Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid non-inertial frames, containing the standard rigidly linear accelereted and rotating ones, is given in the framework of parametrized Galilei theories. Then the multi-temporal quantization, in which the gauge variables, describing the non-inertial effects, are not quantized but considered as c-number generalized times, is applied to non relativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of center of mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid non-inertial frames are recovered as special cases

Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

Fractal geometry of critical Potts clusters

Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are presented. The data are found consistent with the recently derived corrections-to-scaling theory. However, the approach to the asymptotic region is slow, and the present range of the data does not allow a unique identification of the exact correction exponentsComment: 7 pages, 8 figures, Late

Superlattice with hot electron injection: an approach to a Bloch oscillator

A semiconductor superlattice with hot electron injection into the miniband is considered. The injection changes the stationary distribution function and results in a qualitative change of the frequency behaviour of the differential conductivity. In the regime with Bloch oscillating electrons and injection into the upper part of the miniband the region of negative differential conductivity is shifted from low frequencies to higher frequencies. We find that the dc differential conductivity can be made positive and thus the domain instability can be suppressed. At the same time the high-frequency differential conductivity is negative above the Bloch frequency. This opens a new way to make a Bloch oscillator operating at THz frequencies.Comment: RevTeX, 8 pages, 2 figures, to be published in Phys. Rev. B, 15 Januar 200

Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations

Neckties in the Tropics: A Model of International Trade and Cultural Diversity

Some cultural goods, like clothes and films, are consumed socially and are thus characterized by the same consumption network externalities as languages. At the same time, producers of new cultural goods in any one country draw on the stock of ideas generated by previous cultural production in all countries. For such goods, costless trade and communication tend to lead to the dominance of one cultural style, increasing utility in the short run but reducing quality and generating cultural stagnation in the long run. Increasing trade costs while keeping communication costs low may reduce welfare by stimulating production of cultural goods that are “compatible” with the dominant style, thereby capturing consumption network externalities, but that add little to the stock of usable ideas. Our two-country analysis suggests a reform of cultural policy whereby import restrictions in the smaller country are removed, and are replaced by subsidies to the fixed costs of production of new cultural goods in its traditional style

EC 11481-2303 - A Peculiar Subdwarf OB Star Revisited

EC 11481-2303 is a peculiar, hot, high-gravity pre-white dwarf. Previous optical spectroscopy revealed that it is a sdOB star with an effective temperature (Teff) of 41790 K, a surface gravity log(g)= 5.84, and He/H = 0.014 by number. We present an on-going spectral analysis by means of non-LTE model-atmosphere techniques based on high-resolution, high-S/N optical (VLT-UVES) and ultraviolet (FUSE, IUE) observations. We are able to reproduce the optical and UV observations simultaneously with a chemically homogeneous NLTE model atmosphere with a significantly higher effective temperature and lower He abundance (Teff = 55000 K, log (g) = 5.8, and He / H = 0.0025 by number). While C, N, and O appear less than 0.15 times solar, the iron-group abundance is strongly enhanced by at least a factor of ten.Comment: 8 pages, 11 figure

From bi-Hamiltonian geometry to separation of variables: stationary Harry-Dym and the KdV dressing chain

Separability theory of one-Casimir Poisson pencils, written down in arbitrary coordinates, is presented. Separation of variables for stationary Harry-Dym and the KdV dressing chain illustrates the theory.Comment: LaTex 14 pages, Proceedings of the Special Session on Integrable Systems of the First Joint Meeting of the American Mathematical Society and the Hong Kong Mathematical Society, to appear in J. Nonl. Math. Phy