Time-evolution of quantum systems via a complex nonlinear Riccati equation II. Dissipative systems

TL;DR

This paper extends a nonlinear Riccati equation approach to model dissipative quantum systems, demonstrating how environmental factors influence quantum uncertainties, energy, and tunneling, with sensitivity to initial conditions.

Contribution

It introduces an effective method for describing dissipative quantum systems using a complex nonlinear Riccati equation, highlighting environmental effects on quantum dynamics.

Findings

Environmental parameter γ affects initial condition sensitivity.

Quantum uncertainties are influenced by dissipation.

Tunneling currents are modified by environmental interactions.

Abstract

In our former contribution [Ann. Phys. 360 (2015) 44], we have shown the sensitivity to the choice of initial conditions in the evolution of Gaussian wave packets via the nonlinear Riccati equation. The formalism developed in the previous work is extended to effective approaches for the description of dissipative quantum systems. By means of simple examples we show the effects of the environment on the quantum uncertainties, correlation function, quantum energy contribution and tunneling currents. We prove that the environmental parameter $\gamma$ is strongly related with the sensitivity to the choice of initial conditions.