Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with expressions derived from a 0-D nonlinear σ-model of supersymmetry, which coincides with Random Matrix Theory. In contrast, disordered wavefunctions show deviations from this universal behavior due to Anderson localization. A systematic behavior of the distribution function is studied as a function of the localization length, and can be understood in the framework of a 1-D version of the nonlinear σ-model. PACS number(s): 05.45.+b, 03.65.G, 71.55.J Typeset using REVT E X

No abstract

The smooth evolution of the tunneling gap of Bi2Sr2CaCu2O8 with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping, has been interpreted as evidence that the pseudogap must be due to precursor pairing. We suggest an alternative explanation, that the smoothness reflects a hidden SO(N) symmetry near the (π, 0) points of the Brillouin zone (with N = 3, 4, 5, or 6). Because of this symmetry, the pseudogap could actually be due to any of a number of nesting instabilities, including charge or spin density waves or more exotic phases.We present a detailed analysis of this competition for one particular model: the pinned Balseiro-Falicov model of competing charge density wave and (s-wave) superconductivity. We show that most of the anomalous features of both tunneling and photoemission follow naturally from the model, including the smooth crossover, the general shape of the pseudogap phase diagram, the shrinking Fermi surface of the pseudogap phase, and the asymmetry of the tunneling gap away from optimal doping. Below Tc, the sharp peak at ∆1 and the dip seen in the tunneling and photoemission near 2∆1 cannot be described in detail by this model, but we suggest a simple generalization to account for inhomogeneity, which does provide an adequate description.We show that it should be possible, with a combination of photoemission and tunneling, to demonstrate the extent of pinning of the Fermi level to the Van Hove singularity. A preliminary analysis of the data suggests pinning in the underdoped, but not in the overdoped regime.

No abstract

The correct Eqs. (20) and (21) read as follows:Q ab cdQ1982 0031-9007͞96͞76(11)͞1982(1)$10.00