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.     

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.     

Magnetization of an electron plasma by microwave pulses: Faraday induction

It has been argued theoretically that the recently proposed vacuum fieldB ⁽³⁾ is not accompanied by a real electric fieldE ⁽³⁾ . Experimental evidence for this interence is available in the data reported by Deschampset al. [10], using microwave magnetization of an electron plasma set up in helium gas. Faraday induction due toB ⁽³⁾ does not occur in the inert gas and is not observed experimentally in the absence of free electrons. WheneverB ⁽³⁾ interacts with free electrons, however, Faraday induction occurs through a pulse of induced magnetization (i.e., induced orbital electronic angular momentum).     

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.     

Quantum condensates classified in superconductivity with topology in the Minkowski space-time

A substantial problem in the macroscopic theory of pure superconductivity has been left forgotten for a long time since London and London in 1935. An impression survived that the Meissner effect is more substantial than the zero-resistivity. But, the London equation [I], the Newtonian equation of motion, was abandoned, whereas the London equation [II], derived from the Maxwell equations, was postulated. The London equation [II] included the logical gap [ α ] in real time, whereas the London equation [I] has been ignored without even noting the logical gap [ β ] in space. Microscopically, after the publication of F. London's book and the discovery of the isotope effect in 1950, the success of the Bardeen--Cooper--Schrieffer (BCS) theory in 1957 was likely to have finally given the definitive explanation on superconductivity by proving only the London equation [II] that claimed the coherent condensation of Cooper pairs in the momentum space. Since then, these arguments have been regarded to be a standard among various preceding theories. Meanwhile, the London equation [I] has faded away and has been long-forgotten. But we must not abandon the London equation [I], and, rather, retrieve it. We later recognized also that the DC-component of a persistent current can never be determined by using the Fourier transform analysis, because of its singularity at ω?=?0 and q ?=?0 with huge differences of space-time domain. Quite recently, in 2003, we first recognized a proper and harmonious view to simultaneously account for (i) the zero-resistivity in an open system with (i-c) the resultant persistent current in a closed system, and (ii) the perfect diamagnetism at T???0?K in the space-time aspects in terms of the gauge field theory. Here, we further clarify where and how we have lost and found a properly perspective view of the superconductivity. Here, we eliminate two logical gaps [ α ] and [ β ] by using the gauge field theory for further clarifying a position of the previous and present works. We especially classify superconductors with topology which eventually leads us such as (ii-2D) magnetic flux quantization in a ring. By projecting the 3-dimensional BCS-theory with the concept of ‘coherence’ among an enormous number of Bosons like Cooper pairs onto the (1?+?3)-dimensional Minkowski space-time [β?=?(v/c)?=?0], we clarify responses of the ground state Ψ _macro at T???0?K in a set of the basic equations, for (i) the zero-resistivity, [E _K ???qφ( R )]?=?0 at ω?=?0 and (ii) the perfect diamagnetism [?K ???qA ( R )]?=?0 at q ?=?0 as an inevitable consequence at the gauge fields in the proper theory of superconductivity.     

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G _D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G _D(r,r′, N) = G ₀(r,r′, N) - G ₀(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Primitive ideals of C q [SL(3)]

The primitive ideals of the Hopf algebraC _q [SL(3)] are classified. In particular it is shown that the orbits in PrimC _q [SL(3)] under the action of the representation groupH C ^*×C ^* are parameterized naturally byW×W, whereW is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals ofC _q [SL(3)] and symplectic leaves of the associated Poisson algebraic groupSL(3,C).Partially supported by a grant from the N.S.A.     

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.     

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.     

Stable potentials I

We discuss a conjecture of Ruelle concerningstable potentials on a group. For the groupsZ ₂,Z ₃, ₄, andZ ₆ any stable potential can be written as the sum of a non-negative function and a function of non-negative type. This is not true for the groupsZ _k (k odd, 5). For the Euclidean groupR ^v the question is open.Supported by NSF GP 7946.     

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.     

Proton and Carbon‐13 NMR Studies of the Phencyclone Adducts of Medium Alkyl Chain‐Length N‐n‐Alkylmaleimides. Hindered Rotations and Magnetic Anisotropic Effects. Ab initio Calculations for Optimized Structures

Abstract

The Diels–Alder adducts, 3a–e, of phencyclone, 1, have been prepared from a series of N‐n‐alkylmaleimides, 2, with medium chain‐length n‐alkyl groups. The maleimides were obtained by cyclodehydration of the N‐n‐alkylmaleamic acids, 4, formed from reaction of maleic anhydride with the corresponding n‐alkylamines. The five adducts prepared included derivatives from n‐heptyl, 3a; n‐octyl, 3b; n‐nonyl, 3c; n‐decyl, 3d; and n‐dodecyl, 3e. The NMR spectra of the adducts were studied in CDCl₃ at ambient temperatures at 300 MHz for proton and 75 MHz for carbon‐13, with full proton assignments achieved by high‐resolution COSY45 spectra for the aryl and the alkyl regions. Slow exchange limit (SEL) spectra were observed for both ¹H and ¹³C spectra showing slow rotation on the NMR timescales of the unsubstituted bridgehead phenyl groups. Endo Diels–Alder adduct stereochemistry was supported by striking magnetic anisotropic shielding effects in the ¹H spectra of the alkyl groups, with the NCH₂ CH ₂ signal of each adduct appearing upfield of tetramethylsilane (TMS) at ca. ?0.32 ppm. Proton NMR spectra for precursor maleamic acids and maleimides are reported, with some solvent effects found (CDCl₃ vs. d ₆‐acetone) for the carbon‐bound HC?CH protons of 4. Ab initio molecular modeling calculations at the Hartree‐Fock level using the 6‐31G* basis set have been performed for two key conformers of the phencyclone adduct of N‐n‐octylmaleimide, as a representative structure for these hindered adducts, to estimate geometric parameters for the adduct. A syn conformer, with the alkyl chain directed into the adduct cavity, was found to be ca. 0.23 kcal/mol lower energy than an anti conformer (in which the alkyl chain was directed away from the phenanthrenoid moiety).     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

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.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

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.     

Realizations of causal manifolds by quantum fields

Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e., by the homogenous spacesD(n)=GL(C _R ⁿ )/U(n) withn=1 for mechanics andn=2 for relativistic fields. The rankn gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e., two characteristic masses in the relativistic case. ‘Canonical’ field theories with the familiar divergencies are inappropriate realizations of the real 4-dimensional causal manifoldD(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable—in addition to representations with eigenvectors (states, particle), they incorporate principal vectors without a particle (eigenvector) basis as exemplified by the Coulomb field. In theorthogonal andunitary groupsO(N ₊,N ₋), respectively, thepositive orthogonal and unitary ones areO(N) andU(N), respectively.     

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.     

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.