Intrinsic Nonlinearities in Complex
Adaptive Matter
David Pines
University of Illinois, Urbana-Champaign
Physics Department
Urbana, IL 61801
(217) 333-0115
(217) 244-7559 FAX
Intrinsically nonlinear behavior is a common thread running through complex adaptive matter, yet identifying its locus and the way it which it gives rise to measured dynamic behavior (or function in the case of biological matter) poses experimental and theoretical challenges. Among the hard matter members of the cam family, the cuprate superconductors are arguably the best studied example, yet a number of mysteries remain. These are strongly correlated nearly two-dimensional systems, in which the dominant interaction between the quasiparticles in the Cu-O planes is of electronic origin. Since these quasiparticles are both responsible for that interaction and respond to it, one has an inherently nonlinear situation in which both positive and negative feedback play an important role in determining the highly anomalous. Doping and temperature dependent, properties of the normal state as well as the transition at high temperatures to a superconducting state with an unconventional order parameter. A combination of NMR, INS, and ARPES experiments and related theoretical work have now shown that in the magnetically underdoped systems, proximity to an antiferromagnetic quantum critical point leads to dynamical scaling behavior for the low frequency spin fluctuations and to a pseudogap in the quasiparticle spectrum. It is natural to inquire whether similar behavior is found in another quasi-two dimensional system, the organic superconductor, "ET", and the extent to which comparable nonlinear behavior of magnetic origin exists in what are, in many ways, a three dimensional analogue of the cuprates, the heavy electron superconductors.
Among the lessons learned from the cuprates are the importance of having really good samples, and of studying a given sample using a broad spectrum of experimental probes. For example while it has become evident that pattern formation (stripes) and phase separation can occur in some cuprate samples as a result of competing interactions, it is not yet known whether static stripes are found in the superconducting cuprates. Thus the extent to which coupling between the spin and charge (lattice) degrees of freedom plays a role in determining dynamic behavior in the cuprates remains to be determined. "Next generation" inelastic neutron scattering facilities, such as the possible LPSS upgrade at LANSCE, would provide the kind of probe required to answer these and a number of related questions (e.g. the transition from incommensurate to commensurate behavior in the spin fluctuation spectra as the frequency is increased, or the temperature and doping are changed) about nonlinear behavior in the cuprates.
I hope that the ICAM workshop will provide us with an opportunity to begin discussions on the extent to which one may be seeing comparable phenomena, such as pattern formation, proximity to a critical point, etc. in hard, soft, and biomatter, the physical origin of these phenomena, the probes best used to study them, and that such discussions of intrinsically nonlinear behavior can be continued in subsequent ICAM exploratory workshops.