Extrapolated High-Order Propagators for Path Integral Monte Carlo Simulations

We present a new class of high-order imaginary time propagators for path-integral Monte Carlo simulations by subtracting lower order propagators. By requiring all terms of the extrapolated propagator be sampled uniformly, the subtraction only affects the potential part of the path integral. The negligible violation of positivity of the resulting path integral at small time steps has no discernable affect on the accuracy of our method. Thus in principle arbitrarily high order algorithms can be devised for path-integral Monte Carlo simulations. We verify this claim is by showing that fourth, sixth, and eighth order convergence can indeed be achieved in solving for the ground state of strongly interacting quantum many-body systems such as bulk liquid $^4$He.Comment: 9 pages and 3 figures. Submitted to J. Chem. Phy

`St\"uckelberg interferometry' with ultracold molecules

We report on the realization of a time-domain `St\"uckelberg interferometer', which is based on the internal state structure of ultracold Feshbach molecules. Two subsequent passages through a weak avoided crossing between two different orbital angular momentum states in combination with a variable hold time lead to high-contrast population oscillations. This allows for a precise determination of the energy difference between the two molecular states. We demonstrate a high degree of control over the interferometer dynamics. The interferometric scheme provides new possibilities for precision measurements with ultracold molecules.Comment: 4 pages, 5 figure

Magneto-optical Feshbach resonance: Controlling cold collision with quantum interference

We propose a method of controlling two-atom interaction using both magnetic and laser fields. We analyse the role of quantum interference between magnetic and optical Feshbach resonances in controlling cold collision. In particular, we demonstrate that this method allows us to suppress inelastic and enhance elastic scattering cross sections. Quantum interference is shown to modify significantly the threshold behaviour and resonant interaction of ultracold atoms. Furthermore, we show that it is possible to manipulate not only the spherically symmetric s-wave interaction but also the anisotropic higher partial-wave interactions which are particularly important for high temperature superfluid or superconducting phases of matter.Comment: 7 pages 3 figures, some minor errors are corrected, Accepted in J. Phys.

Critical velocity for superfluid flow across the BEC-BCS crossover

Critical velocities have been observed in an ultracold superfluid Fermi gas throughout the BEC-BCS crossover. A pronounced peak of the critical velocity at unitarity demonstrates that superfluidity is most robust for resonant atomic interactions. Critical velocities were determined from the abrupt onset of dissipation when the velocity of a moving one dimensional optical lattice was varied. The dependence of the critical velocity on lattice depth and on the inhomogeneous density profile was studied

Mapping functions and critical behavior of percolation on rectangular domains

The existence probability $E_p$ and the percolation probability $P$ of the bond percolation on rectangular domains with different aspect ratios $R$ are studied via the mapping functions between systems with different aspect ratios. The superscaling behavior of $E_p$ and $P$ for such systems with exponents $a$ and $b$, respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev. Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order approximation of the mapping functions $f_R$ and $g_R$ for $E_p$ and $P$, respectively; the exponents $a$ and $b$ can be obtained from numerically determined mapping functions $f_R$ and $g_R$, respectively.Comment: 17 pages with 6 figure

Analytical and experimental study of stratification and liquid-ullage coupling, 1 June 1964 - 31 May 1965

Closed-form solution for stratification of subcooled fluids in containers subjected to heating, and for liquid-ullage vapor couplin

Dynamical Effects from Asteroid Belts for Planetary Systems

The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.Comment: accepted by International Journal of Bifurcation and Chaos in Aug. 2003, AAS Latex, 27 pages with 6 color figure

Hydrodynamical Simulations of the Barred Spiral Galaxy NGC 1097

NGC 1097 is a nearby barred spiral galaxy believed to be interacting with the elliptical galaxy NGC 1097A located to its northwest. It hosts a Seyfert 1 nucleus surrounded by a circumnuclear starburst ring. Two straight dust lanes connected to the ring extend almost continuously out to the bar. The other ends of the dust lanes attach to two main spiral arms. To provide a physical understanding of its structural and kinematical properties, two-dimensional hydrodynamical simulations have been carried out. Numerical calculations reveal that many features of the gas morphology and kinematics can be reproduced provided that the gas flow is governed by a gravitational potential associated with a slowly rotating strong bar. By including the self-gravity of the gas disk in our calculation, we have found the starburst ring to be gravitationally unstable which is consistent with the observation in \citet{hsieh11}. Our simulations show that the gas inflow rate is 0.17 M_\sun yr$^{-1}$ into the region within the starburst ring even after its formation, leading to the coexistence of both a nuclear ring and a circumnuclear disk.Comment: 32 pages, 14 figures, 1 table, accepted for publication in the Ap

The detection of extragalactic 15^{15}N: Consequences for nitrogen nucleosynthesis and chemical evolution

Detections of extragalactic $^{15}$N are reported from observations of the rare hydrogen cyanide isotope HC$^{15}$N toward the Large Magellanic Cloud (LMC) and the core of the (post-) starburst galaxy NGC 4945. Accounting for optical depth effects, the LMC data from the massive star-forming region N113 infer a $^{14}N/^{15}$N ratio of 111 $\pm$ 17, about twice the $^{12}C/^{13}$C value. For the LMC star-forming region N159HW and for the central region of NGC 4945, $^{14}N/^{15}$N ratios are also $\approx$ 100. The $^{14}N/^{15}$N ratios are smaller than all interstellar nitrogen isotope ratios measured in the disk and center of the Milky Way, strongly supporting the idea that $^{15}$N is predominantly of `primary' nature, with massive stars being its dominant source. Although this appears to be in contradiction with standard stellar evolution and nucleosynthesis calculations, it supports recent findings of abundant $^{15}$N production due to rotationally induced mixing of protons into the helium-burning shells of massive stars.Comment: 15 pages including one postscript figure, accepted for publication by ApJ Letter, further comments: please contact Yi-nan Chi

GEODYN programmer's guide, volume 2, part 2

A computer program for executive control routine for orbit integration of artificial satellites is presented. At the beginning of each arc, the program initiates required constants as well as the variational partials at epoch. If epoch needs to be reset to a previous time, the program negates the stepsize, and calls for integration backward to the desired time. After backward integration is completed, the program resets the stepsize to the proper positive quantity