Role Of Symmetry Research Articles

Investigating the Phase-Dependent Reactivity of Chlorine Dioxide Using Resonance Raman Spectroscopy

Recent progress in understanding the phase-dependent reactivity of chlorine dioxide (OClO) is outlined. Specifically, resonance Raman intensity analysis (RRIA) and time-resolved resonance Raman (TRRR) studies of OClO photochemistry in solution are presented. The RRIA studies demonstrate that the optically prepared excited-state undergoes significant modification in solution relative to the gas phase. Specifically, the substantial evolution that occurs along the asymmetric-stretch coordinate in the gas phase is restricted in solution. The absence of substantial evolution along the asymmetric-stretch coordinate results in the preservation of ground-state symmetry in the excited state. The role of symmetry in defining the reaction coordinate and the solvent−solute interactions responsible for modification of the excited-state potential energy surface are discussed. TRRR studies performed with pump and probe wavelengths at 390 nm are presented which demonstrate that geminate recombination of the primary photo...

Crystal structure of polymorphous modifications of Tm2S3 and related compounds

The role of symmetry in crystal structure formation is revealed for the polymorphous modifications of Tm2S3 and related compounds Tm15S22, Tm5S7, and Tm8S11 using the procedure of selecting and analyzing close-packed planes with cationic, anionic, and combined motifs. The laws of mutual agreement between the cation and anion matrices determining the size of the unit cells are examined, and relationships between the specific cation volumes and symmetry are traced.

Convergence of Normal Form Transformations: The Role of Symmetries

We discuss the convergence problem for coordinate transformations which take a given vector field into Poincare–Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guarantee convergence of these normalizing transformations in a number of scenarios. As an application, we consider a class of bifurcation problems.

Role of symmetry on interface states in magnetic tunnel junctions

When an electron tunnels from a metal into the barrier in a magnetic tunnel junction it has to cross the interface. Deep in the metal the eigenstates for the electron can be labeled by the point symmetry group of the bulk but around the interface this symmetry is reduced and one has to use linear combinations of the bulk states to form the eigenstates labeled by the irreducible representations of the point symmetry group of the interface. In this way there can be states localized at the interface which control tunneling. The conclusions as to which are the dominant tunneling states are different from that conventionally found.

Herman Feshbach

Herman Feshbach

The pair-functional method. III. The pairing forces.

The theory of the pair-functional ensemble is developed to provide estimates of the pairing forces from experimental X-ray intensities. The statistical mechanics of the grand ensemble leads to a diagram expansion for the forces, in terms of the direct correlation function of the fluid ensemble combined with a series of small higher-order corrections. A simpler treatment, based on a biased Gaussian probability distribution, gives approximate formulae, valid for reflections of any type in all space groups. The role of symmetry is analysed. The entropy of an asymmetrical ensemble can always be increased by averaging it over equivalent positions of the atoms in the true space group, with the result that the atoms naturally tend to adopt the highest symmetry compatible with the data. In a cell with different types of atom, the atoms experience a single force function but they interact with a strength proportional to the products of their scattering factors. Numerical estimates are given for typical cases.

Femtosecond nonlinear optical characterisation of silicon wafers: the role of symmetry

Femtosecond second-harmonic generation from the surface of as-grown 6in silicon wafers is used as a tool for in situ characterisation of Czochralski-grown crystals. Exploiting the symmetry sensitivity of surface SHG, we used a particular two-pulse arrangement, similar to a conventional pump-probe set-up, to obtain non-destructive, in situ information about the location of three commonly known different areas of crystal quality: a central zone of vacancy-rich and an outer zone of interstitial-rich crystal which are separated by a ring of stacking faults. Finally, the applicability of the technique for on-line analysis and control during the growth of different types of gate dielectrics is discussed.

Kramers–Heisenberg and Weisskopf–Wigner descriptions of resonant X-ray Raman scattering

Abstract An overview is presented of the theory of X-ray Raman scattering as originally formulated by Kramers and Heisenberg and by Weisskopf and Wigner. Two particular aspects of the theory are described in some detail; the formation of band profiles and the role of symmetry. These aspects are discussed in connection with recent results for atomic and molecular scatterers obtained in radiative and nonradiative scattering experiments conducted with 2nd and 3rd generation synchrotron radiation sources.

