Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Theory of ferromagnetic resonance in metallic and insulator films

Simple intuitive explanations of the frequencies and intensitiesI of magnetostatic modes (with negligible exchange energy) and exchange modes (negligible microwave-field demagnetization energy) are given. The effects of explicit boundary conditions on the transverse, time-varying componentm of the magnetization (i.e., the amount of pinning) and the effects of inhomogeneities in the internal fieldH _i and saturation magnetizationM _s are discussed. A bulk inhomogeneity inM _s changes the effective exchange constant, while a bulk inhomogeneity inH _i lowers the fields for resonance of all high-order exchange modes by the same amount. The pinning conditions affect the values of andI of the exchange modes and the mixed exchange-magnetostatic modes, but have little effect on the magnetostatic modes. A surface-imperfection source of pinning and of the inhomogeneities inH _i andM _s is discussed.Part of this work was performed while the author was atNorth American Rockwell Science Center, Thousand Oaks, California.     

Torque equations for spin and orbital angular momenta of radiation fields and Faraday effect

The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved.     

IR Evidences for N-9 and N-7 Regioisomers of the Acyclic Purine Nucleoside Analogues

The IR spectra have been recorded in the solid state for the parent molecule, 6-(N-pyrrolyl)purine (1) and its N-9-and N-7-substituted derivatives: 9-and 7-(2-hydroxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (2 and 3), 9-and 7-(2-acetoxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (4 and 5), 9-and 7-(2,3-dihydroxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (6 and 7) as well as 9-and 7-(2,3-diacetoxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (8 and 9). Analysis of the characteristic bands has proved to be useful in differentiating between N-9 and N-7 regioisomers.     

CD Spectroscopic Study of Absolute Conformation and Configuration of Some 4-Hydroxychromans

CD data of the optically active 4-hydroxy (1–5) and 4-acetoxy chromans (6–8) were analyzed by two different approaches. The Snatzke-Antus treatment of chiraly perturbed chromane chromophore revealed M absolute conformation and 4S absolute configuration of the alcohols, i.e. P absolute conformation and 4R absolute configuration of the acetates. The proposed absolute configuration of the optically active alcohols was confirmed for 1 and 2 by the chiral excitone coupling method applied on their benzoates 9 and 10.     

A Fluorescence Study of Novel Styrylindoles in Homogenous and Microhetrogeneous Media

In this paper are presented absorption and fluorescence emission properties of 3-styrylindoles viz. 3-(2-phenylethenyl-E)-NH-indole (1), 3-[2-(4-nitrophenyl)ethenyl-E)-NH-indole (2), 3-[2-(4-cyanophenyl)ethenyl-E]-N-ethylindole (3) and 3-[2-(4-cyanophenyl)ethenyl-E]-NH-indole (4) in organic solvents, 1,4-dioxane-water binary mixtures and micelles (SDS, CTAB and Triton-X-100). The fluorescence properties of 2-4 have been utilized to probe the microenvironment (binding constant, CMC, micropolarity and solubilization site) of the micelles.     

Mechanism of giant magnetoresistance in intermetallic compounds of rare-earth ions and actinides

Giant positive or negative magnetoresistance is calculated in a band model. The spectra of the band electrons in a two-sublattice antiferromagnetic intermetallic compound depend on the antiferromagnetism vector L(T,H). The metamagnetic transition to the ferromagnetic phase is accompanied by splitting with respect to the spin σ, displacement of the energy bands, and a decrease in the effective masses of the band electrons. This mechanism of giant negative magnetoresistance is also accompanied by an increase in the relaxation time τ_jσ. Scattering by chemical-bond fluctuations is considered as the main relaxation mechanism. Giant positive magnetoresistance results from a four-subband model of 4f and 5f intermetallic compounds. The electron effective masses m _jσ(J _jT ) of the (j,σ) bands increase with the mean angular momentum J _1T (T,H) of an ion in the jth sublattice of 4(5)f ions. The thermodynamics of such a four-sublattice model, the nonlinear magnetization and magnetoresistance curves, and the nonmonotonic dependence of the specific heat C _m(T,H) on the field H are calculated. Fiz. Tverd. Tela (St. Petersburg) 39, 1806–1814 (October 1997)     

