Optical Möbius strips in three-dimensional ellipse fields: I. Lines of circular polarization

The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three-dimensional optical ellipse fields are shown to be organized into Möbius strips (twisted ribbons). These strips can have either one or three half-twists, and can be either right- or left-handed. The normals to the surrounding ellipses generate cone-like structures. Two special projections, and eight new indices are developed to characterize the rather complex structures of the Möbius strips and cones. These eight indices, together with the two well-known indices used until now to characterize singular lines of circular polarization, could, if independent, generate 16,384 different index combinations. Geometric constraints and 15 selection rules are discussed that reduce the number of combinations to 1676. Of these 1150 have been observed in 10⁶ independent realizations of a simulated random ellipse field. Statistical probabilities are presented for the most important index combinations. It is argued that it is presently feasible to perform experimental measurements of the Möbius strips and cones described here theoretically.     

Quasi-one Dimensional Topological Insulator: Möbius Molecular Devices in Peierls Transition

We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Möbius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z₂ topology of the Möbius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.     

Mechanisms and Möbius strips: understanding dynamic processes in annulenes

Exploratory computational studies on annulenes with planar, Möbius, and two‐twist topologies have resulted in new mechanisms to explain facile thermal configuration change (cis‐trans isomerization) for medium‐sized annulenes ([12]‐ to [16]annulene). Möbius π‐bond shifting through both aromatic and antiaromatic transition states, two‐twist π‐bond shifting, and planar nondegenerate π‐bond shifting can all be invoked to explain experimental results. Moreover, a simple bond‐shift rule, which is based on the change in number of trans C?C double bonds (Δtrans), was developed that predicts the topology of the transition state(s) necessary to effect the desired cis‐trans isomerization. The bond‐shift rule was also applied to configuration change in dehydro[12]annulene. Finally, extensive investigation of the [14]annulene hypersurface revealed that numerous Möbius minima exist within 10 kcal/mol of the global minimum. Copyright © 2012 John Wiley & Sons, Ltd.     

Atomistic study of the pressure-induced phase-transition mechanism in GaAs by Möbius inversion potentials

In this work, the phase transition from zincblende (B3) to rocksalt (B1) structure in bulk GaAs is investigated by using Möbius inversion potentials. A Cm transition path is proposed from the molecular static simulation results, even though it is different from previously proposed transition paths Imm2, R3m and P3₂. The present Cm path is quite close to the previously suggested Imm2 path according to the crystal cell geometries and activation enthalpies. By comparison, the activation enthalpies along the R3m and P3₂ path are relative high. Therefore, the Imm2 mechanism, as a simplified model of the Cm one, is suggested to describe the microscopic process of the B3-B1 phase transition of GaAs. In this way, we investigate the changes of the system features during the transition process characterized by Imm2 mechanism and obtain a concise picture for the common B3-B1 transition. All the calculated results are compared to relevant experimental observations and other calculations.     

Optical anisotropy and pinning of the linear polarization of light in semiconductor microcavities

We report strong experimental evidence of the optical anisotropy in a CdTe-based microcavity: the polarization of light is pinned to one of the crystallographic axes independently of the polarization of the excitation. The polarization degree depends strongly on the excitation power, reaching almost 100% in the stimulated regime. The relaxation time of the polarization is about 1 ns. We argue that all of this is an effect of a splitting of the polariton doublet at k=0. We consider different sources for the splitting and conclude that the most likely one is optical birefringence in the mirrors and/or the cavity.     

Green's functions of linear and three dimensional oscillators in a constant and homogeneous electromagnetic field

The retarded Green's functions are found for linear and three dimensional harmonic oscillators in constant and uniform electric and magnetic fields. These results are applied to the problem of the motion of wave packets of Gaussian shape.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 29–33, August, 1973.In conclusion the authors thank A. A. Sokolov for a discussion of the obtained results.     

The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of “spacelike linearity”. Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.     

