Quantum-classical correspondence for motion on a plane with deficit angle

A particle constrained to move on a cone and bound to its tip by harmonic oscillator and Coulomb-Kepler potentials is considered both in the classical as well as in the quantum formulations. The SU(2) coherent states are formally derived for the former model and used for showing some relations between closed classical orbits and quantum probability densities. Similar relations are shown for the Coulomb-Kepler problem. In both cases a perfect localization of the densities on the classical solutions is obtained even for low values of quantum numbers.     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.     

Strings on a cone and black hole entropy

String propagation on a cone with deficit angle 2π(1 − 1/N) is described by constructing a non-compact orbifold of a plane by a Z_N subgroup of rotations. It is modular invariant and has tachyons in the twisted sectors that are localized at the tip of the cone. A possible connection with the quantum corrections to the black hole entropy is outlined. The entropy computed by analytically continuing in N would receive contribution only from the twisted sectors and be naturally proportional to the area of the event horizon. Evidence is presented for a new duality for these orbifolds similar to the R → 1/R duality.     

Optimization of perpendicular magnetic anisotropy tips for high resolution magnetic force microscopy by micromagnetic simulations

Magnetic Force Microscopy (MFM) tip coated with perpendicular magnetic anisotropy film (PMA tip) is one of the choices for high resolution imaging at low scan height (SH), since it has negligible tip–sample interaction related to its stable magnetic state, sharp, and small tip stray field. In this work, detailed micromagnetic studies are carried out to understand the effect of geometrical and magnetic parameters including the cone angle θ of the PMA tip, intergrain exchange constant $A_{2}^{*}$ , saturation magnetization M _s and uniaxial crystalline anisotropy constant K ₁ of the tip coating on the MFM tip resolution. To evaluate the resolution performance of the optimized PMA tip, MFM images of high-density granular recording media and patterned media are simulated. We find that, for the PMA tip and its coating, a cone angle in a range of 36.9^° to 53.1^°, a saturation M _s of 700 emu/cm³, a large uniaxial crystalline anisotropy constant K ₁ (>4.9×10⁶ erg/cm³) and a high intergrain exchange constant $A_{2}^{*}$ of (0.3–1.0)×10^?6 erg/cm are optimized conditions for high resolution imaging. The optimized PMA tip has an excellent performance on imaging of high-density thin film media (bit size of 8×16 nm²) at low SH of 2–8 nm and bit pattern media with a pitch of 50 nm, edge-edge spacing of 5–15 nm at SH of 8–15 nm.     

Searching for new conditions for fermion N-representability

New elements of the dual cone of the set of fermion N-representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N-representability is obtained for N = 3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction.     

Relativistic Symmetries in the Hulthén-like Potential and Tensor Interaction

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for Hulthén-like potential including a Coulomb-like tensor interaction are obtained with any arbitrary spin–orbit coupling number κ using the Pekeris approximation. The generalized parametric Nikiforov–Uvarov (NU) method is used to obtain the energy eigenvalues and the corresponding wave functions in their closed forms. We show that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.     

Origin of accidental degeneracy in ligand-field splittings of substituted octahedral complexes

Accidental degeneracy seems to be the rule rather than an exception amongst thed orbital energies of substituted octahedral complexes ofd ¹ configuration. By using symmetry and physical arguments, in conjunction with first-order and second-order degenerate perturbation theory, it is shown that such accidental degeneracies arise in crystal-field theory due to the choice of an inflexible basis set of metal orbitals which neglects the polarisation of metal orbitals by the ligand charges.     

Algebraic solution of the supersymmetric hydrogen atom in d dimensions

In this paper the supersymmetric extension of the Schrödinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This symmetry of the system is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions.     

The microwave spectra of ortho-fluorotoluene with the asymmetric internal rotors CH2D and CD2H

The rotational spectra of αd₁- and αd₂-ortho-fluorotoluene in the ground state of the methyl group torsion have been measured. The evaluation of the spectra has been based on the theory for the internal rotation of an asymmetric internal top formulated earlier by several authors. The barrier potential being threefold symmetric (V₃), each torsional level consists of three nondegenerate substates, designated as sy and ±asy. The sy-state is assigned to the conformation with the unique methyl hydrogen isotope within the molecular heavy-atom plane (sy-rotamer), while the ±asy-states belong to the respective out-of-plane conformation (asy-rotamer). In the torsional ground state the level spacing between the ±asy substates is very small and numerous accidental close degeneracies are present between the rotational level systems based on these torsional substates. The rotational levels involved are strongly perturbed by the coupling between molecular overall rotation and internal rotation. Large deviations from a rigid rotor spectrum and (+) ? (?) intersystem (“tunneling”) transitions are observed. The spectrum of the asy-rotamer can be well reproduced by a “two-dimensional” Hamiltonian containing 11 “rotational constants,” 9 of which are determined by a fit to the spectrum. Several are sufficiently barrier-dependent to derive V₃. We obtain (in cal/mole) 567 ± 48 for αd₁-ortho-fluorotoluene, 711 ± 40 for the αd₂-isotope. The deviations from 649 cal/mole for the normal isotope are appreciable, probably indicating shortcomings of the semirigid model. The sy-rotamer presents a rigid rotor spectrum.     

