On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

Quantization of the space－time with topological defect

We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space－time by solving the Wheeler－De Witt equation. De Broglie－Bohm interpretation applied to the wavefunction gives the quantum solution of the space－time. In the end, the quantum effect on Hawking radiation is studied.     

On the Aharonov–Bohm Hamiltonian

Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov–Bohm effect. In general, the resulting Hamiltonians are not rotationally invariant so that the angular momentum is not a constant of motion. Using an explicit formula for the resolvent, we describe the spectrum and compute the generalized eigenfunctions and the scattering amplitude.     

On the vacuum status in Weyl–Dirac theory

A hydrodynamic model of the Weyl–Dirac theory in the non-relativistic approach is established. Any microparticle is permanently interacting with the ‘subquantum level’ through the quantum potential, which depends only on the imaginary part of a complex speed. The complex speed fields indicate a possible connection between the Weyl–Dirac theory and Scale Relativity Theory. In such conjecture, some properties of the vacuum states result: the vacuum states behave as a superconducting state, they act as an energy accumulator etc.     

On the structure of open–closed topological field theory in two dimensions

I discuss the general formalism of two-dimensional topological field theories defined on open–closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying ‘boundary conditions’. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss reducibility of boundary extensions.     

Klein–Gordon oscillator with magnetic and quantum flux fields in non-trivial topological space-time

The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed. We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function. We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues. We find that the energy eigenvalues depend on the quantum flux field tha...     

Spin–orbit interaction for the double ring-shaped oscillator

The spin–orbit interactions (SOI) for the single and double ring-shaped oscillator potentials are studied as an energy correction to the Schrödinger equation. We find that the degeneracy for the energy levels with angular quantum number m=0$m=0$ keeps invariant in the case of the SOI. The degeneracy is still 2 for single ring-shaped potential and 4 for double ring-shaped potential. However, for the energy levels with angular quantum number m≠0$m\ne 0$ the degeneracy is reduced from original 4 for the single ring-shaped potential and 8 for the double ring-shaped potential to 2. That is, their energy levels in the case of the SOI are split to 2 (single) and 4 (double) sublevels. There exists an accidental degeneracy for the cases |m|=2,3,4,…$\left|m\right|=2,3,4,\dots$. We note that around the critical value b₀$b_0$, the energy levels are reversed.   We also discuss some special cases for η=2,3,4,5,6,…$\eta =2,3,4,5,6,\dots$, and the b=0,c>0$b=0,c>0$. It should be pointed out that the parameter b₀$b_0$ is relevant for the angular part parameter b$b$ in the single and double ring-shaped potentials and it makes the energy levels changed from positive to negative, but the parameter c$c$ corresponds to the angular part parameter in double ring-shaped potential and the η$\eta$ is related to it. This model can be useful for investigations of axial symmetric subjects like the ring-shaped molecules or related problems and may also be easily extended to a many-electron theory.     

Bound state solutions of the Dirac equation with the Deng–Fan potential including a Coulomb tensor interaction

Approximate analytical solutions of the Dirac equation in the case of pseudospin and spin symmetry limits are inves- tigated under the Deng-Fan potential by applying the asymptotic iteration method for the arbitrary quantum numbers n and ~~. Some of the numerical results are also represented in both pseudospin symmetry and spin symmetry limits.     

Probing the Energy Spectrum in the Vicinity of Dirac Points with Landau–Zener Transition

Recently a new type of experiment, i.e., Bloch oscillations of ultracold atoms in honeycomb optical potential,realized Landau–Zener transition in the vicinity of Dirac point in 2D optical lattice. We show that the slope of Dirac cone is related to the transition probability of Landau–Zener transition. Therefore, it provides a new tool to directly detect the energy spectrum in the vicinity of Dirac point. Moreover, we numerically demonstrate that our scheme is feasible and effective in a large range of the parameter of anisotropy.     

