Dynamics of Macroscopic Wave Packet Passing through Double Slits: Role of Gravity and Nonlinearity

Using the nonlinear Schroedinger equation (Gross-Pitaevskii equation), the dynamics of a macroscopic wave packet for Bose-Einstein condensates falling through double slits is analyzed. This problem is identified with a search for the fate of a soliton showing a head-on collision with a hard-walled obstacle of finite size. We explore the splitting of the wave packet and its reorganization to form an interference pattern. Particular attention is paid to the role of gravity (g) and repulsive nonlinearity (u_0) in the fringe pattern. The peak-to-peak distance in the fringe pattern and the number of interference peaks are found to be proportional to g^(-1/2) and u_0^(1/2)g^(1/4), respectively. We suggest a way of designing an experiment under controlled gravity and nonlinearity.Comment: 10 pages, 4 figures and 1 tabl

Sound Propagation in Elongated Bose-Einstein Condensed Clouds

We consider propagation of sound pulses along the long axis of a Bose-Einstein condensed cloud in a very anisotropic trap. In the linear regime, we demonstrate that the square of the velocity of propagation is given by the square of the local sound velocity, $c^2=nU_0/m$, averaged over the cross section of the cloud. We also carry out calculations in the nonlinear regime, and determine how the speed of the pulse depends on its amplitude.Comment: 4 pages, revtex, 3 eps figure

Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation

In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion

Internal electrostatic discharge hazard risk assessment to the Galileo orbiter

A worst case assessment was performed on the Command Data System (CDS) multilayer printed circuit board and an output power transformer module in the power subsystem. An estimate of the Jovian environment during the 35 hour orbit insertion was supplied by JPL and used as an input to calculate the electron transport into the Galileo components. A radiation shielding analysis computer code, CHARGE, calculated the electron transport deposition trapped in the anticipated sensitive areas of the multilayer board and transformer module. Based on these trapped charge calculations electric fields were calculated between the identified isolated areas and the spacecraft ground. The results of the assessment of electrostatic discharge (DSD) in the CDS multilayer printed circuit board indicate that the probability of ESD in the FR4 is low. The probability of ESD in the components attached to the multilayer board, however, is uncertain based on a lack of prior experimental data

Real symmetric random matrices and paths counting

Exact evaluation of $$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary probability distribution. These expectations are polynomials in the moments of the matrix entries ; they provide useful information on the spectral density of the ensemble in the large $n$ limit. They also are a straightforward tool to examine a variety of rescalings of the entries in the large $n$ limit.Comment: 23 pages, 10 figures, revised pape