Related papers: Dirac four-potential tunings-based quantum transis…
We revive an approach to solve the Dirac equation originally proposed by Kutzelnigg which makes use of the squared Dirac operator $\hat{\mathfrak{D}}^{2}$. This approach holds the promise to avoid the negative energy solution because the…
The weak convergence theorems of the one- and two-dimensional simple quantum walks, SQW$^{(d)}, d=1,2$, show a striking contrast to the classical counterparts, the simple random walks, SRW$^{(d)}$. The limit distributions have novel…
QFT approaches elaborated for treating quantum effects in time-dependent external electric fields are not directly applicable to time-independent nonuniform electric fields that are given by a step potential and their generalization for the…
Transistors play a vital role in classical computers, and their quantum mechanical counterparts could potentially be as important in quantum computers. Where a classical transistor is operated as a switch that either blocks or allows an…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some…
It is generally acknowledged that neither the Klein-Gordon equation nor the Dirac Hamiltonian can produce sound solitary-particle relativistic quantum mechanics due to the ill effects of their negative-energy solutions; instead their…
We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for…
We suggest and study designed defects in an otherwise periodic potential modulation of a two-dimensional electron gas as an alternative approach to electron spin based quantum information processing in the solid-state using conventional…
Electrostatic confinement of charge carriers in graphene is governed by Klein tunneling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at pn junction boundaries. Reflection and…
Dirac materials have been a unique solid state platform for exploring relativistic quantum phenomena including supercritical atomic collapse, which leads to emergent discrete scale symmetry and logperiodic quantum oscillations. In the…
A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current…
We addressed quantization phenomena in transport and vortex/precession-motion of low-dimensional systems, stationary quantization of confined motion in phase space due to oscillatory dynamics or compacti fication of space and time for…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
Transistors are key elements for enabling computational hardware in both classical and quantum domains. Here, we propose a voltage-gated spin transistor using itinerant electrons in the Hubbard model which acts at the level of single…
We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of…
The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a…
The Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb), which includes post-Newtonian (relativistic) and quantum corrections to the classical potential. The general idea in…
The influence of an externally applied magnetic field upon classic cubic quintic dissipative solitons is investigated using both exact simulations and a Lagrangian technique. The basic approach is to use a spatially inhomogeneous magnetic…
A spin-qubit transformation protocol is proposed for an electron in a mesoscopic quantum ring with tunable Rashba interaction controlled by the external electric field. The dynamics of an electron driven around the ring by a series of…