Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.

Recreation Algorithm: Teleportation

‘Teleportation’ means to teleport an object from one place to other with the help of ‘portals’. This is a ‘2 way’ process involving the dissembling from one point to reassembling to the other point separated by a large distance in space and time. The ‘reassemble’ of one person in the other end is based on an algorithm which is solely a polynomial wavefunctions in correspondence with the ‘Minkowski metric’ and based on this ‘algorithm’ the produced image of the persons or the ‘exact copy’ of the persons being teleported is either very accurate or closed to accurate and all of this is the outcome of transforming the matter to energy by means of the Einstein’s famous mass-energy equivalence called E=mc2 as without the conversion of energy, an object ‘being in a state of matter can’t be teleported. There are certain parameters for the ‘teleportation to happen properly’ and these parameters are as follows… 1. The object needs to be ‘teleported’ through ‘hyperspace’ thereby enabling the need for ‘higher dimensional forces due to gravity’. 2. The cross section of the energy packets that will be teleported will be changed due to Fitz-Gerald Lorentz Contractions while moving through ‘hyperspace’. 3. The ‘time will be dilated infinitely’ for the own reference frame of the ‘packets of the objects’ being teleported as the speed of energy is very close to the speed of light. 4. There will be a pathway through hyperspace called as ‘link line’ which is the main highway of the ‘objects energy packets’ to move during teleportation from one portal to another. 5. The energy packets must be equal to 1 at the other end of the ‘link line’ or ‘portal’. That is no fragmentation can be done. All these parameters are very important to analyze in case of ‘teleportation’ and if the parameters are consistent with the theory and mathematics, then the teleportation would happen at the blink of an eye just as the ‘science fiction movies’ and its always instantaneous for small distance (by small, I mean within the range of at least some light seconds) and its always constant time or time has been dilated infinitely due to the ‘speed of the energy packet’ close to that of light’ from the own reference frame of the ‘teleported object’, however, some amount of time will pass for the observers at the other distant ends and that amount of passing time is proportional to the length of the ‘link line’ through hyperspace. The nature of ‘teleportation that I’m going to be discussing here is ‘classical teleportation’ and not ‘quantum teleportation’. Quantum teleportation although has been achieved in ‘laboratory’ however, they are restricted on a very tiny scale of a pair of electrons (up and down spin) or photons (vertical and horizontal polarizations). However, there is great difficulty in achieving this nature of ‘quantum teleportation’ in a very large scale objects. As because a tiny dot (.) contains more than 10^8 atoms and each atom have a number of electrons in different orbital’s depending on the nature of the element comprising the atoms. So, the number of individual electrons are exponentially large in a large scale cluster of a million atoms when taken to be a large objects. Moreover, in quantum teleportation, there is a need for a ‘classical channels’ to establish the contact as the particles are in ‘Bell’s state or entangled pairs’. So, what I would discuss here is a ‘classical’ approach of teleportation and we will proceed both theoretically and mathematically with the process. A complete metric would be derived in this paper to concatenate the proper channel of teleportation through the help of discrete mapping of both locations and coordinates and then the notion of cylindrical polar coordinates are being used in the metric.

The tilt of the local velocity ellipsoid as seen by Gaia

ABSTRACT The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7224 631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Schönrich, McMillan & Eyer. We exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of the Sun. We find that the tilt of the disc-dominated RVS sample is accurately described by the relation $\alpha = (0.952 \pm 0.007)\arctan (|z|/R)$, where (R, z) are cylindrical polar coordinates. This corresponds to velocity ellipsoids close to spherical alignment (for which the normalizing constant would be unity) and pointing towards the Galactic Centre. Flattening of the tilt of the velocity ellipsoids is enhanced close to the plane and Galactic Centre, whilst at high elevations far from the Galactic Centre the population is consistent with exact spherical alignment. Using the LAMOST catalogue cross-matched with Gaia DR2, we construct thin disc and halo samples of reasonable purity based on metallicity. We find that the tilt of thin disc stars straddles $\alpha = (0.909{\!-\!}1.038)\arctan (|z|/R)$, and of halo stars straddles $\alpha = (0.927{\!-\!}1.063)\arctan (|z|/R)$. We caution against the use of reciprocal parallax for distances in studies of the tilt, as this can lead to serious artefacts.

Computer-extended series solution for laminar flow between a fixed impermeable disk and a porous rotating disk

Purpose The purpose of this paper is to study the laminar boundary layer flow between a stationary nonporous disk and a porous rotating disk, both being immersed in large amount of fluid. Design/methodology/approach The governing nonlinear momentum equations in cylindrical polar coordinates together with relevant boundary conditions are reduced to a system of coupled nonlinear ordinary differential equations (NODEs) using similarity transformations. The resulting coupled NODEs are solved using computer-extended series solution and homotopy analysis method. Findings The analytical solutions are explicitly expressed in terms of recurrence relation for determining the universal coefficients. The nature and location of singularity which restricts the convergence of series is analyzed by using Domb–Sykes plot. Reversion of series is used for the improvement of series. The region of validity of series is extended for much larger values of Reynolds number (R), i.e. R = 6 to 15. Originality/value The resulting solutions are compared with earlier works in the literature and are found to be in good agreement.