Visualizing the collapse and revival of wavepackets in the infinite square well using expectation values

We investigate the short-, medium-, and long-term time dependence of wave packets in the infinite square well. In addition to emphasizing the appearance of wave packet revivals, i.e., situations where a spreading wave packet reforms with close to its initial shape and width, we also examine in detail the approach to the collapsed phase where the position-space probability density is almost uniformly spread over the well. We focus on visualizing these phenomena in both position- and momentum-space as well as by following the time-dependent expectation values of and uncertainties in position and momentum. We discuss the time scales for wave packet collapse, using both an autocorrelation function analysis, as well as focusing on expectation values and find two relevant time scales which describe different aspects of the decay phase. In an Appendix, we briefly discuss wave packet revival and collapse in a more general, one-dimensional power-law potential given by $V_{(k)}(x) = V_0|x/a|^k$ which interpolates between the case of the harmonic oscillator ($k=2$) and the infinite well ($k=\infty$).Comment: 34 pages, 11 figure

RadiX-Net: Structured Sparse Matrices for Deep Neural Networks

The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them. Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology. The resulting neural network is known as a sparse neural network. More recent work has demonstrated the remarkable result that certain sparse DNNs can train to the same precision as dense DNNs at lower runtime and storage cost. An intriguing class of these sparse DNNs is the X-Nets, which are initialized and trained upon a sparse topology with neither reference to a parent dense DNN nor subsequent pruning. We present an algorithm that deterministically generates RadiX-Nets: sparse DNN topologies that, as a whole, are much more diverse than X-Net topologies, while preserving X-Nets' desired characteristics. We further present a functional-analytic conjecture based on the longstanding observation that sparse neural network topologies can attain the same expressive power as dense counterpartsComment: 7 pages, 8 figures, accepted at IEEE IPDPS 2019 GrAPL workshop. arXiv admin note: substantial text overlap with arXiv:1809.0524

NATIONAL FOOD AND NUTRITION POLICIES IN THE UNITED STATES

Agricultural and Food Policy,

Low-cost Active Structural Control Space Experiment (LASC)

The DOE Lab Director's Conference identified the need for the DOE National Laboratories to actively and aggressively pursue ways to apply DOE technology to problems of national need. Space structures are key elements of DOD and NASA space systems and a space technology area in which DOE can have a significant impact. LASC is a joint agency space technology experiment (DOD Phillips, NASA Marshall, and DOE Sandia). The topics are presented in viewgraph form and include the following: phase 4 investigator testbed; control of large flexible structures in orbit; INFLEX; Controls, Astrophysics; and structures experiments in space; SARSAT; and LASC mission objectives

Less than perfect quantum wavefunctions in momentum-space: How phi(p) senses disturbances in the force

We develop a systematic approach to determine the large |p| behavior of the momentum-space wavefunction, phi(p), of a one-dimensional quantum system for wich the position-space wavefunction, psi(x), has a discontinuous derivative at any order. We find that if the k-th derivative of the potential energy function has a discontinuity, there is a corresponding discontinuity in psi^{(k+2)}(x) at the same point. This discontinuity leads directly to a power-law tail in the momentum-space wavefunction proportional to 1/p^{k+3}. A number of familiar pedagogical examples are examined in this context, leading to a general derivation of the result.Comment: 22 pages, 2 figures. To appear in Am. J. Phy