Pedagogical model for transverse relaxation and motional narrowing ofmagnetic resonance spectroscopy

A standard relaxation theory known as the bpp theory is of common use in magnetic resonance spectroscopy. atypical phenomenon that can be briefly elucidated by the theory is a broadening of peaks in fourier spectra due to atransverse relaxation of a spin magnetization. there are, however, drawbacks: this theory is a classical phenomenologicaltheory and often claimed to be insufficient to describe small relaxation time. in addition, it cannot describe amotional narrowing without introducing a phenomenological approach. we introduce a simple model in which asystem spin 1/2.is coupled with an environmental system localized around the system. the environmental systemprobabilistically dissipates into a thermal bath and a thermal environmental system migrates into the place instead.we show analytically that this model can describe a transverse relaxation and a motional narrowing simultaneously.we also show numerical simulations of decoherence in a spin system coupled with on-resonance bosonic modes.our model will hopefully contribute to easier understanding of motional narrowing for a pedagogical purpose