Reversal of the circulation of a vortex by quantum tunneling in trapped Bose systems

We study the quantum dynamics of a model for a vortex in a Bose gas with repulsive interactions in an anisotropic, harmonic trap. By solving the Schr\"odinger equation numerically, we show that the circulation of the vortex can undergo periodic reversals by quantum-mechanical tunneling. With increasing interaction strength or particle number, vortices become increasingly stable, and the period for reversals increases. Tunneling between vortex and antivortex states is shown to be described to a good approximation by a superposition of vortex and antivortex states (a Schr\"odinger cat state), rather than the mean-field state, and we derive an analytical expression for the oscillation period. The problem is shown to be equivalent to that of the two-site Bose Hubbard model with attractive interactions.Comment: 5 pages, 5 figures; published in Phys. Rev. A, Rapid Communication

Electron screening in the liquid-gas mixed phases of nuclear matter

Screening effects of electrons on inhomogeneous nuclear matter, which includes spherical, slablike, and rodlike nuclei as well as spherical and rodlike nuclear bubbles, are investigated in view of possible application to cold neutron star matter and supernova matter at subnuclear densities. Using a compressible liquid-drop model incorporating uncertainties in the surface tension, we find that the energy change due to the screening effects broadens the density region in which bubbles and nonspherical nuclei appear in the phase diagram delineating the energetically favorable shape of inhomogeneous nuclear matter. This conclusion is considered to be general since it stems from a model-independent feature that the electron screening acts to decrease the density at which spherical nuclei become unstable against fission and to increase the density at which uniform matter becomes unstable against proton clustering.Comment: 12 pages, 8 figures, accepted for publication in Physical Review

Chemical Evolution in the Large Magellanic Cloud

We present a new input parameter set of the Pagel model (Pagel & Tautvai$\rm \breve{s}$ien$\rm \dot{e}$ 1998) for the Large Magellanic Cloud (LMC) in order to reproduce the observations, including the star formation rate (SFR) history. It is concluded that the probability for (3-8)$M_{\odot}$ stars to explode as SNe Ia has to be quite high ($\sim 0.17$) in the LMC. As a result, a steep initial mass function (IMF) slope and existence of the outflow are not needed in order to attain the low [O/Fe] ratio in the LMC. As for the current supernova ratio, a high ratio ($\sim 1.3$) is concluded by the new parameter set, which is consistent with the recent X-ray observations.Comment: 20 pages, gzipped tar file including LaTeX text and 8 postscript figures. submitted to Publication of the Astronomical Society of Japa

A Maximum Mass-to-Size Ratio in Scalar-Tensor Theories of Gravity

We derive a modified Buchdahl inequality for scalar-tensor theories of gravity. In general relativity, Buchdahl has shown that the maximum value of the mass-to-size ratio, $2M/R$, is 8/9 for static and spherically symmetric stars under some physically reasonable assumptions. We formally apply Buchdahl's method to scalar-tensor theories and obtain theory-independent inequalities. After discussing the mass definition in scalar-tensor theories, these inequalities are related to a theory-dependent maximum mass-to-size ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but also unity, which we call {\it the black hole limit}, in contrast to general relativity. Next, we numerically examine the validity of the assumptions made in deriving the inequalities and the applicability of our analytic results. We find that the assumptions are mostly satisfied and that the mass-to-size ratio exceeds both Buchdahl's limit and the black hole limit. However, we also find that this ratio never exceeds Buchdahl's limit when we impose the further condition, $\rho-3p\ge0$, on the density, $\rho$, and pressure, $p$, of the matter.Comment: 23 pages, 13 figures and 1 tabl

