Modeling dissipative magnetization exchange dynamics in magnetic resonance

Quantifying the role of the environment in a quantum system of interest has remained an active pursuit for studying the effects of dissipation in a wide-range of problems in chemical physics and spectroscopy. From an operational perspective, the complexities encountered in the description of open systems have ushered in the development of models without explicit consideration of the complete system. To this end, phenomenological descriptions that involve the inclusion of exponential damping terms have remained the method of choice. While such methods have gained prominence in providing a qualitative explanation for observations in spectroscopy, they are of limited utility in quantitative studies that involve the estimation of molecular constraints. As an alternative, the present report explores the possibility of understanding the nuances of dissipation found in open systems through analytic methods. Specifically, the magnetization exchange between a pair of spins (say I₁ and I₂) is examined under periodic modulation in the presence of a surrounding bath of other spins. Employing the concept of effective Hamiltonians and utilizing the block-diagonal structure of the derived effective Hamiltonians, analytic expressions are derived for describing the effects of dissipation (due to neighboring spins) on the system of interest without increasing the dimension of the problem.