scholarly journals Neutrino interaction with background matter in a non-inertial frame

2015 ◽  
Vol 30 (23) ◽  
pp. 1530017 ◽  
Author(s):  
Maxim Dvornikov
Keyword(s):  
Dirac Equation ◽  
Inertial Frame ◽  
Resonance Condition ◽  
Energy Levels ◽  
Neutrino Energy ◽  
Neutrino Interaction ◽  
Rotating Frame ◽  
Mass Eigenstates ◽  
Flavor Oscillations ◽  
Matter Rotation

We study Dirac neutrinos propagating in rotating background matter. First we derive the Dirac equation for a single massive neutrino in the non-inertial frame, where matter is at rest. This equation is written in the effective curved spacetime corresponding to the co-rotating frame. We find the exact solution of the Dirac equation. The neutrino energy levels for ultrarelativistic particles are obtained. Then we discuss several neutrino mass eigenstates, with a nonzero mixing between them, interacting with rotating background matter. We derive the effective Schrödinger equation governing neutrino flavor oscillations in rotating matter. The new resonance condition for neutrino oscillations is obtained. We also examine the correction to the resonance condition caused by the matter rotation.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

scholarly journals Re-Evaluating the Classical Falling Body Problem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 553 ◽  
Author(s):  
Essam R. El-Zahar ◽  
Abdelhalim Ebaid ◽  
Abdulrahman F. Aljohani ◽  
José Tenreiro Machado ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Inertial Frame ◽  
Analytic Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Rotating Frame ◽  
Dimensional Model ◽  
Three Dimensional Model

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.

Perturbative calculation of energy levels for the Dirac equation with generalized momenta

2020 ◽  
Vol 35 (20) ◽  
pp. 2050106
Author(s):  
Marco Maceda ◽  
Jairo Villafuerte-Lara
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Spatial Dimension ◽  
Three Dimensions ◽  
Minimum Length ◽  
Linear Potential ◽  
Perturbative Calculation ◽  
Square Well

We analyze a modified Dirac equation based on a noncommutative structure in phase space originating from a generalized uncertainty principle with a minimum length. The noncommutative structure induces generalized momenta and contributions to the energy levels of the standard Dirac equation. Applying techniques of perturbation theory, we find the lowest-order corrections to the energy levels and eigenfunctions of the Dirac equation in three dimensions for a spherically symmetric linear potential and for a square-well times triangular potential along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones, leading to an upper bound on the parameter fixing the minimum length induced by the generalized uncertainty principle.

SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

2013 ◽  
Vol 28 (31) ◽  
pp. 1350137 ◽  
Author(s):  
GEUSA DE A. MARQUES ◽  
V. B. BEZERRA ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Cosmic String ◽  
Relativistic Particle ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Self ◽  
Dependent Mass ◽  
Scalar Potentials ◽  
Position Dependent Mass

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

scholarly journals The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

2017 ◽  
Vol 21 (2) ◽  
pp. 313-357 ◽  
Author(s):  
Ali Faraj ◽  
Shi Jin
Keyword(s):  
Dirac Equation ◽  
Electrostatic Potential ◽  
Numerical Experiments ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Two Dimensional ◽  
Lagrangian Surface ◽  
Surface Hopping ◽  
Asymptotic Models ◽  
Semiclassical Regime

AbstractA Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition—characterized by the Landau-Zener probability— between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Schurrer, J. Phys. A:Math. Theor. 44 (2011) 265301]may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Schurrer, J. Phys. A: Math. Theor. 44 (2011) 265301].

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

Tunneling spectroscopy by matching energy levels in the spin-rotating frame

1997 ◽  
Vol 56 (10) ◽  
pp. 5954-5960 ◽  
Author(s):  
Changho Choi ◽  
M. M. Pintar
Keyword(s):  
Energy Levels ◽  
Tunneling Spectroscopy ◽  
Rotating Frame

scholarly journals THE DIRAC PARTICLE ON CENTRAL BACKGROUNDS AND THE ANTI-DE SITTER OSCILLATOR

1998 ◽  
Vol 13 (36) ◽  
pp. 2923-2935 ◽  
Author(s):  
ION. COTĂESCU
Keyword(s):  
Dirac Equation ◽  
Special Relativity ◽  
Scalar Product ◽  
Energy Levels ◽  
Specific Form ◽  
Dirac Particle ◽  
Spherically Symmetric ◽  
Spherical Coordinates ◽  
De Sitter

It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific form of the radial scalar product. As an example, we analytically solve the anti-de Sitter oscillator giving the formula of the energy levels and the form of the corresponding eigenspinors.

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