Light-Induced Hofstadter＇s Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper＇s equations from the Schr？dinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper＇s equations. We analyze the properties of the Hofstadter＇s butterfly spectrum and discuss its observability.     

Light-Induced Hofstadter＇s Butterfly Spectrum in Optical Lattices

We propose a scheme to create an effective magnetic field, which can be perceived by cold neutral atoms in a two-dimensional optical lattice, with a laser field with a space-dependent phase and a conventional laser field acting on A-type three-level atoms. When the dimensionless parameter a, being the ratio of flux through a lattice cell to one flux quantum, is rational, the energy spectrum shows a fractal band structure, which is so-called Hofstadter＇s butterfly.     

Response of a Superconducting Quantum Interference Device to Alternating Magnetic Field

We study the response of a superconducting quantum interference device （SQUID） to an alternating magnetic field. It is found that, for some suitably selected parameters＇ values, we can obtain stochastic resonance for the amplitude of the steady average voltage of the SQUID versus the dichotomous noise strength, and frequency （stochastic） resonance for the amplitude of the stationary average voltage of the SQUID as a function of the frequency of the alternating magnetic field. Our results can be useful for electrical power generation using the alternating magnetic field energy of a SQUID.     

Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics

We study the noncoInmutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by intro ducing a shift for the magnetic field, we give the Schrodinger equations in the presence of an external magnetic field both on a noncommutative space and a noncomlnutative phase space, respectively. Then by solving the SchrSdinger equations both on a noneommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. Wc demonstrate that these phases are geometric and dispersive.     

Spin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin-orbit interactionsSpin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin-orbit interactionsSpin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin-orbit interactions

In this study, we investigate theoretically the effect of spin-orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin-orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin-orbit interactions introduce comp｜ex features in spin texturing owing to the couplings in energy subbands. We obtain that spatia~ modulation of the spin density along the wire width can be considerably modified by the spin-orbit coupling strength, magnetic field and charge carrier concentration.     

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...     

A Radio Frequency Field Guide Using Field Induced Adiabatic Potential

We study the behaviour of atoms in a field with both static magnetic field and radio frequency （rf） magnetic field. We calculate the adiabatic potential of atoms numerically beyond the usually rotating wave approximation, and it is pointed that there is a great difference between using these two methods. We find the preconditions when RWA is valid. In the extreme of static field almost parallel to rf field, we reach an analytic formula. Finally, we apply this method to 87 Rb and propose a guide based on an rf field on atom chip.     

Spin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin–orbit interactions

In this study, we investigate theoretically the effect of spin–orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin–orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin–orbit interactions introduce complex features in spin texturing owing to the couplings in energy subbands. We obtain that spatial modulation of the spin density along the wire width can be considerably modified by the spin–orbit coupling strength, magnetic field and charge carrier concentration.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

A novel approach to designing cylindrical-surface shimcoils for a superconducting magnet of magnetic resonance imaging

For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylindrical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.     

Properties of a Bound Polaron under a Perpendicular Magnetic Field

We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit （SO） interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.     

Dust Lattice Waves of Dusty Plasma Chain with an External Magnetic Field

Dust lattice waves of a one-dimensional plasma crystal chain with an external magnetic field are investigated. When the magnetic field is in the vertical direction （θ- 0）, perpendicular to the chain, the vertical transverse mode is not affected, while the horizontal transverse mode is coupled with the longitudinal mode. In the high frequency range, we obtain an ‘upper-hybrid＇ dust lattice mode and in the low frequency range, we obtain a ＇lower-hybrid＇ dust lattice mode. Between the two modes, a ＇gap＇ is formed. When the magnetic field is oriented to the chain （0 = π/2）, the longitudinal mode is not affected while both the horizontal and vertical transverse modes are shifted due to the effect of the magnetic field.     

Tuning Out-of-Plane Spin Polarization Using in-Plane Magnetic Fields in a Quasi-One-Dimensional Quantum Wire Embedded in （110） Plane

We investigate theoretically the combination effect of an in-plane magnetic field and spin-orbit interactions （SOIs） on the spin and charge transport property of a quasi-one-dimensional quantum wire embedded in the （110） crystallographic plane. We find that the oscillations of the conductance induced by the SOIs become more significant and different for the spin-up and spin-down electrons in the presence of the in-plane magnetic field. The conductance exhibits a significant anisotropic behavior and electrons exhibit out-of-plane spin polarization which can be tuned by an in-plane magnetic field. These features offer us an efficient way to control SOI-induced spin transport using in-plane magnetic fields.     

