On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

In this contribution, we discuss the confinement of a nonrelativistic spin-half neutral particle to a hard-wall confining potential induced by noninertial effects. We show that the geometry of the manifold plays the role of a hard-wall confining potential and yields bound state solutions. We also consider a neutral particle with a permanent magnetic dipole moment interacting with a field configuration induced by noninertial effects, and discuss the behaviour of the induced fields and obtain energy levels for bound states.     

Noninertial Effects on a Dirac Neutral Particle Inducing an Analogue of the Landau Quantization in the Cosmic String Spacetime

We discuss the behavior of external fields interacting with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound state solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi?CWalker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau?CHe?CMcKellar?CWilkens quantization in the cosmic string spacetime. Finally, we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.     

Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov–Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov–Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arise from this dependence. Finally, an analogue of the Landau quantization is discussed.     

Torsion and noninertial effects on a nonrelativistic Dirac particle

We investigate torsion and noninertial effects on a spin-1/2$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame.     

Spin edge helices in a perpendicular magnetic field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.     

二维荷电粒子维格纳晶格:边界效应

采用一种非线性的优化方法,研究了处于硬壁限制势下二维带电多粒子系统的基态,分析不同形状边界对系统基态构型的影响.由于圆形边界对称性高,基态结构和抛物限制势下情况相似.在正方形边界下,当系统粒子数N<66时,荷电粒子形成方形晶格;当N≥66时,由于边界影响被削弱,内层粒子形成六角维格纳晶格.进一步分析了椭圆和矩形边界对维格纳晶格的影响.     

Neutral particles with anomalous magnetic moment in external e.m. fields: the proper time formulation

In this paper we evaluate the expression for the Green function of a pseudo-classical neutral spinning particle interacting with constant electromagnetic external fields by taking into account the anomalous magnetic moment of the particle. The spin degrees of freedom are described in terms of Grassmann variables and the evolution operator is obtained through the Fock–Schwinger proper time method.     

Comparing the reliability of networks by spectral analysis

Topological effects on the confinement of a moving neutral particle with an induced electric dipole moment confined to a quantum ring and a two-dimensional quantum dot (described by a hard-wall confining potential) are investigated. It is shown in this work that the spectrum of energy depends on the geometric phase obtained by Wei et al. [H. Wei, R. Han, X. Wei, Phys. Rev. Lett. 75, 2071 (1995)] and persistent currents arise from this dependence in both the quantum ring and the quantum dot. Further, the behaviour of the analogue of the Landau system for a moving electric dipole confined to a two-dimensional quantum dot is discussed, and it is shown that persistent currents are absent in this case.     

Induced electric dipole in a quantum ring

In this contribution, we investigate the quantum dynamics of a neutral particle confined in a quantum ring potential. We use two different field configurations for induced electric dipole in the presence of electric and magnetic fields and a general confining potential, for which we solve the Schrödinger equation and obtain the complete set of eigenfunctions and eigenvalues.     

Anandan quantum phase for a neutral particle with Fermi–Walker reference frame in the cosmic string background

We study geometric quantum phases in the relativistic and non-relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with two distinct field configurations in a cosmic string spacetime. We consider the local reference frames of the observers are transported via Fermi–Walker transport and study the influence of the non-inertial effects on the phase shift of the wave function of the neutral particle due to the choice of this local frame. We show that the wave function of the neutral particle acquires non-dispersive relativistic and non-relativistic quantum geometric phases due to the topology of the spacetime, the interaction between the magnetic dipole moment with external fields and the spin–rotation coupling. However, due to the Fermi–Walker reference frame, no phase shift associated to the Sagnac effect appears in the quantum dynamics of a neutral particle. We show that in the absence of topological defect, the contribution to the quantum phase due to the spin–rotation coupling is equivalent to the Mashhoon effect in non-relativistic dynamics.     

Relativistic bounds states for a neutral particle confined to a parabolic potential induced by noninertial effects

We obtain the solutions of the Dirac equation when the noninertial effects of the Fermi-Walker reference frame break the relativistic Landau-Aharonov-Casher quantization, but they provide bound states in an analogous way to a Dirac neutral particle subject to Tan-Inkson quantum dot potential [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635].     

