Dynamical theory of spin relaxation

Abstract

The dynamics of a spin system is usually calculated using the density matrix. However, the usual formulation in terms of the density matrix predicts that the signal will decay to zero, and does not address the issue of individual spin dynamics. Using stochastic calculus, we develop a dynamical theory of spin relaxation, the origins of which lie in the component spin fluctuations. This entails consideration of random pure states for individual protons, and how these pure states are correctly combined when the density matrix is formulated. Both the lattice and the spins are treated quantum mechanically. Such treatment incorporates both the processes of spin-spin and (finite temperature) spin-lattice relaxation. Our results reveal the intimate connections between spin noise and conventional spin relaxation.

Simultaneous observation of NMR spin noise and maser spontaneous emission

“…It may need to be stressed that in this case, spin noise still exists even though it is not observed. Spin-noise is an intrinsic property of the spin system [9,10] and cannot be removed by these experiments. Further increasing of delay time shows maser peaks disappearing and after 4 s delay time a typical noise spectrum for all resonances is observed again.…”

“…Spin noise has been applied to NMR imagining [7] as well as 2D experiments [8]. However, since spin noise is observed throughout fluctuations of transverse magnetization that is proportional to √ N [1,9,10], therefore, it is expected to be of low sensitivity. Increased sensitivity is desirable and efforts have been made to improve it.…”

Dynamical theory of spin noise and relaxation: Prospects for real-time NMR measurements

“…More recently, it has been observed in several experimental systems [2][3][4][5], including a recent application to imaging [6] and a very thorough experimental study [7]. Although the noise signal is weak compared to the signal following a pulse, it can be detected relatively easily [4,8], since it arises from all of the spins, not just the Boltzmann population difference [9].…”

“…There is also the prospect to distinguish pure T 2 from the inhomogeneous T 2 * via instantaneous volatility measurements, provided one can digitize fast enough. The purpose of the current article is therefore to illustrate how to harness the recent dynamical theory [9] in terms of real-time measurements and inference of NMR parameters. Indeed, we argue that such a dynamical theory formulated in terms of an alternative to the standard density matrix is the only possibility for constructing a scheme to track NMR parameters in real time-any ensemble average technique necessarily fails.…”

“…In general terms, it should be emphasized that the dynamical theory [9] accounts explicitly for the field, temperature, and spin population scaling dependence for both spin-spin and spin-lattice relaxation. It attendantly provides a description for * field@mcmaster.ca; http://www.ece.mcmaster.ca/˜field/; also at Department of Mathematics & Statistics, McMaster University.…”