Coulomb coupling and the role of symmetries in quantum-dot arrays for cellular automata

Using a group-theoretical analysis of the symmetries of a quantum dot array, we investigate the role of defects on the energetics of the system and the resulting charge configurations (or polarization of the cell). We find that for the typical four- or five-element geometries proposed, even small asymmetries introduced by defects in the system, or variations in the local electrostatic environment, can give rise to large effects on the polarization of the ground state and the corresponding low-energy excitations. These shifts are likely to produce important effects in the operation of the cellular automata proposed using these quantum dots. In particular, we find that the sensitivity to polarization changes induced by a driver cell decreases dramatically, and the polarization values are no longer fully defined. These effects would both force the use of stronger driving fields, and may also complicate the dynamical behavior of the cellular automata.

Reply to Isgur’s comments on valence QCD

With the goal of understanding the complexity of QCD and the role of symmetry in dynamics, the authors studied a field theory called Valence QCD (VQCD) in which the Z graphs are forbidden so that the Fock space is limited to the valence quarks. The authors calculated nucleon form factors, matrix elements, and hadron masses both with this theory and with quenched QCD on a set of lattices with the same gauge background. Comparing the results of the lattice calculations in these two theories, the authors drew conclusions regarding the SU(6) valence quark model and chiral symmetry. While recognizing the goal of VQCD, Nathan Isgur disagrees on some of the conclusions the authors have drawn. The foremost objection raised in section 2 is to their suggestion that the major part of the hyperfine splittings in baryons is due to Goldstone boson exchange and not one-gluon-exchange (OGE) interactions. The logic of Isgur's objection is that VQCD yields a spectroscopy vastly different from quenched QCD and therefore the structure of the hadrons (to which hyperfine splittings in a quark model are intimately tied) is also suspect so no definite conclusions are possible. To put this into perspective it should be emphasized atmore » the outset that spectroscopy is only one aspect of hadron physics examined in section 1. The authors have studied the axial and scalar couplings of nucleon in terms of F{sub A}/D{sub A} and F{sub S}/D{sub S}, the neutron to proton magnetic moment ratio {mu}n/{mu}p, and various form factors. None of these results reveal any pathologies of hadron structure and turn out to be close to the SU(6) relations, as expected. In fact this is what motivated the study of valence degrees of freedom via VQCD. In section 2 the authors address specific issues related to spectroscopy in VQCD. Isgur also presented more general arguments against the idea of boson exchange as a contributor to hyperfine effects. A cornerstone of his discussion is the unifying aspect of OGE in a quark model picture. The authors believe that it is also natural and economical to identify chiral symmetry as the common origin for much of the physics being discussed here. Therefore in section 3 the authors take the opportunity to sketch out an effective theory that may serve as a framework to interpret the numerical results of VQCD.« less

A Possible Strategy to Defeat Decoherence in Quantum Computation: The Role of Symmetries, Dynamical Algebras, and All That

A Possible Strategy to Defeat Decoherence in Quantum Computation: The Role of Symmetries, Dynamical Algebras, and All That

A Possible Strategy to Defeat Decoherence in Quantum Computation: The Role of Symmetries, Dynamical Algebras, and All That

The question is addressed whether in the frame of Error Avoiding Codes one can devise strategies whereby a universal set of gates can be constructed allowing for arbitrary quantum computation [in its full extent, from input system preparation, through computation implementation, to output measurement] to be completely performed within the code.

Short-time behavior and universality in irreversible models

We discuss the issue of universality in nonequilibrium phase transitions. We present an introduction to the approach of statistical mechanics that is grounded in the construction and analysis of stochastic lattice models. The concept of irreversibility is studied through the analysis of the condition of detailed balance. The role of symmetry and irreversibility on the critical behavior of the nonequilibrium models is examined. We focus on short-time universal behavior of reversible and irreversible models.

Upper critical fields in superconductor–normal metal type superlattices in the Ginzburg–Landau approximation

The application of the Ginzburg–Landau theory to the superconductor–normal metal–superconductor (SNS) superlattices is considered in the case when normal and superconducting layers have the same thickness. The temperature dependences of the transverse and longitudinal upper critical fields are considered. The theoretical curves are compared with the available experimental results on SNS superlattices [C. Coccorese et al., Phys. Rev. B57, 7922 (1998)]. It is shown that the theoretical model can provide a correct interpretation of the experimental results with the minimum number of fitting parameters. The peculiarities of the order parameter behavior at the dimensional crossover in a parallel magnetic field as a function of the sample symmetry axis are discussed, and practical recommendations are given for an experimental verification of the role of symmetry of SNS-type structures.