Packing of molecules and hole formation in lyotropic systems

A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q: λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)^1/3 and the energy E≈59.79K(λh/K)^1/3. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 575–580 (25 October 1996)     

Spherical harmonics and Cartesian tensor scalar product expansion in the Fokker-Planck equation

On the basis of the expansion of the distribution functionf(v, r,t) in a sum of spherical harmonics, which is equivalent to a Cartesian tensor scalar product expansion of the distribution function, i.e.,f(v, r, t)=f ₀(v,r,t)+v. f ₁(v,r,t)+vvf ₂(v,r,t)+vvvf ₃(v,r,t)+ wheref _k (k=2, 3) arek-th order irreducible tensors, the Rosenbluth potential functions and the Fokker-Planck collision term are expanded in a similar sum. Collisions termsJ _Fk (k=0, 1, 2) and the equations forf _k (k=0, 1, 2) for the case of the Coulomb interactions are also determined.Technická 2, Praha 6, Czechoslovakia.The autor wishes to express his thanks to Prof. J. Kracík, DrSc. for valuable advice and suggestion.     

Conditional expectation and commutativity in von Neumann algebras

LetH be a Hilbert space,A the von Neumann algebra of all bounded operators onH,B a von Neumann subalgebra ofA, andw a bounded linear functional onA. The functionalw is said to commute withBA ifw(AB)=w(BA) for allAA. It is shown that the mapBw (BAB) is a complex measure on the orthocomplemented partially ordered set of all orthogonal projections inB for everyAA if and only ifw commutes with all members ofB. For anyAA, the conditional expectation ofA with respect toB andw is defined and it is shown that this expectation exists for an Abelian separableB ifw commutes with all members ofB. Using Gleason's theorem it is shown thatw commutes withB if and only if the density operator ofw commutes withB.     

The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E ^a and B ^a , as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.     

1H and 13C NMR Spectral Study of Some 2r-Aryl-6c-phenylthian-4-ones,Their 1-Oxides and 1,1-Dioxides

ABSTRACT

Four 2r-aryl-6c-phenylthian-4-ones 1b?1e and their 1-oxides 2b?2e and 1,1-dioxides 3b?3e have been newly synthesized. ¹H and ¹³C NMR spectra have been recorded for all these compounds and 2r,6c-diphenylthian-4-one 1-oxide 2a. ¹³C NMR spectrum has been recorded for the sulfone 3a of 1a. For selected compounds ¹H-¹H COSY, HSQC, HMBC, and NOESY spectra have been recorded. The vicinal proton–proton coupling constants suggest that in all these compounds, the heterocyclic ring adopts chair conformation with equatorial orientations of the aryl and phenyl groups. Proton and carbon chemical shifts suggest that in the sulfoxides, the S=O bond is axial and enhances the J _aa value by some special effect. The S = O bond causes a significant upfield shift even on carbons without hydrogens. Significant solvent shifts also were observed.     

Mechanism for giant electro-optic response of porphyrin J-aggregates in polymer film and aqueous solution

We report the dependence of the polarizability difference Δα on the orientational distribution of porphyrin J-aggregates. For quasi-one-dimensionally oriented aggregates in a polymer film, the red shift in Y ∥ F configuration was about 2 to 3 times smaller than that in Y ∥ F configuration, where Y is the orientational direction of the J-aggregates and F is the applied AC electric field vector. For an aqueous solution where J-aggregates were three-dimensionally oriented, the exciton band showed an electric-field-induced broadening. In addition, a red-shifted signal for two-dimensionally oriented aggregates in the polymer film was reduced by one order of magnitude at 77K compared with that at room temperature. These results were explained reasonably well by the molecular rearrangement model, which was applied to a variety of orientational distributions.     

