Showing papers in "International Journal of Modern Physics B in 1997"

The Theory of Boundary Critical Phenomena

Abstract: An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.

Composite fermions in the Hilbert space of the lowest electronic Landau level

Abstract: Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

Two Dimensional Graphite Films on Metals and Their Intercalation

Abstract: Two-dimensional graphite films (2DGF) on solids are wonderful objects, real nature-made two-dimensional crystals. Formation on active metal surface of a 2DGF with extremely high adsorption, chemical and catalytic passivity leads to a number of staggering effects. The review is devoted to 2DGF on metals and their nature, structure, modes of formation and physico chemical properties. A nature of absorption bond between 2DGF and metal substrate is discussed in details. A special attention is paid to intercalation of 2DGF — a process when foreign atoms and even molecules (fullerenes C60 molecules) spontaneously penetrate between graphite film and metal substrate. Modes of intercalation are discussed and a mechanism of it, based on thermal movements of carbon atoms of a graphite layer, proposed earlier, is used for explanation of experimental data. A new, practically important effect-superefficient diffusion of alkaline atoms into transition metal bulk, covered by 2DGF, is reported.

Exact results for highly correlated electron systems in one dimension

Abstract: One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-Tc superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh-2(r) potentials, are briefly reviewed.

Lattice-gas theory of collective diffusion in adsorbed layers

Abstract: A general theory for collective diffusion in interacting lattice-gas models is presented. The theory is based on the description of the kinetics in the lattice gas by a master equation. A formal solution of the master equation is obtained using the projection-operator technique, which gives an expression for the relevant correlation functions in terms of continued fractions. In particular, an expression for the collective dynamic structure factor Sc is derived. The collective diffusion coefficient Dc is obtained from Sc by the Kubo hydrodynamic limit. If memory effects are neglected (Darken approximation), it turns out that Dc can be expressed as the ratio of the average jump rate and of the zero-wavevector static structure factor S(0). The latter is directly proportional to the isothermal compressibility of the system, whereas is expressed in terms of the multisite static correlation functions gn. The theory is applied to two-dimensional lattice systems as models of adsorbates on crystal surfaces. Three examples are considered. First, the case of nearest-neighbour interactions on a square lattice (both repulsive and attractive). Here, the theoretical results for Dc are compared to those of Monte Carlo simulations. Second, a model with repulsive interactions on the triangular lattice. This model is applied to NH3 adsorbed on Re(0001) and the calculations are compared to experimental data. Third, a model for oxygen on W(110). In this case, the complete dynamic structure factor is calculated and the width of the quasi-elastic peak is studied. In the third example the gn are calculated by means of the discretized version of a classical equation for the structure of liquids (the Crossover Integral Equation), whereas in the other examples they are computed using the Cluster Variation Method.

Physics of the extended neuron

Abstract: We review recent work concerning the effects of dendritic structure on single neuron response and the dynamics of neural populations. We highlight a number of concepts and techniques from physics useful in studying the behaviour of the spatially extended neuron. First we show how the single neuron Green's function, which incorporates details concerning the geometry of the dendritic tree, can be determined using the theory of random walks. We then exploit the formal analogy between a neuron with dendritic structure and the tight-binding model of excitations on a disordered lattice to analyse various Dyson-like equations arising from the modelling of synaptic inputs and random synaptic background activity. Finally, we formulate the dynamics of interacting populations of spatially extended neurons in terms of a set of Volterra integro-differential equations whose kernels are the single neuron Green's functions. Linear stability analysis and bifurcation theory are then used to investigate two particular aspects of population dynamics (i) pattern formation in a strongly coupled network of analog neurons and (ii) phase-synchronization in a weakly coupled network of integrate-and-fire neurons.

Discrete Hirota's Equation in Quantum Integrable Models

Abstract: The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota's bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter's T-Q relation.

Classical trajectory methods for polyatomic molecules

Abstract: Monte Carlo classical trajectory methods for simulating intramolecular dynamics, including chemical reactions, in large polyatomic molecules are described. Methods for performing calculations corresponding to various kinds of experiments are discussed. Some approaches for formulating potential-energy surfaces are described.

Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

Abstract: It is shown that for quantum systems the vector field associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schrodinger and Heisenberg picture. We illustrate these ambiguities in terms of simple examples.

