The master equation approach: Coherence, energy transfer, annihilation, and relaxation

V. M. Kenre

Jiong Cheng, Yanqiang Yang, Wenlin Li +1 more

A fully quantum multiphonon up-pumping model is proposed to characterize coherent energy transfer in energetic materials (EMs) subjected to external shock. After eliminating the degrees of freedom of the phonon bath within a mean-field approximation, we derive a quantum master equation governing the energy transfer among vibrational modes. Our analysis reveals that doorway modes of different frequencies undergo distinct levels of effective coherent driving and dissipation, induced by the shocked phonon environment. This not only clarifies the microscopic origin of coherent phonon generation, but also reveals the possibility of modulating such coherent driving and dissipation. Based on numerical simulations of a simplified model using the master equation, we demonstrate how doorway modes extract energy from the phonon environment and subsequently excite higher-frequency molecular vibrational modes. This work offers a renewed perspective for understanding the mechanisms of energy transfer in energetic materials.

Anton Sergeevich Trushechkin

In the framework of the theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is complemented by slow relaxation processes. We use a generalization of the F\"orster and modified Redfield perturbation theories known in the theory of excitation-energy transfer. Also, we show that the mean-force Gibbs state in the corresponding limits is stationary for the derived master equations.

Tetsuya Yoneda, Aya Nagasato, Tatsuo Akamine +1 more

Z. Nafari Qaleh, A. T. Rezakhani

We provide a comprehensive study of the energy-transfer phenomenon---populating a given energy level---in three- and four-level quantum systems coupled to two thermal baths. In particular, we examine the effects of an external periodic driving and the coherence induced by the baths on the efficiency of the energy transfer. We consider the Floquet-Lindblad and the Floquet-Redfield scenarios, which both are in the Born-Markov, weak-coupling regime but differ in the treatment of the secular approximation, and for the latter we develop an appropriate Floquet-type master equation by employing a partial secular approximation. Throughout the whole analysis we keep Lamb-shift corrections in the master equations. We observe that, especially in the Floquet-Redfield scenario, the driving field can enhance the energy-transfer efficiency compared to the nondriven scenario. In addition, unlike nondriven degenerate systems where Lamb-shift corrections do not contribute significantly to the energy transfer, in the Redfield and the Floquet-Redfield scenarios these corrections have non-negligible effects.