A Clifford Algebra Approach to the Classical Problem of a Charge in a Magnetic Monopole Field

The motion of an electric charge in the field of a magnetic monopole is described by means of a Lagrangian model written in terms of the Clifford algebra of the physical space. The equations of motion are written in terms of a radial equation (involving r=|r|, where r(t) is the charge trajectory) and a rotor equation (written in terms of an unitary operator spinor R). The solution corresponding to the charge trajectory in the field of a magnetic monopole is given in parametric form. The model can be generalized in order to describe the motion of a charge in the field of a magnetic monopole and other additional central forces, and as an example, we discuss the classical ones involving linear and inverse square interactions.     

Dynamic shielding of a charge in a metal

A discussion of the shielding of a charged particle in a current-carrying conductor is given that is based on the linearized Thomas-Fermi approximation. An expression for the force on a particle of charge q is obtained from which the value of the electric field E_c in the conductor may be found:

$\text{E}{}_{\mathrm{c}}\text{=}\text{lim}\text{q→0}\text{F}{}_{\mathrm{q}}\text{/q}$

It is shown that the force on the particle has the form $\text{F}{}_{\mathrm{q}}\text{= q}\text{E}{}_0\text{× (1 + γ(}\text{q}\text{e}\text{) + …}$ to second order in the charge q, where E₀ is the electric field at large distances from q, e is the charge of the carrier, and γ is a material-dependent constant. The shielding correction has the character of a “wind-force,” and the electric field in the conductor is given by Ec = E₀.     

Derivation of the radial distribution function from experimental Compton profiles

The analysis of experimental Compton profiles in position rather than momentum space provides a useful method of interpreting Compton data. A density matrix approach is employed to establish the relationship between the Compton profile J(p), and the Fourier transform of the momentum density B(r), and, for a homogeneous system, the radial distribution function g(r). An earlier Compton profile measurement on sodium provides the data for a demonstration of the long range charge correlations in a metal, in analogy with the Friedel oscillations in a screening charge.     

On the topological charge concentrated at a point

For SU(2) gauge fields over the 4-dimensional sphere with a finite number of points x₁, x₂, ..., and x_N removed, there are gauge transformations which modify the topological charge concentrated at x_j by adding n_j, where n₁, n₂, …, and n_N. are integers such that Σ^N_{j = 1}n_j = 0. However, the reduction modulo Z of the topological charge at a point is well defined, being given in terms of the secondary characteristic classes of Chern and Simons, except when the topological charge is indeterminate.     

p-Type and n-type quaterthiophene based semiconductors for thin film transistors operating in air?

The solution and solid-state properties as well as the organic thin film transistor (OTFT) behavior of α,ω-perfluorohexyl-quaterthiophene (DFH-4T) are presented and compared to those of quaterthiophene (4T) and α,ω-hexyl-quaterthiophene (DH-4T). UV/visible and fluorescence data showed the same weak effect of hexyl and perfluorohexyl substitutions on the optical properties of 4T core. Growth mechanism of DFH-4T based thin films deposited by vacuum deposition on heated Si/SiO₂ substrates has been investigated in details and demonstrated to be identical to that of DH-4T. The characterization in air of the charge transport properties of thin films based on DH-4T and DFH-4T revealed a switch from p- to n-type, respectively, depending on the nature of alkyl chains. A qualitative Schottky-type charge injection barrier model, based on HOMO and LUMO energy levels estimated from cyclic voltammograms and optical absorption spectra of DFH-4T relative to those of 4T and DH-4T, was introduced to explain such change in semiconducting properties observed under ambient conditions (temperature, light, air). In an attempt to answer to the question of “are p-type and n-type quaterthiophene derivatives appropriate semiconductors for thin film transistors operating in air?” we investigated the influence of the nature of the dielectrics to obtain OTFTs operating in air and showing environmentally stable mobility.     

