Semiclassical theory for small displacements

Characteristic functions contain complete information about all the moments of a classical distribution and the same holds for the Fourier transform of the Wigner function: a quantum characteristic function, or the chord function. However, knowledge of a finite number of moments does not allow for accurate determination of the chord function. For pure states this provides the overlap of the state with all its possible rigid translations (or displacements). We here present a semiclassical approximation of the chord function for large Bohr-quantized states, which is accurate right up to a caustic, beyond which the chord function becomes evanescent. It is verified to pick out blind spots, which are displacements for zero overlaps. These occur even for translations within a Planck area of the origin. We derive a simple approximation for the closest blind spots, depending on the Schroedinger covariance matrix, which is verified for Bohr-quantized states.Comment: 16 pages, 4 figures

Local structure study of In_xGa_(1-x)As semiconductor alloys using High Energy Synchrotron X-ray Diffraction

Nearest and higher neighbor distances as well as bond length distributions (static and thermal) of the In_xGa_(1-x)As (0<x<1) semiconductor alloys have been obtained from high real-space resolution atomic pair distribution functions (PDFs). Using this structural information, we modeled the local atomic displacements in In_xGa_(1-x)As alloys. From a supercell model based on the Kirkwood potential, we obtained 3-D As and (In,Ga) ensemble averaged probability distributions. This clearly shows that As atom displacements are highly directional and can be represented as a combination of and displacements. Examination of the Kirkwood model indicates that the standard deviation (sigma) of the static disorder on the (In,Ga) sublattice is around 60% of the value on the As sublattice and the (In,Ga) atomic displacements are much more isotropic than those on the As sublattice. The single crystal diffuse scattering calculated from the Kirkwood model shows that atomic displacements are most strongly correlated along directions.Comment: 10 pages, 12 figure

The abundance of Bullet-groups in LCDM

We estimate the expected distribution of displacements between the two dominant dark matter (DM) peaks (DM-DM displacements) and between DM and gaseous baryon peak (DM-gas displacements) in dark matter halos with masses larger than $10^{13}$ Msun/h. We use as a benchmark the observation of SL2S J08544-0121, which is the lowest mass system ($1.0\times 10^{14}$ Msun/h) observed so far featuring a bi-modal dark matter distribution with a dislocated gas component. We find that $(50 \pm 10)$% of the dark matter halos with circular velocities in the range 300 km/s to 700 km/s (groups) show DM-DM displacements equal or larger than $186 \pm 30$ kpc/h as observed in SL2S J08544-0121. For dark matter halos with circular velocities larger than 700 km/s (clusters) this fraction rises to 70 $\pm$ 10%. Using the same simulation we estimate the DM-gas displacements and find that 0.1 to 1.0% of the groups should present separations equal or larger than $87\pm 14$kpc/h corresponding to our observational benchmark; for clusters this fraction rises to (7 $\pm$ 3)%, consistent with previous studies of dark matter to baryon separations. Considering both constraints on the DM-DM and DM-gas displacements we find that the number density of groups similar to SL2S J08544-0121 is $\sim 6.0\times 10^{-7}$ Mpc$^{-3}$, three times larger than the estimated value for clusters. These results open up the possibility for a new statistical test of LCDM by looking for DM-gas displacements in low mass clusters and groups.Comment: 6 pages, 3 figures, accepted for publication in ApJ Letter

The Phenomenon of Darboux Displacements

For a class of Schrodinger Hamiltonians the supersymmetry transformations can degenerate to simple coordinate displacements. We examine this phenomenon and show that it distinguishes the Weierstrass potentials including the one-soliton wells and periodic Lame functions. A supersymmetric sense of the addition formula for the Weierstrass functions is elucidated.Comment: 11 pages, latex, 2 eps figure

Differential geometry via infinitesimal displacements

We present a new formulation of some basic differential geometric notions on a smooth manifold M, in the setting of nonstandard analysis. In place of classical vector fields, for which one needs to construct the tangent bundle of M, we define a prevector field, which is an internal map from *M to itself, implementing the intuitive notion of vectors as infinitesimal displacements. We introduce regularity conditions for prevector fields, defined by finite differences, thus purely combinatorial conditions involving no analysis. These conditions replace the more elaborate analytic regularity conditions appearing in previous similar approaches, e.g. by Stroyan and Luxemburg or Lutz and Goze. We define the flow of a prevector field by hyperfinite iteration of the given prevector field, in the spirit of Euler's method. We define the Lie bracket of two prevector fields by appropriate iteration of their commutator. We study the properties of flows and Lie brackets, particularly in relation with our proposed regularity conditions. We present several simple applications to the classical setting, such as bounds related to the flow of vector fields, analysis of small oscillations of a pendulum, and an instance of Frobenius' Theorem regarding the complete integrability of independent vector fields.Comment: Improved presentation in various places. To appear in Journal of Logic and Analysi

Displacements analysis of self-excited vibrations in turning

The actual research deals with determining by a new protocol the necessary parameters considering a three-dimensional model to simulate in a realistic way the turning process on machine tool. This paper is dedicated to the experimental displacements analysis of the block tool / block workpiece with self-excited vibrations. In connexion with turning process, the self-excited vibrations domain is obtained starting from spectra of two accelerometers. The existence of a displacements plane attached to the tool edge point is revealed. This plane proves to be inclined compared to the machines tool axes. We establish that the tool tip point describes an ellipse. This ellipse is very small and can be considered as a small straight line segment for the stable cutting process (without vibrations). In unstable mode (with vibrations) the ellipse of displacements is really more visible. A difference in phase occurs between the tool tip displacements on the radial direction and on the cutting one. The feed motion direction and the cutting one are almost in phase. The values of the long and small ellipse axes (and their ratio) shows that these sizes are increasing with the feed rate value. The axis that goes through the stiffness center and the tool tip represents the maximum stiffness direction. The maximum (resp. minimum) stiffness axis of the tool is perpendicular to the large (resp. small) ellipse displacements axis. FFT analysis of the accelerometers signals allows to reach several important parameters and establish coherent correlations between tool tip displacements and the static - elastic characteristics of the machine tool components tested