Scale Invariance of the PNG Droplet and the Airy Process

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single time (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y ^–2. Roughly the Airy process describes the last line of Dyson's Brownian motion model for random matrices. Our construction uses a multi-layer version of the PNG model, which can be analyzed through fermionic techniques. Specializing our result to a fixed value of y, one reobtains the celebrated result of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation.     

Ethanol-induced conformational fluctuations of NMDA receptors

Alcohol addiction ranks among the leading global causes of preventable death and disabilities in human population. Understanding the sites of ethanol action that mediate its acute and chronic neural and behavioural effects is critical to develop appropriate treatment options for this disorder. The N-methyl-d-asparate (NMDA) receptors are ligand-gated heterotetrameric ion channels, which are known to directly interact with alcohol in a concentration-dependent manner. Yet, the exact molecular mechanisms and conformational dynamics of this interaction are not well understood. Here, we conducted a series of molecular dynamics simulations of the interaction of moderate ethanol concentrations with rat's wild-type GluN1–GluN2B NMDA Receptor under physiological conditions. The simulations suggest that glutamate or glycine alone induce an intermediate conformational state and point towards the transmembrane domain (TMD) as the site of action of ethanol molecules. Ethanol interacts by double hydrogen bonds with Trp635 and Phe638 at the transmembrane M3 helix of GluN2B. Alcohol not only reduces the pore radius of the ion channel within the TMD but also decreases accessibility of glutamate and glycine to the ligand-binding sites by altering the structure of the ligand-binding domain and significantly widening the receptor in that area.     

Generaton of tunable 16 μm radiation by stimulated hyper-raman effect in strontium vapour

The generation of tunable 16 μm radiation by stimulated hyper-Raman scattering from atomic strontium vapour is reported. The infrared radiation has a linewidth of 0.4 cm⁻¹ which corresponds to that of the nitrogen laser pumped dye laser used as a pump source. Due to relatively low pump intensity the infrared power was only 20 mW. However, the system is easily scalable to a higher conversion efficiency.     

Transport properties of the Lorentz gas: Fourier's law

We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT ₁ andT ₂ respectively,T ₁ <T ₂. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL ¹-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T ₂-T ₁)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship.