Related papers: Encoding relativistic potential dynamics into free…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
It is shown that in the two-dimensional space-time the dynamic system, described by the free Klein-Gordon equation, turns to the dynamic system, described by the free Dirac equation, provided the current and the energy-momentum tensor are…
We show a procedure to classically simulate the Majorana equation in 1+1 dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose a novel approach that uses a…
We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which…
The ways to construct solution of the evolution equation in the homogeneous free molecular condensation under dynamic conditions are presented in parametric form.
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
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…
Using the position as an independent variable, and time as the dependent variable, we derive the function ${\cal P}^{(\pm)}$, which generates the space evolution under the potential ${\cal V}(q)$ and Hamiltonian ${\cal H}$. Canonically…
We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
A non-relativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between…
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after…
The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
To examine the loss of entanglement in a two-particle Gaussian system, we couple it to an environment and use the Non-Rotating Wave master equation to study the system's dynamics. We also present a derivation of this equation. We consider…
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective…
We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before…