Multiphoton ionization in dielectrics: comparison of circular and linear polarization

Ionization mechanisms in bulk dielectrics irradiated by single intense 50-fs-laser pulses are investigated by ultrafast time-resolved imaging interferometry. Polarization-sensitive 6-photon ionization is shown to be the dominant ionization mechanism in fused silica and sapphire at intensities around 10 TW/cm2. For both materials the cross sections of 6-photon ionization are found to be significantly higher for linear polarization than for circular. Our experimental results corroborate an earlier theoretical prediction on the dominance of linear polarization in high-order multiphoton ionization.     

Vectorial Pauli algebraic approach in polarization optics. II. Interaction of light with the canonical polarization devices

A theoretical approach to the interaction between polarized light and polarization devices, based on the vectorial and pure operatorial form of the Pauli algebra, is presented. In the first part of the paper we have established the vectorial Pauli-algebraic forms of the operators corresponding to various polarization devices and states of light polarization. In this second part we give the vectorial Pauli-algebraic treatment of the interaction between the canonical polarization devices and the various forms of light polarization. Unlike the standard (Jones and Mueller) approaches, this formalism does not appeal to any matrix representation of the involved operators. This approach establishes a bridge between the Hilbert space of the density operators of the polarization states and the Poincaré space of their geometric representations and gives a rigorous justification of the handling of the interactions between the polarization states and polarization systems on the Poincaré sphere and in the Poincaré ball. In such an approach, unlike the standard ones, the three relevant quantities that characterize the interaction - the gain, the Poincaré vector of the outgoing light and its degree of polarization - result straightforwardly, in block. A generalized form of Malus’ law, for any dichroic device and partially polarized light is also obtained this way.     

Electric polarization and dielectric behaviour in dc electric fields of fused KNO2 in phase II at room temperature

On application of dc electric fields to a sample of KNO₂ (99.9% pure) fused between two heavily nickel plated copper plates the sample does not acquire the potential difference equal to the applied emf even though there is no external potential drop in the circuit. Also a very large capacitance of the order of 3000μF is obtained for this sample which is attributed to interfacial polarization effect. An equivalent circuit is given to explain the dc electrical behaviour of the sample. The idea of solid state battery does not seem to be applicable in the case of fused KNO₂. The large value of the capacitance for dc fields in series with large voltage-dependent resistance is the cause of the slow discharge of the condenser.     

Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ in the following three regions:BZ ^4/3,BZ ^4/3 andZ ^4/3BZ³. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsBZ ³ andBZ³ in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.Work partially supported by U.S. National Science Foundation grant PHY90-19433 A02Work partially supported by U.S. National Science Foundation grant DMS 92-03829Work partially supported by the Heraeus Stiftung and the Research Fund of the University of Iceland.     

A local approach to dimensional reduction: II. Conformal invariance in Minkowski space

We consider the problem of obtaining conformally invariant differential operators in Minkowski space. We show that the conformal electrodynamics equations and the gauge transformations for them can be obtained in the frame of the method of dimensional reduction developed in the first part of the paper. We describe a method for obtaining a large set of conformally invariant differential operators in Minkowski space.     

Degree of polarization in near fields of thermal sources: effects of surface waves

We introduce the concept of degree of polarization for electromagnetic near fields. The approach is based on the generalized Stokes parameters that appear as expansion coefficients of the 3 x 3 coherence matrix in terms of the Gell-Mann matrices. The formalism is applied to optical near fields of thermally fluctuating half-space sources with particular interest in fields that are strongly polarized owing to resonant surface plasmons or phonons. This novel method is particularly useful when assessing the full vectorial characteristics of random evanescent fields, e.g., for near-field spectroscopy and polarization microscopy.     

The system of one dimensional balls in an external field. II

We modify the system introduced in [W1] so that we can establish the nonvanishing ofall Lyapunov exponents easily.Supported in part by the NSF Grant DMS-8807077 and the Sloan Foundation     

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum,polarization and quantum‐information measures

Information‐theoretical concepts are employed for the analysis of the interplay between a transverse electric field applied to a one‐dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position and momentum quantum information entropies and their Fisher information and and Onicescu information energies and counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, (Neumann, ), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum‐information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field‐independent sum . Analogously, at and the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as () and its inverse, respectively, leading to the field‐independent product (). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum‐information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

     

The Yukawa coupling of quantum fields in two dimensions. II

The Yukawa coupling in two dimensional space time is considered. A space outoff is introduced in the interaction termV, so that the renormalized HamiltonianH _ren is a rigorously defined bilinear form in the Fock Hilbert space. The main result is thatH _ren is positive provided the finite part of the renormalization terms are suitably chosen. As a consequence, the Schrödinger equation (i/t–H _ren)=0 can be solved.This work was supported in part by the National Science Foundation, GP — 6165.     