The Modified Magnetohydrodynamical Equations

After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the “Lorentz“ force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.     

Spin texturing in quantum wires with Rashba and Dresselhaus spin–orbit interactions and in-plane magnetic field

In this work, we investigate the effects of interplay of spin–orbit interaction and in-plane magnetic fields on the electronic structure and spin texturing of parabolically confined quantum wire. Numerical results reveal that the competing effects between Rashba and Dresselhaus spin–orbit interactions and the external magnetic field lead to a complicated energy spectrum. We find that the spin texturing owing to the coupling between subbands can be modified by the strength of spin–orbit couplings as well as the magnitude and the orientation angle of the external magnetic field.     

Controllable Double-Well Magneto-Optical Trap for Neutral Atoms

We propose a novel controllable double-well magneto-optical trap (MOT) by using a square current-carrying wire and a bias magnetic field. The spatial distributions of the magnetic fields and their gradients are calculated, and the results show that the proposed trap has double magnetic wells with two centres of zero magnetic field and can be continuously evolved as a single-well trap by reducing the current in the wire or increasing the bias field, which can be used to realize a controllable double-well MOT, even to prepare one- and two-dimensional arrays of magneto-optical lattices on the surface of an atom chip. We also estimate the number (～10^7) and temperature (～260μK) of trapped cold atoms in our MOT.     

Investigation the positive moments on the M－T curve of YBCO films measured by using zero-field cooling

The superconducting transition of a YBCO film was measured by a MPMS-5 superconducting quantum interference device magnetometer, using a zero-field cooling process. The experimental results have shown that there are positive magnetic moment and positive peak on the M－T curve. We have proven that these anomalous behaviours are due to measurement error, but not phase transition. We have proposed a simple formula to explain and to calculate quantitatively these anomalous behaviours. It was found that, provided dH>0.59H_p (dH is the inhomogeneous field of the remnant field, H_p is the fully penetrated field of the measured sample), the experimental results will be positive, not negative. If dH≥2H_p, the experimental results will be symmetrical to their real negative values. From the M－T curve, which has positive moment and positive peak below T_c (superconducting transition temperature), we found a new possible method to obtain H_p of the measured sample.     

Metallic Contaminant Detection using a High-Temperature Superconducting Quantum Interference Devices Gradiometer

We develop magnetic metallic contaminant detectors using high-temperature superconducting quantum interference devices （HTS-SQUIDs） for industrial products. Finding ultra-small metallic contaminants is an important issue for manufacturers producing commercial products such as lithium ion batteries. If such contaminants cause damages, the manufacturer of the product suffers a big financial loss due to having to recall the faulty products. Previously, we described a system for finding such ultra-smafi particles in food. In this study, we describe further developments of the system, for the reduction of the effect of the remnant field of the products, and we test the parallel magnetization of the products to generate the remnant field only at both ends of the products. In addition, we use an SQUID gradiometer in place of the magnetometer to reduce the edge effect by measuring the magnetic field gradient. We test the performances of the system and find that tiny iron particles as small as 50 × 50 μm^2 on the electrode of a lithium ion battery could be clearly detected. This detection level is difficult to achieve when using other methods.     

Accidental Degeneracies in N dimensions for Potential Class αr~(2d-2)-βr~(d-2) via Asymptotic Iteration Method(AIM)

In mathematical physics the main goal of quantum mechanics is to obtain the energy spectrum of an atomic system.In many practices,Schrodinger equation which is a second order and linear differential equation is solved to do this analysis.There are many theoretic mathematical methods serving this purpose.We use Asymptotic Iteration Method(AIM) to obtain the energy eigenvalues of Schrodinger equation in N-dimensional euclidean space for a potential class given as αr~(2d-2)-βr~(d-2).We also obtain a restriction on the eigenvalues that gives degeneracies.Besides,we crosscheck the eigenvalues and degeneracies using the perturbation theory in the view of the AIM.