Geometry of the Aharonov–Bohm Effect

We show that the connection responsible for any Abelian or non-Abelian Aharonov–Bohm effect with n parallel “magnetic” flux lines in ℝ³, lies in a trivial G-principal bundle P→M, i.e. P is isomorphic to the product M×G, where G is any path connected topological group; in particular a connected Lie group. We also show that two other bundles are involved: the universal covering space , where path integrals are computed, and the associated bundle P× _G ℂ ^m →M, where the wave function and its covariant derivative are sections.     

Quantum criticality of quantum speed limit for a two-qubit system in the spin chain with the Dzyaloshinsky–Moriya interaction

We study the quantum speed limit (QSL) time of a two-qubit system coupled to a spin–chain model with the Dzyaloshinsky–Moriya (DM) interaction. For the Bell state coupled to the Ising model or anisotropic XY model, we find that there is a prominent corresponding relationship between the QSL time and quantum phase transition in a spin–chain environment with larger scale, and the DM interaction can strongly enhance or suppress the response relation. Remarkably, when the surrounding environment is set to the XX model, the DM interaction makes it possible for us to witness the quantum phase transition by the local anomalous enhancement of the QSL time near the critical point. In addition, our analyses indicate that the entanglement can speed-up the system evolution in many-body environment.     

Relativistic Anandan quantum phase and the Aharonov–Casher effect under Lorentz symmetry breaking effects in the cosmic string spacetime

From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the violation of the Lorentz symmetry and write an effective metric for the cosmic string spacetime. Then, we investigate the arising of an analogue of the Anandan quantum phase for a relativistic Dirac neutral particle with a permanent magnetic dipole moment in the cosmic string spacetime under Lorentz symmetry breaking effects. Besides, we analyse the influence of the effects of the Lorentz symmetry violation and the topology of the defect on the Aharonov–Casher geometric quantum phase in the nonrelativistic limit.     

On the effect of lead concentration on the kinetics of contact melting in the Sn–Pb–Bi system in the presence of electromigration

It is determined by electron microscopy that the contact layer in the Sn–(Bi + 30 wt % Pb) system contains separate solid inclusions, while the contact layer in the Sn–(Bi + 40 wt % Pb) system is microheterogeneous. The observed structural states of alloys in the contact layers are explained by a change in the concentration of the initial contacting samples. The effect of the alloy structure and electromigration on the kinetics of contact melting is found.     

Aharonov–Bohm oscillations caused by non-topological surface states in Dirac nanowires

One intriguing fingerprint of surface states in topological insulators is the Aharonov–Bohm effect in magnetoconductivity of nanowires. We show that surface states in nanowires of Dirac materials (bismuth, bismuth antimony, and lead tin chalcogenides) being in non-topological phase, exhibit the same effect as amendment to magnetoconductivity of the bulk states. We consider a simple model of a cylindrical nanowire, which is described by the 3D Dirac equation with a general T-invariant boundary condition. The boundary condition is determined by a single phenomenological parameter whose sign defines topological-like and non-topological surface states. The non-topological surface states emerge outside the gap. In a longitudinal magnetic field B, they lead to Aharonov–Bohm amendment for the density of states and correspondingly for the conductivity of the nanowire. The phase of these magnetic oscillations increases with B from π to 2π.     

Fermi field and Dirac oscillator in a Som–Raychaudhuri space-time

We investigate the relativistic dynamics of a Dirac field in the Som–Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som–Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov–Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som–Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.     

On the influence of the electron-velocity spread in a beam on the mechanism of Cherenkov beam–plasma interaction

The instability of an electron beam in cold plasma is considered in the linear potential approximation with different velocity-distribution functions of beam electrons. It is demonstrated that the mechanism of beam instability in plasma changes as the electron-velocity spread is increased: the hydrodynamic single-particle instability mode evolves into the hydrodynamic collective mode or the single-particle kinetic one. Instability growth rates in different modes are determined analytically and numerically.     

On the Bose–Einstein Condensate of Excitons in Crystals with Defects

Optics and Spectroscopy - The possibility of formation of a Bose–Einstein condensate (BEC) of excitons in a model nonideal lattice of a molecular crystal is considered. The spectrum of...