Driving a car with custom-designed fuzzy inferencing VLSI chips and boards

Vehicle control in a-priori unknown, unpredictable, and dynamic environments requires many calculational and reasoning schemes to operate on the basis of very imprecise, incomplete, or unreliable data. For such systems, in which all the uncertainties can not be engineered away, approximate reasoning may provide an alternative to the complexity and computational requirements of conventional uncertainty analysis and propagation techniques. Two types of computer boards including custom-designed VLSI chips were developed to add a fuzzy inferencing capability to real-time control systems. All inferencing rules on a chip are processed in parallel, allowing execution of the entire rule base in about 30 microseconds, and therefore, making control of 'reflex-type' of motions envisionable. The use of these boards and the approach using superposition of elemental sensor-based behaviors for the development of qualitative reasoning schemes emulating human-like navigation in a-priori unknown environments are first discussed. Then how the human-like navigation scheme implemented on one of the qualitative inferencing boards was installed on a test-bed platform to investigate two control modes for driving a car in a-priori unknown environments on the basis of sparse and imprecise sensor data is described. In the first mode, the car navigates fully autonomously, while in the second mode, the system acts as a driver's aid providing the driver with linguistic (fuzzy) commands to turn left or right and speed up or slow down depending on the obstacles perceived by the sensors. Experiments with both modes of control are described in which the system uses only three acoustic range (sonar) sensor channels to perceive the environment. Simulation results as well as indoors and outdoors experiments are presented and discussed to illustrate the feasibility and robustness of autonomous navigation and/or safety enhancing driver's aid using the new fuzzy inferencing hardware system and some human-like reasoning schemes which may include as little as six elemental behaviors embodied in fourteen qualitative rules

Single-electron transistors in electromagnetic environments

The current-voltage (I-V) characteristics of single-electron transistors (SETs) have been measured in various electromagnetic environments. Some SETs were biased with one-dimensional arrays of dc superconducting quantum interference devices (SQUIDs). The purpose was to provide the SETs with a magnetic-field-tunable environment in the superconducting state, and a high-impedance environment in the normal state. The comparison of SETs with SQUID arrays and those without arrays in the normal state confirmed that the effective charging energy of SETs in the normal state becomes larger in the high-impedance environment, as expected theoretically. In SETs with SQUID arrays in the superconducting state, as the zero-bias resistance of the SQUID arrays was increased to be much larger than the quantum resistance R_K = h/e^2 = 26 kohm, a sharp Coulomb blockade was induced, and the current modulation by the gate-induced charge was changed from e periodic to 2e periodic at a bias point 0<|V|<2D_0/e, where D_0 is the superconducting energy gap. The author discusses the Coulomb blockade and its dependence on the gate-induced charge in terms of the single Josephson junction with gate-tunable junction capacitance.Comment: 8 pages with 10 embedded figures, RevTeX4, published versio

Macroscopic superposition states in rotating ring lattices

We investigate the effects of rotation on one-dimensional ultracold bosons confined to optical ring lattices. First, we show that there exists a critical rotation frequency at which the ground state of a weakly-interacting and integer-filled atomic gas is fragmented into a macroscopic superposition state with different circulation. Second, we point out several advantages of using slightly non-uniform ring lattices. Finally, we demonstrate that different quasi-momentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency.Comment: 8 pages, 4 figures; PQE-2008 conference proceedings; minor correction

Electroweak interactions in a relativistic Fermi gas

We present a relativistic model for computing the neutrino mean free path in neutron matter. Thereby, neutron matter is described as a non-interacting Fermi gas in beta-equilibrium. We present results for the neutrino mean free path for temperatures from 0 up to 50 MeV and a broad range of neutrino energies. We show that relativistic effects cause a considerable enhancement of neutrino-scattering cross-sections in neutron matter. The influence of the $Q^2$-dependence in the electroweak form factors and the inclusion of a weak magnetic term in the hadron current is discussed. The weak-magnetic term in the hadron current is at the origin of some selective spin dependence for the nucleons which are subject to neutrino interactions.Comment: 11 pages, 7 figures, accepted to Phys. Rev. C, minor changes and updates of the figures are mad

Bessel bridges decomposition with varying dimension. Applications to finance

We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger context where a time-varying drift term can be added. Then in the non-drifted case we extend many results already proven in the case of classical Bessel processes to our context. Our deepest result is a decomposition of the Bridge process associated to this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. On a more practical point of view, we give a methodology to compute the Laplace transform of additive functionals of our process and the associated bridge. This permits in particular to get directly access to the joint distribution of the value at t of the process and its integral. We finally give some financial applications to illustrate the panel of applications of our results