Knot Theory and Statistical Mechanics

Abstract: This paper gives a self-contained exposition of the basic structure of quantum link invariants as state summations for a vacuum-vacuum scattering amplitude. Models of Vaughan Jones are expressed in this context. A simple proof is given that an important subset of these invariants are built from Vassiliev invariants of finite type.

The Heisenberg Chain as a Dynamical Model for Protein Synthesis - Some Theoretical and Experimental Results

Abstract: The integrable Heisenberg quantum chain with certain non-diagonal boundary fields is the generator of a Markov process known as asymmetric exclusion process with open boundary conditions. This is a driven lattice gas where particles hop randomly along a one-dimensional chain and are injected and absorbed at the boundaries. This model has been suggested in 1968 by MacDonald, Gibbs and Pipkin as a model for the kinetics of protein synthesis on nucleic acid templates. The exact solution of the steady state of the system (corresponding to the exact ground state of the Heisenberg chain) which was obtained recently is shown to be in qualitative agreement with experimental data. The exact solution supports some of the original conclusions drawn from a mean field treatment by MacDonald et al. but gives deeper insight into one important aspect.

Star-triangle and star-star relations in statistical mechanics

Abstract: The homogeneous three-layer Zamolodchikov model is equivalent to a four-state model on the checkerboard lattice which closely resembles the four-state critical Potts model, but with some of its Boltzmann weights negated. Here we show that it satisfies a "star-to-reverse-star" (or simply star-star) relation, even though we know of no star-triangle relation for this model. For any nearest-neighbour checkerboard model, we show that this star-star relation is sufficient to ensure that the decimated model (where half the spins have been summed over) satisfies a "twisted" Yang-Baxter relation. This ensures that the transfer matrices of the original model commute in pairs, which is an adequate condition for "solvability".

Statistical Description of the Turbulent Mixing of Scalar Fields

Abstract: A formulation in terms of probability density function (PDF) transport equations is presented for inert and reactive scalar fields undergoing turbulen mixing. The PDF methodology is related to the classical moment equations. The hierarchy of PDF transport equations resembles the BBGKY equations in statistical mechanics. Closure hypothesis, approximating the molecular mixing term, are described and their predictions for simple systems are compared with direct numerical simulations (DNS). Solution algorithms in terms of Monte Carlo particles are also discussed.

Moduli Space of Flat Connections as a Poisson Manifold

Abstract: In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

Tight-Binding Model for DNA Double Chains: Metal–Insulator Transition Due to the Formation of a Double Strand of DNA

Abstract: A tight-binding model is formulated for the calculation of the electronic structure of a double strand of deoxyribonucleic acid (DNA). The theory is applied to DNA with a particular structure such as the ladder and decorated ladder structures. It is found that there is a novel type of metal–insulator transitions due to the hopping anisotropy of the system. A metal-semimetal-semiconductor transition is found in the former and an effective semiconductor-metal transition at finite temperature in the latter, as the effect of base paring between two strands of DNA is increased. The latter mechanism may be responsible for explaining the Meade and Kayyem's recent observation.

Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment

Abstract: We consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with a surrounding spin environment, such as nuclear spins. Our aim is to give a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then study the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a macroscopic spin, using exact diagonalization techniques. We find that the low energy central spin effective Hamiltonian gives very accurate results (with increasing accuracy for large S), provided the typical coupling energies between the giant spin and the microscopic spins are not too large, and provided temperature and external field are sufficiently low. The essential limitation to the applicability of the low-energy effective Hamiltonian is just the semiclassical WKB approximation itself, which inevitably fails for very small S. Our results thus justify previous use of this effective Hamiltonian in calculations of the effects of nuclear spins on the dynamics of nanomagnetic systems.

Raman Scattering in Cuprate Superconductors

Abstract: A theory for electronic Raman scattering in the cuprate superconductors is presented with a specific emphasis on the polarization dependence of the spectra which can infer the symmetry of the energy gap. Signatures of the effects of disorder on the low frequency and low temperature behavior of the Raman spectra for different symmetry channels provide detailed information about the magnitude and the phase of the energy gap. Properties of the theory for finite T will be discussed and compared to recent data concerning the doping dependence of the Raman spectra in cuprate superconductors, and remaining questions will be addressed.

