On the Structure of KMS States of Disordered Systems

We study the set of KMS states of spin systems with random interactions. This is done in the framework of operator algebras by investigating Connes and Borchers –invariants of W*–dynamical systems. In the case of KMS states exhibiting a property of invariance with respect to the spatial translations, some interesting properties emerge naturally. Such a situation covers KMS states obtained by infinite–volume limits of finite–volume Gibbs states, that is the quenched disorder. This analysis can be considered as a step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses, and its connection with the breakdown of the symmetry for replicas.     

Quantum system in a strong electromagnetic field

We have used a projection operator technic to derive approximate analytical expressions for the quasi-energies and quasi-energy states of a multilevel system in a strong electromagnetic field.Translated from Izvestiya Vyssh'ikh Uchebnykh Zavednii, Fizika, No. 3, pp. 84–89, March, 1978.We thank R. Galimzyanov and E. Gandyl' for carrying out the machine calculation.     

Normalized Ricci Flow on Riemann Surfaces and Determinant of Laplacian

In this letter, we give a simple proof of the fact that the determinant of Laplace operator in a smooth metric over compact Riemann surfaces of an arbitrary genus g monotonously grows under the normalized Ricci flow. Together with results of Hamilton that under the action of the normalized Ricci flow a smooth metric tends asymptotically to the metric of constant curvature, this leads to a simple proof of the Osgood–Phillips–Sarnak theorem stating that within the class of smooth metrics with fixed conformal class and fixed volume the determinant of the Laplace operator is maximal on the metric of constant curvatute.Mathematical Subject Classifications (2000). 58J52, 53C44.     

Effect of PbCl2 addition on structure, OH− content, and upconversion luminescence in Yb3+/Er3+-codoped germanate glasses

Yb³⁺/Er³⁺-codoped oxychloride germanate glasses have been synthesized by a conventional melting and quenching method. Structural properties were obtained based on Raman-spectra investigation, indicating that PbCl₂ plays an important role in the formation of the glass network and has an important influence on the phonon density and the maximum phonon energy. The Judd–Ofelt intensity parameters and quantum efficiencies were calculated based on the Judd–Ofelt theory and lifetime measurements. The enhanced upconversion luminescence intensity of Er³⁺ with increasing PbCl₂ content could not be explained only by the maximum phonon-energy change of the host glasses. For the first time, the effect of PbCl₂ addition on phonon density, OH^– content, and upconversion luminescence in oxychloride glasses has been discussed and evaluated. The results show that the effect of phonon density and OH^– content on upconversion luminescence in oxychloride glasses is much stronger than that of the decrease of the maximum phonon energy. The possible upconversion luminescence mechanisms have also been estimated and are discussed.     

Iterative calculation, manufacture and investigation of DOE forming unimodal complex distribution

We present results of iterative calculation, manufacture and experimental as well as theoretical investigations of a novel diffractive optical element (DOE) which transforms a Gaussian TEM₀₀ input beam into a unimodal Gauss–Hermite (1, 0) complex distribution. The iterative calculation procedure is based on the application of the method of generalized projections. The projection operator onto a set of modal functions is implemented through partition of the focal plane into a ‘useful’ and an ‘auxiliary’ domain. This element is manufactured as a 16 level surface profile by (variable dose) electron-beam direct-writing into a PMMA resist film, and a subsequent development procedure of the resist. The final element consists of a fused-silica substrate coated with the structured PMMA film. Both computational and experimental results are presented and demonstrate a good conformity with each other. The achieved results show good prospects of such an approach for the formation of unimodal distributions.     

Dirac–Kähler Equation

Tensor, matrix, and quaternion formulations of Dirac–Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau–Duffin–Kemmer matrix product is considered. We show that the symmetry group of the Dirac–Kähler tensor fields for charged particles is SO(4, 2). The conservation currents corresponding this symmetry are constructed. We analyze transformations of the Lorentz group and quaternion fields. Supersymmetry of the Dirac–Kähler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac–Kähler fields where the gauge group is the noncompact group under consideration.     

