Spectra of the exponential potential with the supposition of minimal length

In the framework of different theories of quantum gravity, such as string theory, dual special relativity, and the physics of black holes, the existence of a minimal length is proposed. It is necessary to modify and generalize the usual Heisenberg principle of uncertainty to incorporate the minimal length into the ordinary quantum mechanics. In this scenario, the momentum of the system is modified, and the Hamiltonian obtains additional terms. It is expected that the energy spectrum of any physical system is modified under the hypothesis of minimal length. In this article, these effects on the spectra of the exponential potential for the ground state are studied by applying a perturbation method. As a popular application of the exponential potential, the deuteron bound state can be explained by using this potential. Here, the modification of the energy spectrum of deuteron under the supposition of the existence of a minimal length is calculated

The solitary solutions of nonlinear Klein-Gordon field with minimal length

The existence of a minimal length is predicted by theories of quantum gravity and it is generally accepted that this minimal length should be of the order of the Planck length and hence can be observed in high energy phenomenon. We study the implications of the presence of the minimal length on the Klein-Gordon filed with ϕ4 self-interaction. Considering the process of spontaneous symmetry breaking, the potential also includes the ϕ3 term. The consequent field equation is a fourth-order differential equation and is considered to have solitary solutions. The sech method is applied and the normalized solutions are obtained in closed forms and the energy spectrum of the solitary fields is determined. The modification parameter of the theory is estimated by the width and the energy of the obtained solitary fields

The quantum exchange effects on the electromagnetic solitonic excitations in warm plasma

The phenomena related to the high energy regime in a plasma medium are studied in the framework of relativistic quantum hydrodynamics at the classical level. This theory leads to nonlinear equations even at the weak relativistic regime. These nonlinearities give rise to interesting and novel phenomena in the dynamics of the medium. Here, we consider these effects on the dynamics of a warm plasma environment. In addition, we study the effects of the exchange interaction between electrons on the dynamic of such a plasma. This interaction is a quantum mechanical effect and its strength is influenced by the spin polarization ratio of the electrons. Both the analytical and the numerical solutions are presented which are stable and bounded soliton waves. For the analytical solutions, an extended tanh approach, and for the numeric approach, the techniques of solving eigenvalue problems are applied. The behavior of the vector potential and the density under the spin polarization effects and thermal effects in terms of the speed of the wave are discussed

Quantum coherence in neutrino oscillation in matter

A closer and more detailed study of neutrino oscillation, in addition to assisting us in founding physics beyond the standard model, can potentially be used to understand the fundamental aspects of quantum mechanics. In particular, we know that the neutrino oscillation occurs because the quantum states of the produced and detected neutrinos are a coherent superposition of the mass eigenstates, and this coherency is maintained during the propagation due to the small mass difference of neutrinos. In this paper, we consider the decoherence due to the neutrino interaction in the material medium with constant density in addition to the decoherence coming from the localization properties. For this purpose, we use $l_1\text{-norm}$ in order to quantify the coherence and investigate its dependence on the matter density. According to our results, in general, the coherence in material medium is less than vacuum. However, there exist exceptions; for some matter densities, the localization coherence lengths become infinite. So, for these cases, $l_1\text{-norm}$ in matter is more than the vacuum.Comment: 11 pages, 5 figure

Overdense plasma heating in Wendelstein 7-X(W7-X) stellarator

High yield nuclear fusion operating in tokamak and stellarator need to heat plasma up to the required temperatures. As the confined plasma is overdensed, the electron cyclotron resonance heating (ECRH) is inefficient due to cut-off layer. A double mode conversion O-SX and finally electron Bernstein waves (EBW) O-SXB, offer an attractive possibility for plasma heating. In this article, a two-step mode conversion process, OXB has been used to examine the influence of critical parameters such as fluctuation amplitude Δnn, ECH frequency (f), poloidal correlation length (λy), magnetic field (B), on the modified transmission function and ultimately increase plasma power for the Wendelstein 7-X(W7-X) stellarator, is studied. Keywords: Overdense plasma, Wendelstein 7-X stellarator, Electron cyclotron resonance heating, O-SX mode conversion, Modified transmission coefficien