Mössbauer and magnetic studies in nickel ferrite nanoparticles: Effect of size distribution

The magnetic properties of nickel ferrite nanoparticles in the form of powders, prepared by the sol-gel process and subjected to different annealing temperatures, were investigated using both static and dynamic measurements namely hysteresis, zero field cooled-field cooled magnetization (ZFC-FC) measurements and Mössbauer spectroscopy. The Transmission Electron Microscopy (TEM) studies reveal particle sizes for the as-prepared particles which increases upto 52 nm with annealing. A bimodal distribution, upto an annealing temperature of was observed. ZFC-FC measurements for the as-prepared samples reveal twin peaks, indicative of the bimodal size distribution. ZFC-FC measurements performed for fields varying from 100 Oe to 3 kOe show a superparamagnetic phase with blocking temperatures between 320 and . Numerical simulations for the ZFC-FC studies indicate that the signature of the bimodal size distribution can be seen only at very low fields. The variation of coercivity with particle size, as determined from the hysteresis measurements, shows a transition from a single domain to a multi domain state for particle sizes larger than 35 nm. Mössbauer measurements performed at room temperature for the as-prepared sample shows a six finger pattern for the samples with higher particle size and a doublet pattern for the samples with smaller particle size, which is indicative of their superparamagnetic nature.     

Laser fields at flat interfaces: II. Plasmon resonances in aluminium photoelectron spectra

Using the model derived in paper I?[G. Ra?eev, Eur. Phys. J. D 66, 167 (2012)], this work presents calculations of the photoelectron spectrum (PES) of low index aluminium surfaces in the 10?C30?eV region. The laser is p or transverse magnetic linearly polarized incident on a flat structureless surface and its fields are modeled in I using the vector potential in the temporal gauge. This model uses a tensor and non-local isotropic (TNLI) susceptibility and solves the classical Ampère-Maxwell equation through the use of the vector potential from the electron density-coupled integro-differential equations (VPED-CIDE). The PE cross sections are the squares of the PE transition moments calculated using the VPED-CIDE vector potential function of the penetration coordinate. The PES is obtained in a one step model using either the Fermi golden rule or the Weisskopf-Wigner (WW) expressions. The WW cross section PES compares favorably with the experimental angle and energy resolved photoelectron yield (AERPY) spectrum of Levinson et?al. [Phys. Rev. Lett. 43, 952 (1979)], Levinson and Plummer [Phys. Rev. B 24, 628 (1981)] for Al(001) and of Barman et?al.?[Phys. Rev. B 58, R4285 (1998)], Barman [Curr. Sci. 88, 54 (2005)] for Al(111) surfaces. As in the experiment, our theoretical AERPY displays the multipole surface plasmon resonance at 11.32/12.75 eV for Al(001)/Al(111), mainly due to the surface contribution |??? _f |p·A|?? _i ?|², the bulk plasmon minimum at 15 eV and the two single particle excitation resonances at about 16 and 22 eV. The nature of the plasmon resonances of the PES is analyzed using the reflectance, the electron density induced by the laser and Feibelman??s parameter d _?? all introduced in paper?I.     

Thermally stimulated electromagnetic-field spectra in planar structures of complex composition: II. Radiative fields

It is demonstrated that the spectral composition of the radiative thermal fields of a Cd _x Zn_{1 ? x}Te solid solution film on a metallic substrate is sensitive to small changes in the impurity concentration and film thickness. The calculated spectral densities of the p- and s-polarized states of the radiative component of thermal fields in a plane-layered system are compared using the refraction additivity principle. The spectral densities are calculated at different values of the impurity concentration and film thickness.