We investigate the relaxation of multilevel systems under the influence of stochastic fields with finite correlation time tau(c). First, we study a system with spin S = 1/2 in a static magnetic field in the presence of dichotomic perturbations. The spectra of the components of the averaged spin vector SBAR are evaluated exactly by resorting to the memory-function approach. The model is then extended to include the influence on the relaxation of SBAR of a different species with spin I = 1/2. The relaxation rates T1 and T2 are given in terms of cumulant expansions and compared with the exact results. Fourth-order calculations recover the inequality T2/2T1 less-than-or-equal-to 1 for correlated noise fields. Furthermore, it is found that T1 can be defined also for long tau(c). T1 is longer than tau(c), provided that r(est) < 1, where r(est) is the squared ratio between the total amplitude of the fluctuating fields and the largest one between the Larmor frequency and 1/tau(c). It is also found that 2r(est) is an upper bound of the relative error between the exact and the second-order cumulant expansion of T1. Generalizations on systems with S = 1/2, I > 1/2, and arbitary kinds of noise are discussed.
RELAXATION INDUCED BY COLORED NOISE - ANALYTICAL RESULTS FOR MULTILEVEL SYSTEMS
ANDREOZZI, LAURA;GIORDANO, MARCO;LEPORINI, DINO
1992-01-01
Abstract
We investigate the relaxation of multilevel systems under the influence of stochastic fields with finite correlation time tau(c). First, we study a system with spin S = 1/2 in a static magnetic field in the presence of dichotomic perturbations. The spectra of the components of the averaged spin vector SBAR are evaluated exactly by resorting to the memory-function approach. The model is then extended to include the influence on the relaxation of SBAR of a different species with spin I = 1/2. The relaxation rates T1 and T2 are given in terms of cumulant expansions and compared with the exact results. Fourth-order calculations recover the inequality T2/2T1 less-than-or-equal-to 1 for correlated noise fields. Furthermore, it is found that T1 can be defined also for long tau(c). T1 is longer than tau(c), provided that r(est) < 1, where r(est) is the squared ratio between the total amplitude of the fluctuating fields and the largest one between the Larmor frequency and 1/tau(c). It is also found that 2r(est) is an upper bound of the relative error between the exact and the second-order cumulant expansion of T1. Generalizations on systems with S = 1/2, I > 1/2, and arbitary kinds of noise are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
