Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis

The Riemann Hypothesis states that the Riemann zeta function ζ(z) admits a set of “non-trivial” zeros that are complex numbers supposed to have real part 1/2. Their distribution on the complex plane is thought to be the key to determine the number of prime numbers before a given number. Hilbert and Pólya suggested that the Riemann Hypothesis could be solved through the mathematical tools of physics, finding a suitable Hermitian or unitary operator that describe classical or quantum systems, whose eigenvalues distribute like the zeros of ζ(z). A different approach is that of finding a correspondence between the distribution of the ζ(z) zeros and the poles of the scattering matrix S of a physical system. Our contribution is articulated in two parts: in the first we apply the infinite-components Majorana equation in a Rindler spacetime and compare the results with those obtained with a Dirac particle following the Hilbert-Pólya approach showing that the Majorana solution has a behavior similar to that of massless Dirac particles and finding a relationship between the zeros of zeta end the energy states. Then, we focus on the S-matrix approach describing the bosonic open string scattering for tachyonic states with the Majorana equation. Here we find that, thanks to the relationship between the angular momentum and energy/mass eigenvalues of the Majorana solution, one can explain the still unclear point for which the poles and zeros of the S-matrix of an ideal system that can satisfy the Riemann Hypothesis, exist always in pairs and are related via complex conjugation. As claimed in the literature, if this occurs and the claim is correct, then the Riemann Hypothesis could be in principle satisfied, tracing a route to a proof.

Thermal Correction to the Kinnersley Black Hole in a Lorentz-Violating Dirac Field Theory

According to Lorentz-violating theory, the dynamical equation of Dirac particles in the Kinnersley black hole with variably accelerated linear motion is modified. The Hawking quantum tunneling radiation characteristics of Kinnersley black hole are obtained by solving the modified equation. The expression of the Hawking temperature of Kinnersley black hole has been updated.

Screening effect for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of screening effect for energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. The excitonic hamiltonian in the product base of the Dirac single-particle is used. The corresponding energy eigenvalue system of the first order ODE (radial equations) was solved using the finite difference method. This enables to determine the energy eigenvalues of the discrete excitonic spectrum and the wave functions. We compare the results for the energy spectrum and the corresponding eigen-functions forms for WS 2 and WSe 2 computed for two different potentials: pure Coulomb and screened Coulomb (Keldysh potential). It is demonstrated that excitonic energy levels for unscreened potential lie dipper, and the corresponding eigen-functions’ forms differ from those obtained for screened one.

Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of the energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. In the multiband model, we use the excitonic Hamiltonian in the product base of the Dirac single-particle states at the conduction and valence band edges. Following the separation of variables, we decouple the corresponding energy eigenvalue system of the first-order ODE radial equations rigorously and solve the resulting second-order ODE self-consistently, using the finite difference method, thus we determine the energy eigenvalues of the discrete excitonic spectrum and the corresponding wave functions. We also developed a WKB approach to solve the same spectral problem in semiclassical approximation for the resulting ODE. We compare the results for the energy spectrum and the corresponding eigen-function forms for WS 2 and WSe 2 obtained by means of both methods. We also compare our results for the energy spectrum with other theoretical works for excitons, and with available experimental data.

Superradiation of Dirac particles in KN ds black hole

In this article, we process the approximate wave function of the Dirac particle outside the horizon of the KN ds black hole to obtain V, and then derive V (including real and imaginary parts). We deal with the real and imaginary parts separately. When V (real part or imaginary part) has a maximum value, there may be a potential barrier outside the field of view to have a chance to produce superradiation.

Dirac particles in the presence of a constant magnetic field and harmonic potential with spin symmetry

In this paper, we study the effect of the constant magnetic field on energy levels of the Dirac particles such as electron, proton and heavy ions. We calculate the energy eigenvalues of the Dirac equation in the presence of the magnetic field and two-dimensional harmonic oscillator potential with spin symmetry by using the supersymmetric quantum mechanics and asymptotic iteration methods.