Quantum Mechanical Tunneling of Dislocations: Quantization and Depinning from Peierls Barrier

Theories of Mott and Weertmann pertaining to quantum mechanical tunneling of dislocations from Peierls barrier in cubic crystals are revisited. Their mathematical calculations about logarithmic creep rate and lattice vibrations as a manifestation of Debye temperature for quantized thermal energy are found correct but they can not ascertain to choose the mass of phonon or “quanta” of lattice vibrations. The quantum mechanical yielding in metals at relatively low temperatures, where Debye temperatures operate, is resolved and the mathematical formulas are presented. The crystal plasticity is studied with stress relaxation curves instead of logarithmic creep rate. With creep rate formulas of Mott and Weertmann, a new formula based on logarithmic profile of stress relaxation curves is proposed which suggests simultaneous quantization of dislocations with their stress, i.e., and depinning of dislocations, i.e., , where is quantum action, σ is the stress, N is the number of dislocations, A is the area and t is the time. The two different interpretations of “quantum length of Peierls barrier”, one based on curvature of space, i.e., yields quantization of Burgers vector and the other based on the curvature of time, i.e., yields depinning of dislocations from Peierls barrier in cubic crystals, are presented. , i.e., the unitary operator on shear modulus yields the variations in the curvature of time due to which simultaneous quantization, and depinning of dislocations occur from Peierls barrier in cubic crystals.

Application of Electrodynamic Theory on Quantum Hall Effect

The quantum electrodynamic (QED) behaviour is studied for quantum Hall effect (QHE). Quantum theory with conjecture of fractional charge quantization (quantum dipole moment), eigenfunctions for fractional charge quantization at the surface of a twisted and twigged electron quanta and above its surface, fractional Fourier transform and Hermite function for fractional charge quantization is developed. With energy eigen value equation for QHE and with energy operator on an eigenfunction of a twisted and twigged electron quanta, the corresponding eigenfunctions are normalized with Schrodinger’s quantum wave mechanical equation for electric scalar and magnetic potentials, respectively (QED behavior). The fractional electric and magnetic fields with their corresponding potentials for the quantized fractional states in semiconducting hereto structures are theoretically calculated. Such mathematical expressions are in good agreement with experimental results of Nobel Prize winning scientists Klitzing, Haroche, Peter and Gruebber. Our results can also explain the hybridized states of orbits with emphasis on sigma and pi bonding and their corresponding antibonding orbitals as a manifestation of electrophilic and nucleophilic chemical reactions.

Eigenfunctions for a Quantum Wire on a Single Electron at Its Surface and in the Quantum Well with Beaded Fractional Quantized States for the Fractional Charges

We developed energy profiles for the fractional quantized states both on the surface of electron due to overwhelming centrifugal potentials and inside the electron at different locations of the quantum well due to overwhelming attractive electrodynamic potentials. The charge as a physical constant and single entity is taken as density and segments on their respective sub-quanta (floats on sub quanta) and hence the fractional charge quantiz at in. There is an integrated oscillatory effect which ties all fractional quantized states both on the surface and in the interior of the volume of an electron. The eigenfunctions, i.e., the energy profiles for the electron show the shape of a string or a quantum wire in which fractional quantized states are beaded. We followed an entirely different approach and indeed thesis to reproducing the eigenfunctions for the fractional quantized states for a single electron. We produced very fascinating mathematical formulas for all such cases by using Hermite and Laguerre polynomials, spherical based and Neumann functions and indeed asymptotic behavior of Bessel and Neumann functions. Our quantization theory is dealt in the momentum space.

Quantum Theory of Mesoscopic Fractional Electric Fields in a Cavity of Viscous Medium

With conjecture of fractional charge quantization (quantum dipole/multiple moments), Fourier transform stretching, twisting and twigging of an electron quanta and waver strings of electron quanta, the mathematical expressions for mesoscopic fractional electron fields in a cavity of viscous medium and the associated quantum dielectric susceptibility are developed. Agreement of this approach is experimentally evidenced on barite and Fanja site molecular sieves. These findings are in conformity with experimental results of 2012 Physics Nobel prize winning scientists, Serge Haroche and David J. Wineland especially for cavity quantum electro-dynamics electron and its associated mesoscopic electric fields. The mover electron quanta strings lead to warping of space and time following the behaviour of quantum electron dynamics.

Applications of Quantum Physics on Resistivity, Dielectricity, Giant Magneto Resistance, Hall Effect and Conductance

Quantum theory with conjecture of fractional charge quantization, eigenfunctions for fractional charge quantization, fractional Fourier transform, Hermite function for fractional charge quantization, and eigenfunction for a twisted and twigged electron quanta is developed and applied to resistivity, dielectricity, giant magneto resistance, Hall effect and conductance. Our theoretical relationship for quantum measurements is in good conformity and in agreement with most of the experimental results. These relationships will pave a new approach to quantum physics for deciphering measurements on single quantum particles without destroying them. Our results are in agreement with 2012 Physics Nobel Prize winning Scientists, Serge Haroche and David J. Wineland.

Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with Born Approximation

Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δl for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.

Earthquake Statistics and Earthquake Research Studies in Pakistan

This paper is about short review of earthquake statistics and efforts for earthquake mitigation, hazard and risk assessment studies in Pakistan. Pakistan and adjoining region lying between longitude 60°E to 78°E and latitude 20°N to 45°N are selected for the study as this region has a history of many large earthquakes because of its location in the region of intersection of three plates namely Indian, Eurasian and Arabian Sea plate. This paper is based on the study of both seismological history of the region which includes recent and historical seismicity based on earthquake catalogue as well as geological knowledge supplemented with available fault system information. In this study, Pakistan and adjoining regions are divided into 14 seismogenic zones. Seismicity of each zone is studied considering also the major cities in the respective zone and type of infrastructure which is mainly responsible for earthquake disaster rather than earthquake itself.

Calibration of local magnitude scale for Hindukush continental subduction zone

Hindukush is an active subduction zone where at least one earthquake occurs on daily basis.For seismic hazard studies,it is important to develop a local magnitude scale using the data of local seismic network.We have computed local magnitude scale for Hindukush earthquakes using data from local network belonging to Center for Earthquake Studies(CES)for a period of three years,i.e.2015–2017.A total of 26,365 seismic records pertaining to 2,683 earthquakes with magnitude 2.0 and greater,was used with hypocentral distance less than 600 km.Magnitude scale developed by using this data comes to be M_(L)=logA+0.929logr+0.00298r-1.84.The magnitude determined through formulated relation was compared with that of standard relation for Southern California and relation developed by the same authors for local network for Northern Punjab.It was observed that Hindukush region has high attenuation as compared to that of Southern California and Northern Punjab which implies that Hindukush is tectonically more disturbed as compared to the said regions,hence,seismically more active as well.We have calculated station correction factors for our network.Station correction factors do not show any pattern which probably owes to the geological and tectonic complexity of this structure.Standard deviation and variance of magnitude residuals for CES network determined using Hutton and Boore scale and scale developed in this study were compared,it showed that a variance reduction of 44.1%was achieved.Average of magnitude residuals for different distance ranges was almost zero which showed that our magnitude scale was stable for all distances up to 600 km.Newly developed magnitude scale will help in homogenization of earthquake catalog.It has been observed that b-value of CES catalog decreases when magnitude is calculated by using newly developed magnitude scale.