Role of rational surfaces on fluctuations and transport in the plasma edge of the TJ-II stellarator

It has been shown that transport barriers in toroidal magnetically confined plasmas tend to be linked to regions of unique magnetic topology such as the location of a minimum in the safety factor, rational surfaces or the boundary between closed and open flux surfaces. In the absence ofE×B sheared flows, fluctuations are expected to show maximum amplitude near rational surfaces, and plasma confinement might tend to deteriorate. On the other hand, if the generation ofE×B sheared flows were linked to low order rational surfaces, these would be beneficial for confinement. Experimental evidence ofE×B sheared flows linked to rational surfaces has been obtained in the plasma edge region of the TJ-II stellarator. Presented at the Workshop on the Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June, 2000.     

Computational study of linear and nonlinear optical properties of substituted thiophene imino dyes using long-range corrected hybrid DFT methods

The molecular structures, linear and nonlinear optical properties of a series constituted by four R-substituted thiophene imino dyes, namely A(R?=?SO₂Me), B(R?=?SO₂Ph), C(R?=?NO₂), and D(R?=?C₂(CN)₃) were analysed using CAM-B3LYP, ωB97XD and LC-ωPBE hybrid DFT functionals in combination of the 6-311++G(d,p) standard basis set. The dipole moments, polarisabilities, HOMO-LUMO energy gaps, maximum absorption wavelengths and first hyperpolarisabilities were calculated in the gas phase and the obtained results are in good agreement with experimental NLO activity order A?<?B?<?C. Compared to synthesised dyes A-C, the designed dye D presents a longer maximum absorption wavelength and a lower HOMO-LUMO gap because of the appreciable stabilisation of its LUMO energy. These results were confirmed by the calculation of the total second-order stabilisation energy E⁽²⁾ defined in the context of the NBO population analysis. Consequently, dye D is predicted to exhibit a higher first hyperpolarisability in comparison with dyes A-C. This result can be justified by the enhanced intramolecular charge transfer in dye D due to the stronger electron-withdrawing ability and the cumulative action of the long π-conjugation of the tricyanovinyl moiety. The very high total hyperpolarisability (27 times greater than that of para-nitroaniline) of the designed dye D suggests its promising use in organic NLO devices.     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

Finite Quantum Tomography and Semidefinite Programming

Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, N-qubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981; Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany (1999); Pegg and Barnett Physical Review A 39 (1989) 1665; Barnett and Pegg Journal of Modern Optics 36 (1989) 7; St. Weigert Acta Physica Slov. 4 (1999) 613). PACs index: 03.65.Ud     

Synthesis of Pyrazolopyridine Annulated Heterocycles and Study the Effect of Substituents on Photophysical Properties

Pyrazolo[3,4-b]pyridines having 4-chloro-5-chloroethyl side chain are synthesized by the reaction of 5-aminopyrazole and cyclic β-formylester gave aminopyrazolodihydrofuranone intermediate, which on cyclization in phosphorous oxychloride exclusively converted in to 4-chloro-5-chloroethyl pyrazolo[3,4-b]pyridines 4(a-b) in major amount. The side chain with acetic acid, thiourea and aromatic amines are used to form angular ring leads to formation of tricyclic Furo[2,3-d]pyrazolo[2,3-b]pyridines 5(a-b), pyrazolo[3,4-b]thieno[2,3-d]pyridines 6(a-b) and pyrazolo[3,4-b]pyrrolo[2,3-d]pyridines 7(a-n) respectively. The substituents effect at C₄ position on fluorescence properties of pyrazolopyridines has been studied. Moreover the effect of electron donor and halogen substituents on fluorescence properties of pyrazolopyrrolopyridines 7(a-n) has been investigated along with their fluorescent quantum yield.     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.