Relativistic Quantum Motion of an Electron in Spinning Cosmic String Spacetime in the Presence of Uniform Magnetic Field and Aharonov-Bohm Potential

In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation and write the first- and second-order equations from it, and then, we solve these equations for bound states. We show that there are bound state solutions for the first-order equation Dirac. For the second-order equation, we obtain the corresponding wave functions, which depend on the Kummer functions. Then, we determine the energies of the particle. We examine the behavior of the energies as a function of the physical parameters of the model, such as rotation, curvature, magnetic field, Aharonov-Bohm flux, and quantum numbers. We find that, depending on the values of these parameters, there are energy nonpermissible levels.

Observation of interaction-induced phenomena of relativistic quantum mechanics

Relativistic quantum mechanics has been developed for nearly a century to characterize the high-energy physics in quantum domain, and various intriguing phenomena without low-energy counterparts have been revealed. Recently, with the discovery of Dirac cone in graphene, quantum materials and their classical analogies provide the second approach to exhibit the relativistic wave equation, making large amounts of theoretical predications become reality in the lab. Here, we experimentally demonstrate a third way to get into the relativistic physics. Based on the extended one-dimensional Bose-Hubbard model, we show that two strongly correlated bosons can exhibit Dirac-like phenomena, including the Zitterbewegung and Klein tunneling, in the presence of giant on-site and nearest-neighbor interactions. By mapping eigenstates of two correlated bosons to modes of designed circuit lattices, the interaction-induced Zitterbewegung and Klein tunneling are verified by measuring the voltage dynamics. Our finding not only demonstrates a way to exhibit the relativistic physics, but also provides a flexible platform to further investigate many interesting phenomena related to the particle interaction in experiments.

A feasible and practically secure quantum bit commitment protocol

As a fundamental cryptographic primitive, bit commitment has lots of important and practical applications in modern cryptography. All previously proposed non-relativistic quantum bit commitment protocols cannot evade the Lo–Chau and Mayers attacks. Furthermore, relativistic quantum bit commitment protocols require rigorous spacetime constraints. In this paper, we present a simple, feasible but practically secure quantum bit commitment protocol without any spacetime constraint. The security of the proposed protocol is based on non-relativistic quantum mechanics, but it can resist all known attacks, including the Lo–Chau and Mayers attacks in practice.

Discrete phase space and continuous time relativistic quantum mechanics II: Peano circles, hyper-tori phase cells, and fiber bundles

The discrete phase space and continuous time representation of relativistic quantum mechanics are further investigated here as a continuation of paper I.1 The main mathematical construct used here will be that of an area filling Peano curve. We show that the limit of a sequence of a class of Peano curves is a Peano circle denoted as [Formula: see text], a circle of radius [Formula: see text] where [Formula: see text]. We interpret this two-dimensional (2D) Peano circle in our framework as a phase cell inside our 2D discrete phase plane. We postulate that a first quantized Planck oscillator, being very light, and small beyond current experimental detection, occupies this phase cell [Formula: see text]. The time evolution of this Peano circle sweeps out a 2D vertical cylinder analogous to the worldsheet of string theory. Extending this to 3D space, we introduce a [Formula: see text]-dimensional phase space hyper-tori [Formula: see text] as the appropriate phase cell in the physical dimensional discrete phase space. A geometric interpretation of this structure in state space is given in terms of product fiber bundles. We also study free scalar Bosons in the background [Formula: see text]-dimensional discrete phase space and continuous time state space using the relativistic partial difference-differential Klein–Gordon equation. The second quantized field quanta of this system can cohabit with the tiny Planck oscillators inside the [Formula: see text] phase cells for eternity. Finally, a generalized free second quantized Klein–Gordon equation in a higher [Formula: see text]-dimensional discrete state space is explored. The resulting discrete phase space dimension is compared to the significant spatial dimensions of some of the popular models of string theory.

Relativistic free fermions in spiral dislocation space–time with a distortion of a radial line into a spiral

Relativistic quantum mechanics of free fermions in the presence of the spiral dislocation of space–time with a distortion of a radial line into a spiral is studied within the Katanaev–Volovich geometric approach. The generalized Dirac equation in this background is constructed. Exact closed-form solutions are found by reducing the problem to that of a nonrelativistic two-dimensional [Formula: see text]-problem with a complex coupling constant. The influence of the defect parameter related to the spiral dislocation on these solutions is investigated. We also study the charge density of free fermions in the presence of such a spiral dislocation in space–time. Based on the Bender–Boettcher approach for non-Hermitian Hamiltonians we study, in addition, bound-state solutions of the system.

A new theoretical study of the deformed unequal scalar and vector Hellmann plus modified Kratzer potentials within the deformed Klein–Gordon equation in RNCQM symmetries

In this paper, within the framework of relativistic quantum mechanics and using the improved approximation scheme to the centrifugal term for any [Formula: see text]states via Bopp’s shift method and standard perturbation theory, we have obtained the modified energy eigenvalues of a newly proposed modified unequal vector and scalar Hellmann plus modified Kratzer potentials (DUVSHMK-Ps) for some diatomic N2, I2, CO, NO, O2 and HCl molecules. This study includes corrections of the first-order in noncommutativity parameters [Formula: see text]. This potential is a superposition of the attractive Coulomb Yukawa potential plus the Kratzer potential and new central terms appear as a result of the effects of noncommutativity properties of space–space. The obtained energy eigenvalues appear as a function of noncommutativity parameters, the strength parameters [Formula: see text] and [Formula: see text] of the (scalar vector) Hellmann potential, the screening range parameter [Formula: see text], the dissociation energy of the vector, and scalar potential [Formula: see text], the equilibrium inter-nuclear distance [Formula: see text] in addition to the atomic quantum numbers [Formula: see text]. Furthermore, we obtained the corresponding modified energy of DUVSHMK-Ps in the symmetries of non-relativistic noncommutative quantum mechanics (NRNCQM). In both relativistic and non-relativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM.