Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

Charge quantization and detector resolution

Charge quantization, or the absence thereof, is a central theme in quantum circuit theory, with dramatic consequences for the predicted circuit dynamics. Very recently, the question of whether or not charge should actually be described as quantized has enjoyed renewed widespread interest, with however seemingly contradictory propositions. Here, we intend to reconcile these different approaches, by arguing that ultimately, charge quantization is not an intrinsic system property, but instead depends on the spatial resolution of the charge detector. We show that the latter can be directly probed by unique geometric signatures in the correlations of the supercurrent. We illustrate these findings at the example of Josephson junction arrays in the superinductor regime, where the transported charge appears to be continuous. Finally, we comment on potential consequences of charge quantization beyond superconducting circuits.

Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds

We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of $$ \mathcal{N} $$ N = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.

Quaternionic electrodynamics

We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy conservation, and the stress-energy tensor. The formalism also enabled us to generalize the Dirac monopole and the charge quantization rule.

Quantum Mechanical Analysis on Modeling of Surface Potential and Drain Current for Nanowire JLFET

This paper presents an analytical model for ultra scaled symmetric double gate (SDG) nanowire junctionless field effect transistor (JLFET), which includes charge quantization in all the regions of operation. This model is based on a first-order correction for the confined energies obtained by solving the Schrodinger’s equation. The model is able to predict the quantum mechanical effects (QME) on the surface potential, drain current and transconductance for a highly doped and extremely thin silicon layer of thickness down to 4nm. The results obtained are validated by comparing with GENIUS 3D TCAD quantum simulations.

Gravity or Magnetic Monopoles? You Cannot Have Both!

In this paper, we argue that gravity breaks the symmetry between electric and magnetic equations (without sources) within the Standard Model. As a result, the motivation for introducing magnetic monopoles disappears (without affecting charge quantization): magnetic monopole probably do not exist in the presence or gravity. It is consistent with the absence of observation of magnetic monopoles and resolves the magnetic monopole cosmology problem. This result could have serious implications for supersymmetry, supergravity, GUTs and ToEs, including in particular superstrings. Some of these implications, and possible ways forward, are discussed.

A New Spacetime Symmetry

Based on detection of elliptic particle tracks, $\simeq 137^2 n^2$ bigger than Bohr-Sommerfeld electron orbits, indicating the possible detection of superluminal electrons masquerading as magnetic monopoles, a new structure emerges leading to: (i) a new set of seven elementary lengths; (ii) replacement of the usual motion (Lorentz) transformations by scale transformations between $v^2<c^2$ and $v^2>c^2$ frames; (iii) equivalence of charge between $v^2<c^2$ and $v^2>c^2$ frames based on the Dirac-Schwinger quantization condition; (iv) a relativistic foundation for the Dirac-Schwinger quantization condition; (v) a possible cause of charge quantization; and (vi) the prospect of symmetry in Maxwell's equations. If the elliptic particle tracks are viewed as a magnification of electron orbits, the effect is suggestive of a spacetime distortion such as those predicted in general relativistic theories.