Relationships in infrared intensity theories,in particular the Mayants-Averbukh theory

A brief survey is given of the Mayants-Averbukh infrared intensity theory in relation to the more well-known but equivalent polar tensor theory. In addition, the appearances of the symmetry invariant parameter matrices D_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries about the midpoint of bond n. The use of these matrices and a single bond coordinate system will offer a convenient alternative to the Mayants-Averbukh treatment of a central, symmetric bond. The rotational mode equations of the Mayants-Averbukh and polar tensor theories have been investigated to elucidate the constrainsts which they impose on infrared intensity theories based on the bond dipole moment model and the atomic point charge model. It was found that the valence-optical theory is in full conformity with the rotational modes only if all electrooptical parameters $\text{?μ}{}_{\mathrm{n}}\text{?γ}{}_{\mathrm{i}}$ are neglected, where γ_i is the ith internal angular coordinate. The constraints imposed on the equilibrium charge-charge flux theory correspond to neglect of all charge flux parameters. The generalized valence-optical theory was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic dipole moment equation was found useful for suggesting a unique interpretation of a set of d parameters (elements of D_n⁰) in terms of bond dipole moment components.     

Charge displaced by a one-body potential in a Fermion assembly in terms of the highest occupied state

For (i) a slowly varying potential V(r) in a Fermi gas and (ii) N particles moving in a linear harmonic-oscillator potential, the total displaced charge and the particle density are respectively written in terms of the highest occupied state.     

X-ray diffraction study of the CDW phase in (TaSe4)2I: Determination of the CDW modulation amplitude

An extensive X-ray diffraction study of charge density wave (CDW) phase in (TaSe₄)₂I is reported. We have observed the superstructure satellites at 2q in addition to those at q reported by Fujishita et al. The results imply a sinusoidal lattice modulation with polarization almost perpendicular to q (i.e. transverse) and the existence of CDW domains. At 15 K we have extracted an approximate value for the amplitude of the lattice modulation perpendicular to q to be μ_⊥ ∽ 0.087 Å.     

Macroscopic behaviour of a charged Boltzmann gas

We consider a classical charged gas (with self-consistent Coulomb interaction) described by a solvable linearized Boltzmann equation with thermalization on uniformly distributed scatterers. It is shown that if one scales the time t, the reciprocal space coordinate k and the Debye length l as λ²t, (1/λ)k, λl, respectively, in the λ → ∞ limit the charge density is equal to the solution of the corresponding diffusion-conduction (macroscopic) equation.     

The inverse problem for a general N × N spectral equation

The spectral transform ?u/?x = {A(ζ)+B(x,ζ)} · u, where u is an n-element column vector and A(ζ) and B(x,ζ) are nxn matrices, is considered. A set of spectral data is given and the problem of reconcstructing B(x, ζ) from this spectral data is solved for a large class of cases. A special case of this spectral transform is used to solve the Boussinesq equation.     

SU(7) GUT and evasion of the survival hypothesis

Characteristic features of an SU(7) GUT are discussed, in which the fundamental representation 7 consists of SU(5)′5 and its two singlets with charge $\text{q = ±}\text{1}\text{2}$. The so-called survival hypothesis for fermions is naturally evaded by a kind of electric charge conservation due to $\text{q = ±}\text{1}\text{2}$, and a brief comment on the suppression of the ν_e? mass is given also.     

Photoelectron (He(I), He(II) and X-ray) spectroscopy of γ-pyrone and its related sulphur derivatives: valence and core ionization energies and shake-up satellites

The photoelectron He(I) and He(II) spectra of 4H-pyran-4-one (1), 4H-thiopyran-4-one (2), 4H-pyran-4-thione (3) and 4H-thiopyran-4-thione (4) are reported. The assignments are based on experimental evidence, taking into account the results of theoretical calculations. The outermost orbital sequences proposed (X = O, S) are n_X (σ), 3b₁ (π), 1a₂(π) for 1, 2 and 4; and 3b₁(π), n_X(σ) and 1a₂(π) for 3. The shifts of the core-ionization energy values for 1–4 are ascribed to a drift of π-charge from the intracyclic heteroatom towards the carbonyl or thiocarbonyl group. Low-energy shake-up satellites (up to 25% with respect to the main line) are observed in the various energy regions of the XPS spectra. They are qualitatively reproduced by CNDO/2 calculations. The most important satellites derive from the transition in the ion corresponding to the 3b₁ (π) → 4b₁(π*) transition in the UV-visible spectra of the neutral molecules. Charge rearrangements accompanying this transition lead to charge depletion of the core-ionized atom.     

Diffusion in very chaotic hamiltonian systems

We study nonintegrable hamiltonian dynamics: H(I,θ) = H₀(I) + kH₁(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I₀, θ₀, t₀) that the system is at I, θ at t, given it was at I₀, θ₀ at t₀. By discretizing time into steps of size ?, we show how to evaluate physical observables for large k, fixed ?. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Passage to ? = 0, the original hamiltonian flow, is discussed.     

