Dynamic structure factor of ultracold Bose and Fermi gases in optical lattices

We investigate the dynamic structure factor of atomic Bose and Fermi gases in one-dimensional optical lattices at zero temperature. The focus is on the generic behaviour of S(k,omega) as function of filling and interaction strength with the aim of identifying possible experimental signatures for the different quantum phase transitions. We employ the Hubbard or Bose-Hubbard model and solve the eigenvalue problem of the Hamiltonian exactly for moderate lattice sizes. This allows us to determine the dynamic structure factor and other observables directly in the phase transition regime, where approximation schemes are generally not applicable. We discuss the characteristic signatures of the various quantum phases appearing in the dynamic structure factor and illustrate that the centroid of the strength distribution can be used to estimate the relevant excitation gaps. Employing sum rules, these quantities can be evaluated using ground state expectation values only. Important differences between bosonic and fermionic systems are observed, e.g., regarding the origin of the excitation gap in the Mott-insulator phase.Comment: 15 pages, 7 figure

BCS Theory for Trapped Ultracold Fermions

We develop an extension of the well-known BCS-theory to systems with trapped fermions. The theory fully includes the quantized energy levels in the trap. The key ingredient is to model the attractive interaction between two atoms by a pseudo-potential which leads to a well defined scattering problem and consequently a BCS-theory free of divergences. We present numerical results for the BCS critical temperature and the temperature dependence of the gap. They are used as a test of existing semi-classical approximations.Comment: 4 pages, 3 figures, submitted to PR

Collective excitations of atomic Bose-Einstein condensates

We apply linear-response analysis of the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate confined in a time-averaged orbiting potential trap. Our calculated values are in excellent agreement with those observed in a recent experiment.Comment: 11 pages, 2 Postscript figures, uses psbox.tex for automatic figure inclusion. More info at http://amo.phy.gasou.edu/bec.htm

No evidence that FLT3 status should be considered as an indicator for transplantation in acute myeloid leukemia (AML): an analysis of 1135 patients, excluding acute promyelocytic leukemia, from the UK MRC AML 10 and 12 trials

Fetal liver tyrosine kinase 3 (FLT3) internal tandem duplications (ITDs) are powerful adverse prognostic indicators for relapse in acute myelold leukemia (AML) but the most efficacious therapy for FLT3/ ITD+ patients is currently unknown. We evaluated outcome according to FLT3/ITD status in 1135 adult patients treated according to United Kingdom Medical Research Council (UK MRC) AML protocols: 141 received an autograft, and 170 received a matched sibling allograft in first complete remission (CR). An FLT3/ITD was detected in 25% of patients and was an independent predictor for relapse (P < .001). It remained prognostic for increased relapse in patients who received a transplant (odds ratio [OR] = 1.91; 95% confidence intervals [CIs] 1.13-3.21; P = .02), with no evidence of a difference in effect between patients who received an autograft (OR = 2.39; CIs = 1.24-4.62) and patients who received an allograft (OR = 1.31; CIs = 0.56-3.06) (test for interaction, P = .3) or between patients who did or did not receive a transplant (P = .4). These results were confirmed in an analysis of 186 patients randomized to receive or not receive an autograft in first CR and in a donor-versus-no donor analysis of 683 patients to assess the role of allograft (for latter, FLT3/ITD- OR = 0.70, CIs = 0.53-0.92; FLT3/ITD+ OR = 0.59, CIs = 0.40-0.87; test for interaction, P = .5). These results suggest that at present there is no strong evidence that FLT3 status should influence the decision to proceed to transplantation

Formation of fundamental structures in Bose-Einstein Condensates

The meanfield interaction in a Bose condensate provides a nonlinearity which can allow stable structures to exist in the meanfield wavefunction. We discuss a number of examples where condensates, modelled by the one dimensional Gross Pitaevskii equation, can produce gray solitons and we consider in detail the case of two identical condensates colliding in a harmonic trap. Solitons are shown to form from dark interference fringes when the soliton structure, constrained in a defined manner, has lower energy than the interference fringe and an analytic expression is given for this condition.Comment: 7 pages, 3 figures, requires ioplppt.st

Creation of macroscopic superposition states from arrays of Bose-Einstein condensates