The Many Faces of the Chiral Potts Model

Abstract: In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star–triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic hypergeometric functions at root of unity, and possible applications.

Mode fluctuations as fingerprints of chaotic and non-chaotic systems

Abstract: The mode-fluctuation distribution P(W) is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the E(k,L) functions being the probability of finding k energy levels in a randomly chosen interval of length L, and the distribution of n(L), where n(L) is the number of levels in such an interval, and their cumulants ck(L). It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants Ck, k ≥ 3, implies a Gaussian behaviour of P(W), which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of P(W). For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution P(W).

A higher-level Bailey lemma

Abstract: We propose a generalization of Bailey's lemma, useful for proving q-series identities. As an application, generalizations of Euler's identity, the Rogers–Ramanujan identities, and the Andrews–Gordon identities are derived. This generalized Bailey lemma also allows one to derive the branching functions of higher-level cosets.

Atomic number scaling of the nickel-like soft x-ray lasers

Abstract: We report the review of the experimental results obtained at the Institute of Laser Engineering, Osaka University, of the soft X-ray lasing in various Ni-like ions whose atomic numbers range from 47(Ag) to 66(Dy). The lasing wavelengths are between 14 nm and 5 nm. X-ray lasing in these materials were obtained when the plasma profiles were properly controlled in time and space by irradiation of curved slab targets with multiple laser pulses. We also describe the original work of the atomic physics calculations which provide the transition energies, transition probabilities and other atomic constants for Ni-like ion species whose atomic numbers range from 36 to 92 calculated with GRASP code (multi-configuration Dirac Fock code) and YODA code (relativistic distorted wave code). Based on these atomic constants, we have calculated the kinetics of the population inversion with a simplified rate equation model in conjunction with a one-dimensional hydrodynamic code to find out the desired pumping conditions. We ...

Theoretical Models for the Optical Properties of Clusters and Nanostructures

Abstract: Applications of the Time Dependent Density Functional Formalism to calculate the response of metallic and semiconducting nanostructures to static and time-dependent electric fields in the linear regime are reviewed. The paper focuses on the presentation of models of increasing sophistication for the cluster structure, ranging from the simple spherical jellium model to a fully ab initio description of the ionic structure. Simple models explain the main features of the spectrum. For instance the existence of a pronounced surface plasmon resonance in the absorption spectrum of alkali metal clusters, and its redshift with respect to the classical Mie resonance are well explained within the framework of the simple jellium model. However, the detailed understanding of the experimental optical spectra can only be achieved by complementary ab initio calculations. In fact, the optical spectrum appears to carry detailed information on the cluster structure. Details of the new theories and computational schemes to deal with the optical properties of complex systems are also presented: linear and nonlinear susceptibilities, quasiparticle excitations, core-polarization. These methods are of relevance in the physics of nanostructures and nanoscale technology.

Band Degeneracy and the Mott Transition: Dynamical Mean Field Study

Abstract: We investigate the Mott transition in infinite dimensions in the orbitally degenerate Hubbard model. We find that the qualitative features of the Mott transition found in the one-band model are also present in the orbitally degenerate case. Surprisingly, the quantitative aspects of the density driven Mott transition around density one are not very sensitive to orbital degeneracy, justifying the quantitative success of the one-band model which was previously applied to orbitally degenerate systems. We contrast this with quantities that have a sizeable dependence on the orbital degeneracy and comment on the role of the intra-atomic exchange J.

Boundary Weights for Temperley–Lieb and Dilute Temperley–Lieb Models

Abstract: We use a direct approach to obtain the general diagonal solutions of the boundary Yang–Baxter equation for the Temperley–Lieb and dilute Temperley–Lieb models and their elliptic extensions.

An Analytical Approach to the Fredrickson–Andersen Model in One Dimension

Abstract: The dynamics of a modified kinetic Ising model usual noted as Fredrickson–Andersen model (FAM) is formulated in terms of Pauli-operators using a Fock-space representation of the Master equation. The method is appropriate to study the cooperativity by including topological restrictions explicitly. Following the concept of the FAM the block distribution function of m+1 adjacent liquid-like (spin down) or solid-like (spin up) regions is analysed in one dimension. The hierarchy of evolution equations for those functions can be solved exactly at zero temperature leading to a double exponential decay and to a nonergodic behaviour. In case of nonzero temperatures, we are able to solve this set of infinite nonlinear first order differential equations only after a well motivated decoupling procedure. It results an implicit solution for the averaged density. For short time scale the system behaves like an ordinary Ising model with exponential relaxation. In the long time limit, we observe already in lowest order a ...

