The Scattering of Dirac Spinors in Rotating Spheroids

• URL: http://arxiv.org/abs/2007.02685v1
• Date: Mon, 6 Jul 2020 12:34:06 GMT
• Title: The Scattering of Dirac Spinors in Rotating Spheroids
• Authors: Zhi Fu Gao (Xinjiang Astronomical Observatory, CAS, 150, Science 1-Street, Urumqi, Xinjiang, 830011, China), Ci Xing Chen (Department of Astronomy, University of Sciences and Technology of China, CAS, Hefei 230026, China) and Na Wang (Xinjiang Astronomical Observatory, CAS, 150, Science 1-Street, Urumqi, Xinjiang, 830011, China)
• Abstract summary: We study the scattering of spinors of the Dirac equation, and in particular investigate the scattering issue in the limit case of rotating Maclaurin spheroids. Because of weak gravitational field and constant mass density, our results are reasonable.
• Score: 12.498585449297476
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: There are many stars that are rotating spheroids in the Universe, and studying them is of very important significance. Since the times of Newton, many astronomers and physicists have researched gravitational properties of stars by considering the moment equations derived from Eulerian hydrodynamic equations. In this paper we study the scattering of spinors of the Dirac equation, and in particular investigate the scattering issue in the limit case of rotating Maclaurin spheroids. Firstly we give the metric of a rotating ellipsoid star, then write the Dirac equation under this metric, and finally derive the scattering solution to the Dirac equation and establish a relation between differential scattering cross-section, $\sigma$, and stellar matter density, $\mu$. It is found that the sensitivity of $\sigma$ to the change in $\mu$ is proportional to the density $\mu$. Because of weak gravitational field and constant mass density, our results are reasonable. The results can be applied to white dwarfs, main sequence stars, red giants, supergiant stars and so on, as long as their gravitational fields are so weak that they can be treated in the Newtonan approximations, and the fluid is assumed to be incompressible. Notice that we take the star's matter density to be its average density and the star is not taken to be compact. Obviously our results cannot be used to study neutron stars and black holes. In particular, our results are suitable for white dwarfs, which have average densities of about $10^{5}-10^{6}$\,g~cm$^{-3}$, corresponding to a range of mass of about $0.21-0.61 M_{\bigodot}$ and a range of radius of about $6000-10000$\,km.

