in a time-dependent electric field

• A many-body generalization of the Quantum Brownian motion model perturbed by a time-dependent homogeneous electric field is proposed.
• The analytical wave function of this model is obtained.
• The Harmonic Potential Theory is generalized to the quantum dissipative systems.

We investigate the many-body wave function of a dissipative system of interacting particles confined by a harmonic potential and perturbed by a time-dependent spatially homogeneous electric field. Applying the method of Yu and Sun (1994), it is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent (TD) Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical damped driven equation of motion, plus an addition fluctuation term due to the Brownian motion. The wave function reduces to that of the Harmonic Potential Theorem (HPT) wave function in the absence of the dissipation. An example of application of the results derived is also given.