Nash estimates and the asymptotic behavior of diffusions

Journal ArticleIn order to analyze the asymptotic behavior of a particle diffusing in a drift field derived from a smooth bounded potential, we develop Nash-type a priori estimates on the transition density of the process. As an immediate consequence of the estimates, we find that for a rapidly decaying potential in Rd, the mean squared displacement behaves like td + C(t), where C(t) (the time integral of the "velocity autocorrelation function") decays like t-d/2. We also prove, using the estimates, that for a potential in Rd of the form V + B, where V is stationary random ergodic and B has compact support, the diffusion converges under space and time scaling to the same Brownian motion as does the diffusion with B = 0

Arbitrarily slow approach to limiting behavior

Journal ArticleABSTRACT. Let f(k, t): RN x [0, oo) -- R be jointly continuous in k and t, with lim(t)--(oo) f(k, t) = F(k) discontinuous for a dense set of k's. It is proven that there exists a dense set T of k's such that, for k e T , |f(k, t) - F(k)| approaches 0 arbitrarily slowly, i.e., roughly speaking, more slowly than any expressible function g(t) -- 0 . This result is applied to diffusion and conduction in quasiperiodic media and yields arbitrarily slow approaches to limiting behavior as time or volume becomes infinite. Such a slow approach is in marked contrast to the power laws widely found for random media, and, in fact, implies that there is no law whatsoever governing the asymptotics

Research and education in management of large- scale technical programs Semiannual progress report

Research and education in management of large scale technical programs - education and integration of interdisciplinary tea

Technology and management of large-scale programs Semiannual progress report

Technology and management of large scale program

Manifestation of spin-charge separation in the dynamic dielectric response of one--dimensional Sr2CuO3

We have determined the dynamical dielectric response of a one-dimensional, correlated insulator by carrying out electron energy-loss spectroscopy on Sr2CuO3 single crystals. The observed momentum and energy dependence of the low-energy features, which correspond to collective transitions across the gap, are well described by an extended one-band Hubbard model with moderate nearest neighbor Coulomb interaction strength. An exciton-like peak appears with increasing momentum transfer. These observations provide experimental evidence for spin-charge separation in the relevant excitations of this compound, as theoretically expected for the one-dimensional Hubbard model.Comment: RevTex, 4 pages+2 figures, to appear in PRL (July 13

Modeling of anisotropic electromagnetic reflection from sea ice

Journal ArticleThe contribution of brine layers to observed reflective anisotropy of sea ice at 100 MHz is quantitatively assessed, and a theoretical explanation for observed reflective anisotropy is proposed in terms of anisotropic electric flux penetration into the brine layers. The sea ice is assumed to be a stratified dielectric consisting of pure ice containing ellipsoidal conducting inclusions (brine layers) uniformly aligned with their long axes perpendicular to the preferred crystallographic c axis direction. The asymmetrical geometry of the brine layers is shown to produce an anisotropy in the complex dielectric constant of sea ice