Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics

The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins both classical and quantum. It is shown that, even though the characteristic timescale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by the spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian timescale. The formalism resulting from that conjecture can be described as ``correlated diffusion in finite volumes.''Comment: text as published, Section 4 added and other minor change

Universal Long-Time Relaxation on the Lattices of Classical Spins: Markovian Behavior on non-Markovian Timescales

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two- and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.Comment: text as in published version, minor changes in comparison with the original on

Temperature dependence of the superconducting gap in high-Tc cuprates

It is proposed that (i) the temperature dependence of the superconducting gap Delta(T) in high-Tc cuprates can be predicted just from the knowledge of Delta(0) and the critical temperature Tc; and, in particular, (ii) Delta(0)/Tc > 4 implies that Delta(Tc) is not equal to zero, while Delta(0)/Tc < 4 corresponds to Delta(Tc) = 0. A number of tunneling experiments appear to support the above proposition, and, furthermore, show reasonable quantitative agreement with a model (cond-mat/0308428), which is based on the two-dimensional stripe hypothesis.Comment: Text close to the published version. Minor textual corrections in comparison to the previous versio

On the long-time behavior of spin echo and its relation to free induction decay

It is predicted that (i) spin echoes have two kinds of generic long-time decays: either simple exponential, or a superposition of a monotonic and an oscillatory exponential decays; and (ii) the long-time behavior of spin echo and the long-time behavior of the corresponding homogeneous free induction decay are characterized by the same time constants. This prediction extends to various echo problems both within and beyond nuclear magnetic resonance. Experimental confirmation of this prediction would also support the notion of the eigenvalues of time evolution operators in large quantum systems.Comment: 4 pages, 4 figure