We are concerned with the understanding of the processes governing the evolution of non-equilibrium states of spin observables in protons of highly correlated systems, like nematic liquid crystals, LC. An outline of our present interests follows.

As a consequence of the orientational order, molecules in LC present considerable residual intramolecular dipolar spin-spin interaction energy. Nuclear spins of different molecules are magnetically isolated in the average because of the fast relative motion of the molecules (rotational and translational diffusion), and the whole spin system can be viewed as an ensemble of representative molecules. In one molecule of a LC the number of protons is not macroscopic, however, experiments confirm that the thermodynamic picture is also perfectly valid in LC, since over a short time interval (hundreds of microseconds) the spin system arrives to a state of internal equilibrium [1, 2]. For example, after a time interval of about 300 microseconds following the preparation pulses of the Jeener-Broekaert experiment, the proton system attains a state of dipolar order, which can be described by a semiequilibrium spin density operator .

Experiments also showed that associated with the anisotropy of the proton distribution in the molecule, two kinds of dipolar quasiinvariant can be created, namely "intrapair" and "interpair" order. The nature of the mechanisms that bring the spins to a quasi stationary state in LC is being investigated at present; particularly we consider the role of the non-observed degrees of freedom in the decay of the quantum coherences [3].

Spin-lattice relaxation of the dipolar order showed to be a useful technique to investigate cooperative molecular dynamics in liquid crystals. Associated with the long range orientational order, these systems present cooperative correlated thermal motions (order fluctuations) superimposed on the individual liquid-like motions.   The intrapair dipolar relaxation time is mostly due to fluctuations of the order director, over a broad Larmor frequency range, unlike to Zeeman relaxation time, which reflects the slow fluctuations only at low Larmor frequencies [4]. The interpair dipolar order relaxes to equilibrium with a different rate and provides relevant, independent information about the several superimposed molecular motions [1].

Our theoretical calculations of the relaxation times based on the traditional theory of weak order, showed that other mechanisms than those taken into account by the "usual" high temperature theory play a significant role in the relaxation of the dipolar order [5]. Instead, a theoretical approach which starts from the full-quantum master equation in the Markovian limit, shows that the quantum correlation of spin and lattice variables are of importance when the fluctuations of the spin-lattice interaction are longlived (ω_{D 1} ) [6]. A correction term arises which is consistent with the experimental results. Occurrence of very long fluctuation lifetimes (comparable with T_1D) might provide another source of relaxation. In principle, such ultraslow mechanisms can be considered as quasiadiabatic motions; in such a case, they would selectively affect the interpair order, as happens in hydrated salts (gypsum) subjected to quasiadiabatic rigid rotation of the sample [7]. A non-Markovian full-quantum theory could conceivably account for correlation effects associated with the long-time memory [8].

Together with the Zeeman energy, the dipolar energies are relevant observables of the nuclear spin system in LC, however designating dipolar couplings as intrapair and interpair is still a vague denomination. In general, whenever one wants to start from a dipolar ordered state in a liquid crystal molecule, and manipulate the quantum states it is necessary to have a precise representation of both the initial density matrix and the unitary time evolution operator.

Examples of experiments which demand a sharp definition of the relevant interactions associated with each quasiinvariant are dipolar order spin-lattice relaxation and experiments of multiple quantum coherences which start from non conventional initial states, like dipolar ordered states or pseudo pure states [9,10]. It is our aim to disclose the actual form of the Hamiltonians representing the dipolar quasiinvariants in order to interpret several kinds of experiments involving dipolar ordered states. In this sense, we studied the experimental double quantum coherence spectrum in nematic 5CB starting from a state of intrapair dipolar order, and compared it with the calculated one corresponding to a dipole coupled 8-spin system which represents the core of the 5CB molecule. The salient frequency components of the spectra can be better reproduced if the LC molecule is viewed as a cluster of spins coupled by dipole-dipole interactions rather than as a set of weakly coupled spin pairs, generalizing the standard definitions of intrapair and interpair Hamiltonians [11]. Similarly, we recently studied the transient towards the establishment of the dipolar order in LC by performing a spin counting experiment which starts from the Jeener-Broekaert sequence (originally designed for solids [9]) in the nematic 5CB.