Numerical study of tip opening of hydrogen/air Bunsen flame

To understand tip opening of a hydrogen–air Bunsen flame, the detailed flow, temperature and concentration fields of the flame were studied based on numerical calculations that use the exact transport properties and the full chemical reaction mechanism. The study has revealed that the local chemical reactions along the flame cone portion do not remain uniform; the H₂ consumption rate decreases in the downstream direction. The lowering H₂ concentration of the mixture coming into the cone, caused by the radial outward diffusion of mobile H₂ molecules, leads to the slowdown of the main H₂-consuming reactions downstream and causes the breakdown of the reaction at the downstream end of the cone. This is the tip opening.     

One-Dimensional Traps,Two-Body Interactions,Few-Body Symmetries: I. One,Two, and Three Particles

This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly-unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article sequentially analyzes the symmetries of one, two and three particles in asymmetric, symmetric, and harmonic traps; the sequel article treats the N particle case.     

Interaction between laser beam and target in pulsed laser deposition: laser fluence and ambient gas effects

The most prominent phenomena on the target surface induced by laser irradiation in pulsed laser deposition is the formation of conical morphologies in the irradiated area. The conical morphologies formed under different laser fluences and the ambient oxygen pressures in KrF laser ablation of Pb(Zr_0.53Ti_0.47)O₃ were studied in detail by using scanning electron microscopy. The results indicate that, depending on the melting extent of the irradiated surface, there are two kinds of cones: one type with well-defined cone tip and cone body and the other having only a cone tip. Pb is very deficient in cone tip. The gas ambient pressure plays a remarkable role in the laser-target interaction. These results are interpreted by employing the impurity shielding mechanism and the surface instability mechanism.     

Semi-local cosmic strings and the cosmological constant problem

We study the cosmological constant problem in a three-dimensional N = 2 supergravity theory with gauge groupSU (2)_global × U(1)_local. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solitonic solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomol'nyi bound, as a consequence of an Aharonov-Bohm-like effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.     

FABRICATION AND APPLICATION OF NEAR-FIELD OPTICAL FIBRE PROBE

In this paper, the fabrication of a large cone angle near-field optical fibre probe, using the two-step chemical etching method and bent probe, is introduced, and the controlling parameters of the coated Cr－Al film at the probe tip are presented. The scanning electron microscopy images display that the tip diameter of the uncoated large cone angle fibre probe obtained is less than 50nm, the cone angle over 90°, and the diameter of light aperture at the coated probe tip is less than 100nm. The measured results of the optical transmission efficiency for various probe tips show that the uncoated straight optical fibre probe, film-coated straight probe and film-coated bent probe are 3×10^-1, 2×10^-3, and 1×10^-4 times that of the flat fibre probe, respectively. In addition, the force images and near-field optical images of a standard sample are acquired using a large cone angle and film-coated bent probe.     

Modification of interface structure and contact resistance between a carbon nanotube and a gold electrode by local melting

The electrical connection between a multiwalled carbon nanotube (MWNT) and a gold electrode on applying an electric current was studied by performing in situ transmission electron microscopy observations while simultaneous measuring the bias voltage and the electric current. The tip of the MWNT was brought into contact with the gold surface. When a current density of ∼10⁸ A/cm² flowed through the contact, the gold surface started to melt along the surface of the MWNT tip due to Joule heating. At about twice the current density, a drastic change was observed in the structure of the gold surface in the contact region. This structural change increased the contact area between the MWNT tip and gold, which reduced the electrical contact resistance.     

One-Dimensional Traps,Two-Body Interactions,Few-Body Symmetries. II. N Particles

This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly–unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article analyzes the symmetries of N particles in asymmetric, symmetric, and harmonic traps; the prequel article treats the one, two and three particle cases.     

Photonic band structure in the nearly plane wave approximation

For photons propagating in a periodic dielectric lattice, the dispersion curve forms photonic bands separated by forbidden gaps. When the dielectric lattice deviates only slightly from being homogenous, the photonic band structure resembles the linear dispersion relation for photons folded into the first Brillouin zone, i.e., the so-called empty lattice bands. Using group theoretical technique, we calculate the splitting of the accidental degeneracies in the empty lattice bands at symmetry points for a simple cubic dielectric lattice. Received 23 June 1998     

Semiclassical quantization of the nonlinear Schrödinger equation

Using the functional integral technique of Dashen, Hasslacher, and Neveu, we perform a semiclassical quantization of the nonlinear Schrödinger equation, which reproduces McGuire's exact result for the energy levels of the theory's bound states. We show that the stability angle formalism leads to the one-loop normal ordering and self-energy renormalization expected from perturbation theory and demonstrate that taking into account center-of-mass motion gives the correct nonrelativistic energymomentum relation. We interpret the classical solution in the context of the quantum theory, relating it to the matrix element of the field operator between adjacent bound states in the limit of large quantum numbers. Finally, we quantize the NLSE as a theory of N component fermion fields and show that the semiclassical method yields the exact energy levels and correct degeneracies.     

The approximate ABCD matrix for a parabolic lens of revolution and its application in calculating the coupling efficiency

Using ray optics, we present an explicit formulation of the ABCD matrix for reflection and refraction of light beams at a parabolic interface separating media of different refractive indices under paraxial approximation. Based on the formulated ABCD matrix for refraction by a parabolic lens tip, we present a simple theoretical investigation of the coupling efficiency between a laser diode and a single-mode fiber with a parabolic lens formed on the fiber tip. The results show that this technique is effective and will be of benefit to designing suitable microlenses applying the laser-coupling technique.