Computation of multiphase systems with phase field models

Phase field models offer a systematic physical approach for investigating complex multiphase systems behaviors such as near-critical interfacial phenomena, phase separation under shear, and microstructure evolution during solidification. However, because interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations require resolution of very thin layers to capture the physics of the problems studied. This demands robust numerical methods that can efficiently achieve high resolution and accuracy, especially in three dimensions. We present here an accurate and efficient numerical method to solve the coupled Cahn–Hilliard/Navier–Stokes system, known as Model H, that constitutes a phase field model for density-matched binary fluids with variable mobility and viscosity. The numerical method is a time-split scheme that combines a novel semi-implicit discretization for the convective Cahn–Hilliard equation with an innovative application of high-resolution schemes employed for direct numerical simulations of turbulence. This new semi-implicit discretization is simple but effective since it removes the stability constraint due to the nonlinearity of the Cahn–Hilliard equation at the same cost as that of an explicit scheme. It is derived from a discretization used for diffusive problems that we further enhance to efficiently solve flow problems with variable mobility and viscosity. Moreover, we solve the Navier–Stokes equations with a robust time-discretization of the projection method that guarantees better stability properties than those for Crank–Nicolson-based projection methods. For channel geometries, the method uses a spectral discretization in the streamwise and spanwise directions and a combination of spectral and high order compact finite difference discretizations in the wall normal direction. The capabilities of the method are demonstrated with several examples including phase separation with, and without, shear in two and three dimensions. The method effectively resolves interfacial layers of as few as three mesh points. The numerical examples show agreement with analytical solutions and scaling laws, where available, and the 3D simulations, in the presence of shear, reveal rich and complex structures, including strings.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

Wave Functions for Arbitrary Operator Ordering in the de Sitter Minisuperspace Approximation

We derive exact series solutions for the Wheeler–DeWitt equation corresponding to a spatially closed Friedmann–Robertson–Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. The resulting wave functions are those relevant to the approximation which has been widely used in two-dimensional minisuperspace models with an inflationary scalar field for the purpose of predicting the period of inflation which results from competing boundary condition proposals for the wave function of the universe. The problem that Vilenkin's tunneling wave function is not normalizable for general operator orderings, is shown to persist for other values of the spatial curvature, and when additional matter degrees of freedom such as radiation are included.     

A Spin-Shift Operator of the Multi-particle Ruijsenaars–Schneider Hamiltonian

We obtain a spin-shift operator for the multi-particle trigonometric Ruijsenaars–Schneider Hamiltonian. This result is a generalization of the argument in Phys. Lett. B 375 (1996), 89–97, where the integrability of the one-particle Ruijsenaars–Schneider system is shown by using the existence of a spin-shift operator.     

De Morgan Property for Effect Algebras of von Neumann Algebras

It is shown that the unit interval of a von Neumann algebra is a Sum Brouwer–Zadeh algebra when equipped with another unary operation sending each element to the complement of its range projection. The main result of this Letter says that a von Neumann algebra is finite if and only if the corresponding Brouwer–Zadeh structure is de Morgan or, equivalently, if the range projection map preserves infima in the unit interval. This provides a new characterization of finiteness in the Murray–von Neumann structure theory of von Neumann algebras in terms of Brouwer–Zadeh structures.     

Fluorescence of Acridine Orange in inorganic glass matrices

Steady-state, time-resolved and polarization-resolved fluorescence studies of glasses doped with acridine orange with concentrations near 10^–3 M/L are reported. It was found that at this concentration a noticeable part of dye molecules exists in the form of dimers. By means of a polarization-resolved spectroscopic technique the structure of dimers was found to be consistent with the simple exciton theory.     

Two-dimensional thermofield bosonization

The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion–Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi–Dirac to Bose–Einstein statistics is realized.     

Anisotropic relaxation and motion of half-integer quadrupole nuclei studied by central transition nuclear magnetic resonance spectroscopy

An efficient theoretical formalism and advanced experimental methods are presented for studying the effects of anisotropic molecular motion and relaxation on solid-state central transition NMR spectra of half-integer quadrupole nuclei. The theoretical formalism is based on density operator algebra and involves the stochastic Liouville–von Neumann equation. In this approach the nuclear spin interactions are represented by the Hamiltonian while the motion is described by a discrete stochastic operator. The nuclear spin interactions fluctuate randomly in the presence of molecular motion. These fluctuations may stimulate the relaxation of the system and are represented by a discrete relaxation operator. This is derived from second-order perturbation theory and involves the spectral densities of the system. Although the relaxation operator is valid only for small time intervals it may be used recursively to obtain the density operator at any time. The spectral densities are allowed to be explicitly time dependent making the approach valid for all motional regimes. The formalism has been applied to simulate partially relaxed central transition ¹⁷O NMR spectra of representative model systems. The results have revealed that partially relaxed central transition lineshapes are defined not only by the nuclear spin interactions but also by anisotropic motion and relaxation. This has formed the basis for the development of central transition spin-echo and inversion-recovery NMR experiments for investigating molecular motion in solids. As an example we have acquired central transition spin-echo and inversion-recovery ¹⁷O NMR spectra of polycrystalline cristobalite (SiO₂) at temperatures both below and above the α–β phase transition. It is found that the oxygen atoms exhibit slow motion in α-cristobalite. This motion has no significant effects on the fully relaxed lineshapes but may be monitored by studying the partially relaxed spectra. The α–β phase transition is characterized by structural and motional changes involving a slight increase in the Si–O–Si bond angle and a substantial increase in the mobility of the oxygen atoms. The increase in the Si–O–Si angle is supported by the results of ¹⁷O and ²⁹Si NMR spectroscopy. The oxygen motion is shown to be orders of magnitude faster in β-cristobalite resulting in much faster relaxation and characteristic lineshapes. The measured oscillation frequencies are consistent with the rigid unit mode model. This shows that solid-state NMR and lattice dynamics simulations agree and may be used in combination to provide more detailed models of solid materials.     

Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes

We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan–Paton factor is given by a trace over elements of Poincaré algebra and Iwahori–Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan–Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.     

Oxidation state of iron in mantle-derived magmas of the Icelandic rift zone

Olivine tholeiites are mantle-derived magmas that are formed by partial melting of their deep sources and which have equilibrated with mineral assemblages at slightly different subcrustal pressure-temperature conditions prior to eruption. The minimum depth of the pre-eruptive reservoirs of these magmas is in the order of 10–15 km and their liquidus temperatures fall within the range of 1180–1240 C. Three types of primitive olivine tholeiites are exposed along the rift zones in Iceland. In the present study, the ferric/ferrous ratios of natural glasses (pillow crusts) of the three types of olivine tholeiites were obtained by Mössbauer spectrometry. This technique is particularly well suited for the analysis of high-Mg glasses since it resolves microcrystallites of olivine which contribute to ferrous iron in chemical analysis. All results fall within 10–15% Fe(III). At the liquidus temperature of these glasses, this ferric/ferrous ratio corresponds to fugacity close to the fayalite-magnetite-quartz-oxygen (FMQ) buffer with an uncertainty of less than one log unit in fO₂. This result confirms that there is no significant difference in the oxidation state of the three magma types.     

Formation of embedded patterns in glasses using femtosecond irradiation

Channel formation in glasses is demonstrated and discussed. Photosensitive glass (Foturan) was microstructured using femtosecond irradiation at 800 nm and 400 nm wavelengths, with subsequent thermal annealing, and HF etching of a lithium-silicate phase formed by exposure-annealing. It was found that there is a significant difference in the volume of lithium-silicate when the exposure was made with and without optical breakdown. Channels with a minimum cross section of approximately 10 m were achieved.In silicate glasses, the optically induced dielectric breakdown was used for the recording of channel patterns. The highest wet etching rate in a HF based solution was observed when the irradiance corresponded to the 2.5–3.0 thresholds of dielectric breakdown and the adjacent pulses were overlapping by more than 50% of the diameter of the focussed beam. Under these conditions, the formation of a void inside the glass was confirmed by optical observation of single shot damage under a microscope. The mechanism of selective wet etching in silicate glasses is discussed in terms of the stress corrosion effect, which explains crack propagation in glasses via the reaction of stretched Si–O–Si bonds at the tip of a crack with water, resulting in SiOH formation. It is shown that intra-connection of voxels was the key factor to achieve etching of high aspect ratio patterns in silica glass. PACS 42.70.Ce; 81.05.Kf; 82.50.Pt; 87.80.Mj     

On non-linear non-equilibrium statistical mechanics

The exact equations of motion for slow variables, which characterize a macroscopic system far from equilibrium, are derived with the help of a new time-dependent projection operator. The present formalism is a natural extension of Mori's approach to the non-linear region far from equilibrium, or of Kawasaki-Gunton's approach to quantal systems.     

Optimally chosen Nakajima–Zwanzig master equation for mean field approximation

We define an ensemble of projection operators, each of which has an exact associated Nakajima–Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields a completely determined inhomogeneous master equation for every projection operator. A specific projection operator is then chosen so that the master equation optimally matches an abstract mathematical form which preserves positivity, complete positivity, and correctly equilibrates. We study a nitrogen vacancy center in diamond interacting with ¹³C impurities to illustrate the method.     

Approximate diagonalization of the energy operator of a system of interacting particles

The present work considers a method of diagonalization of the energy operator of a system of valence electrons in a simple model of a semiconductor, and in a simple model of a metal. The results obtained are used in the theory of superconductivity and in the theory of superfluidity.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 43–47, December, 1971.