Rashba coupling induced by Lorentz symmetry breaking effects

The arising of a Rashba‐like coupling, a Zeeman‐like term and a Darwin‐like term induced by Lorentz symmetry breaking effects in the non‐relativistic quantum dynamics of a spin‐1/2 neutral particle interacting with external fields is studied. Moreover, the influence of a Rashba‐like coupling induced by a Lorentz symmetry violation background on the Tan–Inkson potential [W.‐C. Tan and J. C. Inkson, Semicond. Sci. Technol. 11 , 1635 (1996)] is discussed.     

Lagrangian dynamics of spinning particles and polarized media in general relativity

The general form of the Lagrangian equations of motion is derived for a spinning particle having arbitrary multipole structure in arbitrary external fields. It is then shown how these equations, together with the complete system of field equations can be recovered from a fourdimensional action integral representing a polarized dustlike medium interacting with an arbitrary set of fields. These general results are then specialized to the case of Einstein-Maxwell fields in order to obtain the general-relativistic extension of Lorentz's dielectric theory.     

Response of a system of strongly interacting particles to an inhomogeneous external field

We show that a system of N strongly interacting quantum particles in a parabolic confining potential can be unstable under the action of a time-dependent quadrupole external field. The instability leads to the generation or amplification of dipole oscillations. Parameters of the instability are independent of the number of particles and the inter-particle interaction.     

Interacting quantum fields around a black hole

If one studies interacting fields on a black hole background using ordinary Feynman diagrams, one is faced with a problem of what to do with lines that cross the horizon. To avoid this difficulty a formulation is developed which can be expressed graphically in terms of a new class of diagram with external lines only at infinity. This formalism is applied to study the question of whether spontaneously broken symmetry would be restored near the black hole. It is also used to show that a black hole can emit more particles than antiparticles even in theories where the particle number is locally conserved by a globalU(1) symmetry.     

Phase behaviour of lyotropic liquid crystals in external fields and confinement

This mini-review discusses the influence of external fields on the phase behaviour of lyotropic colloidal liquid crystals. The liquid crystal phases reviewed, formed in suspensions of highly anisotropic particles ranging from rod- to board- to plate-like particles, include nematic, smectic and columnar phases. The external fields considered are the earth gravitational field and electric and magnetic fields. For electric and magnetic fields single particle alignment, collective reorientation behaviour of ordered phases and field-induced liquid crystal phase transitions are discussed. Additionally, liquid crystal phase behaviour in various confining geometries, e.g. slit-pore, circular and spherical confinement will be reviewed.     

Two-electron quantum dot in tilted magnetic fields: Sensitivity to the confinement model

Semiconductor quantum dots are conventionally treated within the effective-mass approximation and a harmonic model potential in the two-dimensional plane for the electron confinement. The validity of this approach depends on the type of the quantum-dot device as well as on the number of electrons confined in the system. Accurate modeling is particularly demanding in the few-particle regime, where screening effects are diminished and thus the system boundaries may have a considerable effect on the confining potential. Here we solve the numerically exact two-electron states in both harmonic and hard-wall model quantum dots subjected to tilted magnetic fields. Our numerical results enable direct comparison against experimental singlet-triplet energy splittings. Our analysis shows that hard and soft wall models produce qualitatively different results for quantum dots exposed to tilted magnetic fields. Hence, we are able to address the sensitivity of the two-body phenomena to the modeling, which is of high importance in realistic spin-qubit design.     

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.     

On the influence of a Rashba-type coupling induced by Lorentz-violating effects on a Landau system for a neutral particle

We study a possible scenario of the Lorentz symmetry violation background that allows us to build an analogue of the Landau system for a nonrelativistic Dirac neutral particle interacting with a field configuration of crossed electric and magnetic fields. We also discuss the arising of analogues of the Rashba coupling, the Zeeman term and the Darwin term from the Lorentz symmetry breaking effects, and the influence of these terms on the analogue of the Landau system confined to a two-dimensional quantum ring. Finally, we show that this analogy with the Landau system confined to a two-dimensional quantum ring allows us to establish an upper bound for the Lorentz symmetry breaking parameters.     

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.