Brownian motion with restoring drift: The petit and micro-canonical ensembles

Letf(Q) be odd and positive near +∞. Then the non-linear wave equation ?² Q/?t ²??² Q/?x ²?f(Q)=0, considered on the circle 0≤x<L, can be written in Hamiltonian formQ ^⊙ =?H/?P, P ^⊙ =??H/?Q with $$P = Q^\cdot and H = \tfrac{1}{2}\mathop \smallint \limits_0^L (Q')^2 + \mathop \smallint \limits_0^L F(Q) + \tfrac{1}{2}\mathop \smallint \limits_0^L P^2 ;$$ the corresponding flow preserves the (suitably interpreted) “petit ensemble”e ^?H d ^∞ Qd ^∞ P; and forL↓∞,Q settles down to the stationary diffusion with infinitesimal operator 1/2 ?²/?Q ²+m(Q)?/?Q,m being the logarithmic derivative of the ground state of ?d ²/dQ ² ‖F(Q). This diffusion is the “Brownian motion with restoring drift”; see McKean-Vaninsky [1993(1)]. For reasons suggested by the paper of Lebowitz-Rose-Speer [1988] on NLS, it is interesting to study the “micro-canonical ensemble” obtained by restricting to the sphere $\int\limits_0^L {Q^2 } = N$ and makingL↓∞ with fixedD=N/L. Now, forF(Q)/Q ²→∞, the same type of diffusion appears, but with drift arising from the modified potentialF(Q)+cQ ²,c being chosen so that the mean ofQ ² is the assigned numberD. The proof employs Döblin's method of “loops” [1937] and steepest descent. The same is true forF(Q)=m ² Q ², only now the proof is elementary. The outcome is also the same ifF(Q)/Q ²→0, providedD is smaller than the petit canonical mean ofQ ²; forD larger than this mean, the matter is more subtle and the outcome is unknown.     

Excitonic detectors of infrared and submillimeter radiation

The theory of new type detectors based on the quenching of secondary emission in direct-gap semiconductors (lines of Raman light scattering due to interaction between free and bound excitons in the crystal, and also bands of edge radiation) caused by IR or submillimeter radiation is proposed. The results obtained are confirmed by the experiment performed for CdS crystal excited by ultraviolet radiation of mercury lamp, at liquid helium temperature.     

The influence of the local surrounding on the hyperfine interactions in Zr(Fe1−x Ni x )2 compounds

Mössbauer spectroscopy and the TDPAC method have been used to study Zr(Fe_1–x Ni _x )₂ compounds forx0.30. The hyperfine magnetic field at the Fe sites and the quadrupole splitting as functions of nickel concentration were analysed by use of⁵⁷Fe Mössbauer spectroscopy. Values of the internal magnetic field on¹⁸¹Ta nuclei have been found by means of the TDPAC method.     

Spin correlations in amorphous Bi2Sr2CaCu2Ox

Zero and longitudinal field SR has been used to probe the magnetic state of amorphous Bi₂Sr₂CaCu₂O_x prepared by rapid quenching from the melt. The results suggest quasi-static spin correlations between extremely dilute Cu²⁺ ions.Work performed while at the J J Thomson Physical Laboratory, University of Reading.     

Products obtained by microbially-induced corrosion of steel in a marine environment: Role of green rust two

An unusual low-water corrosion of steel sheet piles has been systematically investigated in a channel harbour (Boulogne sur Mer, France). An analysis of the environment reveals that all sampling of dark rust taken at different heights above marine sediments and kept in anaerobic conditions present unusual concentrations of sulfate-reducing bacteria. The rust products have been characterized by Mössbauer spectroscopy and X-ray diffraction, comprising the ferrous—ferric sulfated compounds of formula 4Fe(OH)₂ · 2FeOOH · FeSO₄ ·nH₂O, called green rust 2, mixed sometimes with magnetite and a small amount of ferrous sulfide.     

Relaxed excited states and anomalous hyperfine structure of muonium centers in KBr

We report on the luminescence induced by positive muons implanted (with 4 MeV) into KBr crystal, which evidences a long-lived (lifetime=13.3 s excited state produced by muon radiolysis. The temperature dependence of the luminescence yield has a strong correlation with the amplitude of an anomalous muonium center: both are observed only below 50 K. This correlation strongly suggests that the muonium center is perturbed by the muon-induced excitons to cause the anomalous hyperfine structure. Moreover, the luminescence energy and decay time indicate that the observed luminescence is not associated with the intrinsic or impurity-related self-trapped excitons, but with a relaxed excited state specific to the muon(ium)-KBr system.