Convex-envelope formulation for separable many-particle interactions

The exact result for the free energy per particle in systems described by a hamiltonian of the type NP(V_N), where NV_N denotes a set of short-range operators, is reformulated in terms of a convex-envelope construction. A comparison is given with results obtained for classical systems with interactions of the so-called Kac-type.     

Particles of nonzero rest mass and spin algebras

We construct a family of parametrized spin-Z_α algebras from the (canonical) spin-S and (helicity)spin-Z ones in the case of irreducible unitary representations [m, s] of the Poincaré group. The parameter α refers to a rotation angle around the third axis. Equivalences of such constructions are given through a family of unitary transformations containing, for definite values of α, well established and very useful transformations. General formulas referring to the so-called Shirokov-Foldy form of the Poincaré generators and to typical Shirokov's operators are given explicitly.     

The molecular vibration-rotation kinetic-energy operator for general internal coordinates

The molecular kinetic-energy operator for general internal coordinates is formulated in terms of simple generalisations of the matrices A, B, α, and β of Crawford. A new matrix γ of the gradients of the translational and rotational constraints facilitates the calculation of the β matrix. It is shown that the kinetic pseudo-potential U is most conveniently calculated as an atomic sum, and results are given for valence coordinates in various types of molecules.     

A classical model of EPR experiment with quantum mechanical correlations and bell inequalities

A simple model of a classical break-up process is given in which the correlation E(a,b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result $\text{?cos(}\text{a·b}\text{)}$. The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell's inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.     

Influence of the degenerate d level and of the Jahn-Teller effect on the manganite electronic structure calculated in the tight-binding approximation

E(k) dispersion curves for the charge carriers in the LaMnO₃-like perovskites were calculated for the basic types of canted antiferromagnetic ordering of the Mn sublattice in the framework of the tight-binding approximation. The E(k) spectrum of the antiferromagnetic structures was calculated for the first time taking into account the degeneracy of the Mn e _g level and the Jahn-Teller distortion of the cubic perovskite structure. This calculation involved diagonalization of the 8×8 Hamiltonian matrix. Analytical expressions for the E(k) function at separate points and symmetry lines of the Brillouin zone were derived. The calculations showed that the properties of the La_1?x Ca_xMnO₃ system do not have electron-hole symmetry.     

Effect of doping with iron on the charge ordering in La0.33Ca0.67Mn1−y Fe y O3 (y = 0, 0.05) manganites

The formation and specific features of the superstructure in La_0.33Ca_0.67Mn_1?y Fe _y O₃ (y = 0, 0.05) manganites doped with iron are investigated using transmission electron microscopy. The electron diffraction patterns of the manganites are studied in the temperature range 90–300 K, and the high-resolution electron microscope images recorded at temperatures of 91–92 K are analyzed. In both manganites, the structural transition that is accompanied by the formation of the superstructure and which is directly observed from the appearance of additional peaks in the electron diffraction patterns occurs at a temperature that is in close agreement with the charge ordering temperature T _CO determined from the temperature dependences of the magnetization M(T). In the temperature range 90 < T < 200 K, the undoped compound has a commensurate superstructure characterized by the vector q = 1/3a* and triple the unit cell «3a × b × c» (where a ≈ b ≈ √2a _c , c ≈ 2a _c , and a _c ～ 3.9 Å is the lattice parameter of a simple perovskite). The doping with iron (5 at. %) brings about a decrease in the charge ordering temperature T _CO by 50 K and the formation of an incommensurate structure for which the magnitude of the vector q is smaller by approximately 15%. The unit cell of the superstructure in the iron-doped compound is not triple the unit cell but involves defects of ordering, such as quadrupling of the unit cell, numerous translations by a _c √2 along the a direction, and dislocation-type defects in the stripe structure of the charge ordering. These pseudoperiodic defects lead to a decrease in the magnitude of the vector q and are responsible for the incommensurability of the structure. A decrease in the charge ordering temperature T _CO due to the doping with iron and the incommensurability of the superstructure correlate with the change in the concentration of Mn³⁺ Jahn-Teller ions as a result of their replacement by Fe³⁺ non-Jahn-Teller ions.