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Violation of the Spin-Temperature Hypothesis

W.-K. Rhim, A. Pines, J. S. Waugh

1970
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Physical Review Letters
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p"(t, ) = exp(~z , tp(0) exp ',~x , 't, ) p, q(2') = (I/Z) exp(M, H, /k T), (I) where M=yRQI; is the operator for the total magnetic moment. Now a very short && rf pulse is applied at resonance (or H, is abruptly rotated through -, '&) converting the density matrix to an initial value p(0) which is the same as (I) except that M, is replaced by M".The magnetization (M) =(~")i decays' in a time T, -(yH1") ' under the influence of the truncated dipolar Hamiltonian A "Loschmidt demon" is exhibited
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... hich effectively reverses the spin-spin relaxation of a system of interacting magnetic dipoles in a strong external field, thereby demonstrating that this system does not approach internal thermodynamic equilibrium in a time T2 as was implicitly recognized by Philippot. The coupled nuclear spins in a solid with very this line of thought. Following a Bloeh decay in slow spin-lattice relaxation comprise an isolated Cap, we apply a strong rf perturbation to be desystem which for many purposes can be treated scribed presently, after which the magnetization by thermodynamic methods. ' One begins with the (M")returns in the form of an echo. This echo system in equilibrium at the lattice temperature is of a quite different nature from the superficial-T, performs various manipulations on the spins, ly similar one produced by Hartmann and Hahn, ' waits a time T, characteristic of the spin-spin which depends on the inhomogeneous character coupling, during which the spin system is imof the dipolar interaction between unlike spins agined to approach internal equilibrium, and caland throws no suspicion on any aspect of spin culates a final spin temperature T, through conthermodynamics. servation of energy or other constants of the mo- The contradiction just mentioned is an illustration. The purpose of this Letter is to report tion of Loschmidt's paradox. ' We remind the some experiments for which this simple spin-reader that the microcanonical distribution is an temperature picture is not valid. arbitrary one which is chosen for mathematical Consider the common situation in which a sinsimplicity when one knows nothing about the degle-species solid is first brought to equilibrium tailed dynamical history of the system. Yet in with the lattice in a magnetic field Hok. If H, is fact we know a great deal: The actual density sufficiently strong compared with the dipolar lomatrix at time t, (in the rotating reference frame) cal field H1", one describes the spin-density is in fact matrix by the canonical distribution the truncation being increasingly valid as H, /H q" is made large. At a time t, &T, one commonly assumes the system has undergone an irreversible approach to an internal equilibrium state. If so, conservation of energy requires that the appropriate microcanonical distribution be characterized by infinite spin temperature: p(t, ) = p,~(~) = I/Z. The magnetization will never recur and cannot be recalled by applying any external fields, since their Hamiltonian commutes trivially with p,~(~). Figure I exhibits a striking contradiction of FIG. 1. Transient NMR of the F nuclei in solid CaF&. Following a normal Bloch decay, an rf burst of length 260 @sec with H& =95 G (see text) was applied during the noise-free portion of the trace. Thereupon an echo occurs at a total delay of 365 @sec from the beginning of the experiment. In other experiments the initial decay was allowed to disappear fully before applying the burst. 218

doi:10.1103/physrevlett.25.218
fatcat:inqibgibhnadnoadjju6wqkuqa