We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider th...We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.展开更多
In this study,we consider an open system from the thermodynamic perspective for an adiabatic FRW universe model in which particle creation occurs within the system.In this case,the modified continuity equation is obta...In this study,we consider an open system from the thermodynamic perspective for an adiabatic FRW universe model in which particle creation occurs within the system.In this case,the modified continuity equation is obtained,and then,we make it correspond to the continuity equation of f(T)gravity.Therefore,we take f(T)gravity with a viscous fluid in the flat-FRW metric,where T is the torsion scalar.We assume the contents of the universe to be dark matter and dark energy and consider an interaction term between them.An interesting point of this study is that we make the modified continuity equation resulting from particle creation equivalent to the matter continuity equation resulting from f(T)gravity.The result of this evaluation establishes a relationship between the number of particles and scale factor.In what follows,we write the corresponding cosmological parameters in terms of the number of particles and also reconstruct the number of particles in terms of the redshift parameter.We then parameterize the Hubble parameter derived from power-law cosmology with 51 data points from the Hubble observational parameter data.Next,we plot the corresponding cosmological parameters for dark energy in terms of the redshift to investigate the accelerated expansion of the universe.In addition,by using the sound speed parameter,we discuss the stability and instability analyses of the present model in different eras of the universe.Finally,we plot the density parameter values for dark energy and dark matter in terms of the redshift parameter.展开更多
文摘We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.
文摘In this study,we consider an open system from the thermodynamic perspective for an adiabatic FRW universe model in which particle creation occurs within the system.In this case,the modified continuity equation is obtained,and then,we make it correspond to the continuity equation of f(T)gravity.Therefore,we take f(T)gravity with a viscous fluid in the flat-FRW metric,where T is the torsion scalar.We assume the contents of the universe to be dark matter and dark energy and consider an interaction term between them.An interesting point of this study is that we make the modified continuity equation resulting from particle creation equivalent to the matter continuity equation resulting from f(T)gravity.The result of this evaluation establishes a relationship between the number of particles and scale factor.In what follows,we write the corresponding cosmological parameters in terms of the number of particles and also reconstruct the number of particles in terms of the redshift parameter.We then parameterize the Hubble parameter derived from power-law cosmology with 51 data points from the Hubble observational parameter data.Next,we plot the corresponding cosmological parameters for dark energy in terms of the redshift to investigate the accelerated expansion of the universe.In addition,by using the sound speed parameter,we discuss the stability and instability analyses of the present model in different eras of the universe.Finally,we plot the density parameter values for dark energy and dark matter in terms of the redshift parameter.
