Related papers: Levinson's Theorem for Dirac Equation
One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…
The Jarzynski Equality relates the free energy difference between two equilibrium states of a system to the average of the work over all irreversible paths to go from one state to the other. We claim that the derivation of this equality is…
The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a vector potential is studied in the arrangements associated with the…
We describe the occurrence and physical role of zero-energy modes in the Dirac equation with a topologically non-trivial background.
It is well known that steady states of the Vlasov-Poisson system, a widely used model in non-relativistic galactic dynamics, have negative energy. In this paper we derive the analogous property for two relativistic generalizations of the…
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
We consider the energy levels of a hydrogen-like atom in the framework of $\theta $-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
The nilpotent version of the Dirac equation is applied to the baryon wavefunction, the strong interaction potential, electroweak mixing, and Dirac and Klein-Gordon propagators. The results are used to interpret a quaternion-vector model of…
Using an effective strongly coupled lattice QCD Hamiltonian and Wilson fermions we calculate the equation of state for cold and dense quark matter by constructing an ansatz which exactly diagonalizes the Hamiltonian to second order in field…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…
In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions…
By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz…
This article investigates some solutions of the time-dependent free Dirac equation. Visualizations of these solutions immediately reveal strange phenomena that are caused by the interference of positive- and negative-energy waves. The…
It is investigated how the shielding of a moving point charge in a one-component fully degenerate fermion plasma affects the bound states near the charge at velocities smaller than the Fermi one. The shielding is accounted for by using the…
This talk presents a study of massless relativistic Dirac fields in three Euclidean dimensions, at finite temperature and density, in the presence of a uniform electromagnetic background. Apart from explaining the behavior of Hall's…
Dirac delta-function potential is widely studied in quantum mechanics because it usually can be exactly solved and at the same time is useful in modeling various physical systems. Here we study a system of delta-potential trapped spinorbit…
The Lorentz-Dirac radiation reaction formula predicts that the position shift of a charged particle due to the radiation reaction is of first order in acceleration if it undergoes a small acceleration. A semi-classical calculation shows…
The quantum Rabi model has been a useful and pedagogical quantum model in the past decades, sufficiently simple to be solved analytically and intuitively understood, while sufficiently complex as to provide highly non-trivial eigenstates…