Role of Symmetry and Dimension in Pseudogap Phenomena

The attractive Hubbard model in d=2 is studied through Monte Carlo simulations at intermediate coupling. There is a crossover temperature $T_X$ where a pseudogap appears with concomitant precursors of Bogoliubov quasiparticles that are not local pairs. The pseudogap in $A(k,\omega)$ occurs in the renormalized classical regime when the correlation length is larger than the direction-dependent thermal de Broglie wave length, $\xi_{th}=\hbar v_{F}(k)/k_{B}T.$ The ratio $T_{X}/T_{c}$ for the pseudogap may be made arbitrarily large when the system is close to a point where the order parameter has SO(n) symmetry with n>2. This is relevant in the context of SO(5) theories of high $T_c$ but has more general applicability.

Characterization of selective adsorption resonances for helium scattering from a highly corrugated surface using quantum wave packet dynamics

We have studied the characteristics of selective adsorption resonances (SAR) for helium scattering from the highly corrugated Xe/Ag(111) surface. A time-dependent quantum mechanical procedure developed previously for the study of resonances in gas-phase molecular collisions was employed. Converged resonance positions, lifetimes, partial widths, and resonance wave functions were obtained for states lying below 20 meV. The zero-order separable description of SAR was found to fail badly for the assignment of the states as well as for their energies and lifetimes, as expected. However, it was found that the separable model improves noticeably for SAR’s with higher energy and for those states localized farther from the surface. More sophisticated separable models have been developed which can improve the agreement with exact results to some degree. The dynamical characteristics of SAR states are analyzed in detail and the role of symmetry is discussed. Energies and lifetimes along the bands of SAR were also generated.

Left-handed DNA Crossovers. Implications for DNA-DNA Recognition and Structural Alterations

The close approach of DNA segments participates in many biological functions including DNA condensation and DNA processing. Previous crystallographic studies have shown that B-DNA self-fitting by mutual groove-backbone interaction produces right-handed DNA crossovers. These structures have opened new perspectives on the role of close DNA-DNA interactions in the architecture and activity the DNA molecule. In the present study, the analysis of the crystal packing of two B-DNA decamer duplexes d(CCIIICCCGG) and d(CCGCCGGCGG) reveals the existence of new modes of DNA crossing. Symmetric left- handed crossovers are produced by mutual fitting of DNA grooves at the crossing point. New sequence patterns contribute to stabilize longitudinal fitting of the sugar-phosphate backbone into the major groove. In addition, the close approach of DNA segments greatly influences the DNA conformation in a sequence dependent manner. This study provides new insights into the role of DNA sequence and structure in DNA-DNA recognition. In providing detailed molecular views of DNA crossovers of opposite chirality, this study can also help to elucidate the role of symmetry and chirality in the recognition of complex DNA structures by protein dimers or tetramers, such as topoisomerase II and recombinase enzymes. These results are discussed in the context of the possible relationships between DNA condensation and DNA processing.

Protonation microequilibrium treatment of polybasic compounds with any possible symmetry

Microequilibrium treatment that has previously been limited to tridentate ligands is generalized to arbitrary number of functional groups in the molecule and the role of symmetry is also investigated. Cumulative microconstant, a new type of equilibrium parameter, is introduced, allowing an equivalent, but more compact mathematical treatment of large microequilibrium systems. The sufficient number of independent pieces of information for the unambiguous determination of all microconstants is deduced. It has been concluded that even if protonation mole fraction for all the basic sites is available, determinability of all the microconstants is rather the exception than the case, without a priori simplifying assumptions. It has been shown that all microconstants can only be determined from protonation mole fractions for molecules of up to three groups. For molecules of four groups and beyond, only specific symmetry and the concomitant simplification of the microequilibrium system make the strict, complete microspeciation feasible. As a case study, the protonation scheme and the complete microspeciation of a tetradentate ligand is analyzed in detail.

Closing the hierarchy of moment equations in nonlinear dynamical systems

The moment equations associated with the evolution of the probability density are known to form an infinite hierarchy of coupled equations in nonlinear dynamical systems. In the present paper a systematic approach for closing this hierarchy is proposed, based on the ansatz that in the long time limit there exist groups of moments varying on the same time scale. The method is applied to a one-dimensional vector field in the presence of noise, and to two prototypes of chaotic behavior. Excellent agreement with numerical results is obtained. Special emphasis is placed on the role of symmetries, and on the origin of the composite oscillations found for certain types of moments in the chaotic systems.

A linearizing transformation for the Korteweg–de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of (nonlinear) transformations to the solution of the linear differential equation. It is also shown that similar concepts apply to the nonlinear Schrödinger equation. The role of symmetry is discussed. Finally, the procedure which is followed in the one-dimensional cases is successfully applied to find special solutions of higher-dimensional nonlinear partial differential equations.