Related papers: Solving Dirac equations on a 3D lattice with inver…
The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $\psi$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $\omega$, respectively. This theory is connected to…
In this paper we propose a new approach to formulate the field theory on a lattice. This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation for both Fermion and Boson…
This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…
A new theoretical method is developed to solve the two-body bound-state Dirac equation for positronium. Only Coulomb potential was included in the Dirac Hamiltonian. It is shown that the two-body Dirac Hamiltonian can be written in the…
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…
In this paper, we present an innovative approach to resolving type IV singularities in fermionic quantum cosmology. The Eisenhart-Duval lift procedure is employed to construct an extended minisuperspace metric, which allows for the…
We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of…
Within an effective Dirac-Weyl theory we solve the scattering problem for massless chiral fermions impinging on a cylindrical time-dependent potential barrier. The set-up we consider can be used to model the electron propagation in a…
The inverse scattering approach for the defocusing Davey-Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We…
Kramers escape from a metastable state in the presence of both thermal and quantum fluctuations under strong damping is treated as a thermally activated process in a quantum modified semiclassical potential. Dirac's time-dependent…
We introduce a lattice model for a static and isotropic system of relativistic fermions. An action principle is formulated, which describes a particle-particle interaction of all fermions. The model is designed specifically for a numerical…
We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite…
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 a potential scattering of Bose-Hubbard dimer in 1D optical lattice. A numerical approach based on effective non-Hermitian Hamiltonian has been developed for solving the scattering problem. It allows to compute the tunneling and…
We formulate an algebraic relativistic method of scattering for systems with spatially dependent mass based on the J-matrix method. The reference Hamiltonian is the three-dimensional Dirac Hamiltonian but with a mass that is…
We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and…
We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $\epsilon$-regime of QCD. This correlation function has a unique and strong dependence on $F_\pi$, and thus provides an novel…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately…
In this work, we apply a fast and accurate numerical method for solving fractional reaction-diffusion equations in unbounded domains. By using the Fourier-like spectral approach in space, this method can effectively handle the fractional…