Optical billiards for atoms

One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a closed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off beams of light. These beams create the desired spatial pattern, forming an "optical billiard." We find excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new testing ground for classical and quantum chaos.     

Measurement of the high energy two-body deuteron photodisintegration differential cross section

The first measurements of the d(gamma,p)n differential cross section at forward angles and photon energies above 4 GeV were performed at the Thomas Jefferson National Accelerator Facility (JLab). The results indicate evidence of an angular dependent scaling threshold. Results at straight theta(cm) = 37 degrees are consistent with the constituent counting rules for E(gamma) greater, similar 4 GeV, while those at 70 degrees are consistent with the constituent counting rules for E(gamma) greater, similar 1.5 GeV.     

Optimal control problem on insect pest populations

In this article we present a model of insect infestation of grape vines and consider the optimal control of the pest through egg population removal. Existence and uniqueness of solutions are proved.     

Precise measurement of deuteron tensor analyzing powers with BLAST

We report a precision measurement of the deuteron tensor analyzing powers T(20) and T(21) at the MIT-Bates Linear Accelerator Center. Data were collected simultaneously over a momentum transfer range Q=2.15-4.50 fm(-1) with the Bates Large Acceptance Spectrometer Toroid using a highly polarized deuterium internal gas target. The data are in excellent agreement with calculations in a framework of effective field theory. The deuteron charge monopole and quadrupole form factors G(C) and G(Q) were separated with improved precision, and the location of the first node of G(C) was confirmed at Q=4.19±0.05 fm(-1). The new data provide a strong constraint on theoretical models in a momentum transfer range covering the minimum of T(20) and the first node of G(C).     

On directed graphs with an independent covering set

We prove that if a directed graph,D, contains no odd directed cycle and, for all but finitely many vertices, EITHER the in-degrees are finite OR the out-degrees are at most one, thenD contains an independent covering set (i.e. there is a kernel). We also give an example of a countable directed graph which has no directed cycle, each vertex has out-degree at most two, and which has no independent covering set.Research supported by N.S.E.R.C. grants #69-0982 and #69-0259.     

Temperature hysteretic effect and its influence on colossal magnetoresistance of La0.33Nd0.33Ca0.33MnO3

Electrical resistance (R) measurements of a bulk La_0.33Nd_0.33Ca_0.33MnO₃ perovskite in magnetic fields up to 40 kOe have revealed anomalous temperature hysteretic effects both in 0 Oe and 20 kOe magnetic fields. The sharp peak observed in the R vs. T plot indicates the occurrence of metal-to-insulator (M-I) transition at a temperature of T _MI=110 K and 140 K, for cooling and warming paths, respectively. An applied magnetic field of 20 kOe reduces the resistance and shifts T _MI to 160 K and 185 K for cooling and warming, respectively. We have observed a much higher resistance in the cooling path than in the warming path leading to the hysteretic resistance ratio (R _cool/R _warm) of 200 at 110 K and 1.8 at 160 K for 0 Oe and 20 kOe, respectively. Record values of colossal magnetoresistance (CMR) have been achieved. The CMR value reaches nearly 99% in the temperature ranges of 90 K to 140 K and 90 K to 170 K for 20 kOe and 40 kOe magnetic fields in the cooling mode, respectively. The observed unusual behavior is attributed to the co-existence of La-rich and Nd-rich domains assumed to be distributed randomly in the compound.     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.