We consider how macroscopic quantum superpositions may be created from arrays of Bose-Einstein condensates. We study a system of three condensates in Fock states, all with the same number of atoms and show that this has the form of a highly entangled superposition of different quasi-momenta. We then show how, by partially releasing these condensates and detecting an interference pattern where they overlap, it is possible to create a macroscopic superposition of different relative phases for the remaining portions of the condensates. We discuss methods for confirming these superpositions.Comment: 7 pages, 5 figure

Assessing the Quality of Regulatory Impact Analyses

This study provides the most comprehensive evaluation of the quality of recent economic analyses that agencies conduct before finalizing major regulations. We construct a new dataset that includes analyses of forty-eight major health, safety, and environmental regulations from mid-1996 to mid-1999. This dataset provides detailed information on a variety of issues, including an agency's treatment of benefits, costs, net benefits, discounting, and uncertainty. We use this dataset to assess the quality of recent economic analyses and to determine the extent to which they are consistent with President Clinton's Executive Order 12866 and the benefit-cost guidelines issued by the Office of Management and Budget (OMB). We find that economic analyses prepared by regulatory agencies typically do not provide enough information to make decisions that will maximize the efficiency or effectiveness of a rule. Agencies quantified net benefits for only 29 percent of the rules. Agencies failed to discuss alternatives in 27 percent of the rules and quantified costs and benefits of alternatives in only 31 percent of the rules. Our findings strongly suggest that agencies generally failed to comply with the executive order and adhere to the OMB guidelines. We offer specific suggestions for improving the quality of analysis and the transparency of the regulatory process, including writing clear executive summaries, making analyses available on the Internet, providing more careful consideration of alternatives to a regulation, and estimating net benefits of a regulation when data on costs and benefits are provided.

Design of a miniature hydrogen fueled gas turbine engine

The design, development, and delivery of a miniature hydrogen-fueled gas turbine engine are discussed. The engine was to be sized to approximate a scaled-down lift engine such as the teledyne CAE model 376. As a result, the engine design emerged as a 445N(100 lb.)-thrust engine flowing 0.86 kg (1.9 lbs.) air/sec. A 4-stage compressor was designed at a 4.0 to 1 pressure ratio for the above conditions. The compressor tip diameter was 9.14 cm (3.60 in.). To improve overall engine performance, another compressor with a 4.75 to 1 pressure ratio at the same tip diameter was designed. A matching turbine for each compressor was also designed. The turbine tip diameter was 10.16 cm (4.0 in.). A combustion chamber was designed, built, and tested for this engine. A preliminary design of the mechanical rotating parts also was completed and is discussed. Three exhaust nozzle designs are presented

Assessing Regulatory Impact Analyses: The Failure of Agencies to Comply With Executive Order 12,866

None.Environment, Health and Safety, Regulatory Reform

Just how long can you live in a black hole and what can be done about it?

We study the problem of how long a journey within a black hole can last. Based on our observations, we make two conjectures. First, for observers that have entered a black hole from an asymptotic region, we conjecture that the length of their journey within is bounded by a multiple of the future asymptotic ``size'' of the black hole, provided the spacetime is globally hyperbolic and satisfies the dominant-energy and non-negative-pressures conditions. Second, for spacetimes with ${\Bbb R}^3$ Cauchy surfaces (or an appropriate generalization thereof) and satisfying the dominant energy and non-negative-pressures conditions, we conjecture that the length of a journey anywhere within a black hole is again bounded, although here the bound requires a knowledge of the initial data for the gravitational field on a Cauchy surface. We prove these conjectures in the spherically symmetric case. We also prove that there is an upper bound on the lifetimes of observers lying ``deep within'' a black hole, provided the spacetime satisfies the timelike-convergence condition and possesses a maximal Cauchy surface. Further, we investigate whether one can increase the lifetime of an observer that has entered a black hole, e.g., by throwing additional matter into the hole. Lastly, in an appendix, we prove that the surface area $A$ of the event horizon of a black hole in a spherically symmetric spacetime with ADM mass $M_{\text{ADM}}$ is always bounded by $A \le 16\pi M_{\text{ADM}}^2$, provided that future null infinity is complete and the spacetime is globally hyperbolic and satisfies the dominant-energy condition.Comment: 20 pages, REVTeX 3.0, 6 figures included, self-unpackin