We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum-mechanical mean values of their co-ordinates and momenta we have derived a c number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of the temperature and friction. While almost all the earlier theories rest on quasiprobability distribution functions (e.g., Wigner function) and path integral methods, the present work is based on true probability distribution functions and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermally activated processes and tunneling.

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Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers' turnover and the quantum Arrhenius plot.

Meticulous surface engineering of layered structures toward new functionalities is a demanding challenge to the scientific community.Here, we introduce defects on varied MoS 2 surfaces by suitable doping of nitrogen atoms in a sulfur-rich reaction environment, resulting in stable and scalable phase conversion. The experimental characterizations along with the theoretical calculations within the framework of density functional theory establish the impact of nitrogen doping on stabilization of defects and reconstruction of the 2H to 1T phase. The as-synthesized MoS 2 samples exhibit excellent dye removal capacity in the dark, facilitated by a synergistic effect of reactive oxygen species (ROS) generation and adsorption. Positron annihilation spectroscopy and electron paramagnetic resonance studies substantiate the role of defects and associated sulfur vacancies toward ROS generation in the dark. Further, on the basis of its ample ROS generation in the dark and in the light, the commendable antimicrobial activity of the prepared MoS 2 samples against fungal pathogen Alternaria alternata has been demonstrated. Thus, the present study opens up a futuristic avenue to develop newer functional materials through defect engineering by suitable dopants toward superior performances in environment issues.