Related papers

• Detecting gravitational waves with spin systems [8.587398029054809]
  We propose that spin systems can be employed to detect gravitational waves in this unexplored frequency regime.<n>We derive the spin's response to gravitational waves and identify three distinct effects: the well-known Gertsenshtein effect, a metric-induced interaction, and the gravitational spin Hall effect.<n>The proposed experimental scheme is capable of probing gravitational waves in the kilohertz to gigahertz range, with projected sensitivities reaching $sqrtS_happrox10-20mathrmHz-1/2$.
  arXiv  Detail & Related papers  (2025-10-13T04:58:10Z)
• Entanglement through high-energy scattering in noncommutative quantum electrodynamics [0.0]
  We analyze the generation of entanglement through some key scattering processes in massless quantum electrodynamics.<n>The scattering processes we shall study do not occur in ordinary Minkowski spacetime.
  arXiv  Detail & Related papers  (2025-06-18T11:03:51Z)
• Dynamics of Spinning Test Body in quadratic Einstein-Cartan Theory and its Free-fall Test [11.547161673346894]
  We study the dynamics of the non-relativistic spinning test body (STB) in the framework of Einstein-Cartan theory.<n>We find that the trajectories of STB deviate from the traditional Mathissontextendash Papapetrou equation.
  arXiv  Detail & Related papers  (2025-03-31T13:41:00Z)
• Probing Lambda-Gravity with Bose-Einstein Condensate [39.58317527488534]
  A novel detector concept exploits the dynamics of quantum phononic excitations in a trapped Bose-Einstein condensate (BEC) The BEC exhibits sensitivity unique to the two key components of the gravitational potential in $Lambda$-gravity. This experiment could establish the best Earth-based upper limit on $Lambda$ at $10-31$ m$-2$, marking the first laboratory-based probe of the cosmological constant.
  arXiv  Detail & Related papers  (2024-09-29T19:56:18Z)
• Helicity is a topological invariant of massless particles: C=-2h [18.79946237767752]
  We show that a subtler relation exists between the topological and geometry of massless particles. We generate all massless bundle representations via an abelian group structure of massless particles.
  arXiv  Detail & Related papers  (2024-07-03T20:48:18Z)
• Full quantum tomography of top quark decays [0.0]
  Quantum tomography in high-energy physics processes has usually been restricted to the spin degrees of freedom. We address the case of top quark decays $t to W b$, in which the orbital angular momentum ($L$) and the spins of $W$ and $b$ are intertwined into a 54-dimensional $LWb$ density operator. The entanglement between $L$ and the $W$ or $b$ spin is large and could be determined for decays of single top quarks produced at the Large Hadron Collider with Run 2 data.
  arXiv  Detail & Related papers  (2024-02-22T17:33:33Z)
• Photon topology [22.20907440445493]
  We show that there are no photons with $boldsymbolk=0$, creating a hole in momentum space. While the set of all photons forms a trivial vector bundle $gamma$ over this momentum space, the $R$- and $L$-photons form topologically nontrivial subbundles. We also demonstrate that the spin-Chern number of photons is not a purely topological quantity.
  arXiv  Detail & Related papers  (2023-08-22T03:05:37Z)
• Quantum Tunneling of Ultralight Dark Matter Out of Satellite Galaxies [0.0]
  We analyze tunneling of the scalar field in dwarf satellites due to the tidal gravitational force from the host halo. By demanding that the core of the Fornax dwarf halo can survive for at least the age of the universe places a bound on the dark matter particle mass $2times 10-22,mboxeVlesssim mlesssim 6times 10-22,$eV.
  arXiv  Detail & Related papers  (2022-12-14T18:14:28Z)
• Catapulting towards massive and large spatial quantum superposition [0.0]
  Large spatial quantum superposition of size $cal O (1-10)rm mu textm$ for mass $m sim 10-17-10-14textkg$ is required to probe the foundations of quantum mechanics. We will show that it is possible to accelerate the two spin states of a macroscopic nano-crystal sourced by the inhomogeneous nonlinear magnetic field in the Stern-Gerlach type setup.
  arXiv  Detail & Related papers  (2022-06-08T18:00:12Z)
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space [8.25487382053784]
  We develop an action formulation of dynamics in the Hilbert space. By coupling the random to quantum fields, we obtain a random-number action which has the statistical spacetime translation. We prove that the QFT is renormal even in the presence of interaction.
  arXiv  Detail & Related papers  (2021-12-28T04:58:43Z)
• Spin-1/2 particles under the influence of a uniform magnetic field in the interior Schwarzschild solution [62.997667081978825]
  relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. Results are relevant to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense.
  arXiv  Detail & Related papers  (2021-11-30T14:46:00Z)
• Resolving the gravitational redshift within a millimeter atomic sample [94.94540201762686]
  Einstein's theory of general relativity states that clocks at different gravitational potentials tick at different rates. We measure a linear frequency gradient consistent with the gravitational redshift within a single millimeter scale sample of ultracold strontium.
  arXiv  Detail & Related papers  (2021-09-24T23:58:35Z)
• Newton, entanglement, and the graviton [0.0]
  Many experiments have recently been proposed to test whether non-relativistic gravitational interactions can generate entanglement. I demonstrate that this "Newtonian entanglement" requires the existence of massless bosons, universally coupled to mass, in the Hilbert space of low-energy scattering states.
  arXiv  Detail & Related papers  (2021-08-13T17:20:47Z)
• Remarks on Fermions in a Dipole Magnetic Field [0.0]
  This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center. We extend our computations in two significant ways. The first is to a relativistic spin-$frac12$ fermion and the second concerns the interpretation of the physics.
  arXiv  Detail & Related papers  (2021-07-21T13:42:03Z)
• Relativistic generalization of the Schrodinger-Newton model for the wavefunction reduction [0.0]
  We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by Diosi, Penrose et al. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. The equivalence principle is fulfilled with an extremely high precision.
  arXiv  Detail & Related papers  (2020-10-07T12:43:44Z)
• Hyperfine and quadrupole interactions for Dy isotopes in DyPc$_2$ molecules [77.57930329012771]
  Nuclear spin levels play an important role in understanding magnetization dynamics and implementation and control of quantum bits in lanthanide-based single-molecule magnets. We investigate the hyperfine and nuclear quadrupole interactions for $161$Dy and $163$Dy nucleus in anionic DyPc$.
  arXiv  Detail & Related papers  (2020-02-12T18:25:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.