Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr\"{o}dinger equation called time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.Comment: 4 pages, 2 figure

Atmospheric chemistry-climate feedbacks

We extend the theory of climate feedbacks to include atmospheric chemistry. A change in temperature caused by a radiative forcing will include, in general, a contribution from the chemical change that is fed back into the climate system; likewise, the change in atmospheric burdens caused by a chemical forcing will include a contribution from the associated climate change that is fed back into the chemical system. The theory includes two feedback gains, G_(che) and G_(cli). G_(che) is defined as the ratio of the change in equilibrium global mean temperature owing to long-lived greenhouse gas radiative forcing, under full climate-chemistry coupling, to that in the absence of coupling. G_(cli) is defined as the ratio of the change in equilibrium mean aerosol or gas-phase burdens owing to chemical forcing under full coupling, to that in the absence of coupling. We employ a climate-atmospheric chemistry model based on the Goddard Institute for Space Studies (GISS) GCM II', including tropospheric gas-phase chemistry, sulfate, nitrate, ammonium, black carbon, and organic carbon. While the model describes many essential couplings between climate and atmospheric chemistry, not all couplings are accounted for, such as indirect aerosol forcing and the role of natural dust and sea salt aerosols. Guided by the feedback theory, we perform perturbation experiments to quantify G_(che) and G_(cli). We find that G_(che) for surface air temperature is essentially equal to 1.00 on a planetary scale. Regionally, G_(che) is estimated to be 0.80–1.30. The gains are small compared to those of the physical feedbacks in the climate system (e.g., water vapor, and cloud feedbacks). These values for G_(che) are robust for the specific model used, but may change when using more comprehensive climate-atmospheric chemistry models. Our perturbation experiments do not allow one to obtain robust values for G_(cli). Globally averaged, the values range from 0.99 to 1.28, depending on the chemical species, while, in areas of high pollution, G_(cli) can be up to 1.15 for ozone, and as large as 1.40 for total aerosol. These preliminary values indicate a significant role of climate feedbacks in the atmospheric chemistry system