Bethe ansatz and classical Hirota equation

Abstract: We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up. namely, the eigenvalues of the quantum transfer matrix and the scattering S-matrix itself are identified with a certain τ-functions of the discrete Liouville equation. The Bethe ansatz equations are obtained as dynamics of zeros. For comparison we also present the Bethe ansatz equations for elliptic solutions of the classical discrete Sine-Gordon equation. The paper is based on the recent study of classical integrable structures in quantum integrable systems.1

A non-critical string (Liouville) approach to brain microtubules: state vector reduction, memory coding and capacity

Abstract: Microtubule (MT) networks, subneural paracrystalline cytoskeletal structures, seem to play a fundamental role in the neurons. The authors cast here the complicated MT dynamics in the form of a (1 + 1)-dimensional noncritical string theory, thus enabling them to provide a consistent quantum treatment of MTs, including environmental friction effects. They suggest, thus, that the MTs are the microsites, in the brain, for the emergence of stable, macroscopic quantum coherent states, identifiable with the preconscious states. Quantum space-time effects, as described by noncritical string theory, trigger than an organized collapse of the coherent states down to a specific or conscious state. The whole process they estimate to take {Omicron}(1 sec), in excellent agreement with a plethora of experimental/observational findings. The microscopic arrow of time, endemic in noncritical string theory, and apparent here in the self-collapse process, provides a satisfactory and simple resolution to the age-old problem of how the, central to one`s feelings of awareness, sensation of the progression of time is generated. In addition, the complete integrability of the stringy model for MT the authors advocate in this work proves sufficient in providing a satisfactory solution to memory coding and capacity. Such features might turn out to be importantmore » for a model of the brain as a quantum computer.« less

Magnetization Profile in the D= 2 Semi-Infinite Ising Model and Crossover Between Ordinary and Normal Transition

Abstract: We study the two-dimensional semi-infinite Ising model with a free surface at or near bulk criticality. Special attention is paid to the influence of a boundary magnetic field h1 on the surface-near regime and the crossover between the fixed points at h1=0 and h1=∞. Near the surface, a smallh1 causes a steeply increasing magnetization m(z)~z3/8 log z as the distance z increases away from the surface. By means of a phenomenological scaling analysis, this phenomenon can be related to the well-known logarithmic dependence of the surface magnetization m1 on h1. Our analysis provides a deeper understanding of the existing exact results on m(z) and relates the short-distance phenomena in d=2 to those in higher dimensions. Both the results of the scaling analysis and the exact analytic profiles are corroborated by Monte Carlo simulations.

Angular-resolved vleed from o-cu(001) : valence bands, chemical bonds, potential barrier, and energy states

Abstract: It is shown that the VLEED, furnished with appropriate modelling approaches, is able to reveal comprehensive information about the details of a surface. Constructing Brillouin zones from the critical positions on the angular-resolved VLEED spectra yields information about valence bands and in-plane reconstruction of the O-Cu(001) surface. Decoding the fine-structure features with new models [J. Phys. Chem. Solids58 903 (1997) and J. Phys.: Condens. Matt., C9, 5823 (1997)] rewards us with consistent understanding of the bond formation and its consequences. It is interpreted that the bond forming results in the dislocation of surface atoms, the variation of energy states, the nonuniformity and anisotropy of the potential barrier, and the reduction in both work function and inner potential of the surface.

Damping of Oscillations in Layer-by-Layer Growth

Abstract: We present a theory for the damping of layer-by-layer growth oscillations in molecular beam epitaxy. The surface becomes rough on distances larger than a layer coherence length which is substantially larger than the diffusion length. The damping time can be calculated by a comparison of the competing roughening and smoothening mechanisms. The dependence on the growth conditions, temperature and deposition rate, is characterized to be a power law. The theoretical results are confirmed by computer simulations.