Exact solution of an exciton energy for a monolayer medium

Abstract

We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2 + 1 space-time dimensions. The 2 × 2 spinor equations of 2-interacting fermions through general central potential were separated covariantly into the relative and center of mass coordinates. First of all, the coupled first order differential equations depending on radial coordinate were derived from 2 × 2 spinor equations. Then, a second order radial differential equation was obtained and solved for Coulomb interaction potential. We apply our solutions to exciton phenomena for a free-standing monolayer medium. Since we regard exciton as isolated 2-interacting fermions in our model, any other external effect such as substrate was eliminated. Our results show that the obtained binding energies in our model are in agreement with the literature. Moreover, the decay time of an exciton was found out spontaneously in our calculations.

Effects of Rotating Frame on a Vector Boson Oscillator

“…According to signature of eq. (2) the space-independent dirac matrices can be chosen as = , = , = [29][30][31], in which , and are the pauli spin matrices. Also, we can obtain the spinorial connections for spin-1/2 fields via the following expression [15], ( ,σ,μ,ν,a,b=0,1,2.…”

“…On the other hand, the investigations about the effects of rotating frames on the quantum systems have provided very interesting results and accordingly such studies have attracted great attention for a long time [20][21][22] since these investigations have discovered very important effects [23][24][25][26][27][28][29]. The sagnac effect [23], mashhoon effect [24], persistent currents in the quantum ring and the coupling between the angular momentum of the quantum systems with the velocity of uniformly rotating frame [25] can be considered among these effects.…”

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

“…On the other hand, a phenomenological way to describe the dynamics of many-body systems is to use one-time equations including free Hamiltonians for each particle plus interparticle interaction potentials [41,42]. In the relativistic quantum theory, the history of such equations goes long way back [43,44] but there are still different relativistic manybody equations in use today in the literature [43][44][45][46][47][48]. In this study, we will use the corresponding form of a fully-covariant two-body Dirac equation (FCTBE) [9,[48][49][50][51][52][53][54], derived from quantum electrodynamics (QED) with the help of action principle [47], in order to obtain relativistic Landau levels for a composite system formed by a fermion-antifermion (ff) pair interacting via DO coupling.…”

“…In the relativistic quantum theory, the history of such equations goes long way back [43,44] but there are still different relativistic manybody equations in use today in the literature [43][44][45][46][47][48]. In this study, we will use the corresponding form of a fully-covariant two-body Dirac equation (FCTBE) [9,[48][49][50][51][52][53][54], derived from quantum electrodynamics (QED) with the help of action principle [47], in order to obtain relativistic Landau levels for a composite system formed by a fermion-antifermion (ff) pair interacting via DO coupling. The FCTBE is a one-time equation including the most general electric and magnetic potentials [48][49][50][51][52][53][54].…”

“…In this study, we will use the corresponding form of a fully-covariant two-body Dirac equation (FCTBE) [9,[48][49][50][51][52][53][54], derived from quantum electrodynamics (QED) with the help of action principle [47], in order to obtain relativistic Landau levels for a composite system formed by a fermion-antifermion (ff) pair interacting via DO coupling. The FCTBE is a one-time equation including the most general electric and magnetic potentials [48][49][50][51][52][53][54]. This equation leads a 16 × 16 matrix equation in 4-dimensions [52][53][54] and the separation of angular and radial variables requires group theoretical methods [52][53][54][55].…”