Showing papers in "Advances in Physics in 2003"

Glassy dynamics of kinetically constrained models

Abstract: We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying ‘equilibrium glass transition’. After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, ageing and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.

Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis

Abstract: We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ g¯/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms...

Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr2RuO4

Abstract: In this paper, we review a large set of experimental data acquired over the past decade by several groups, and demonstrate how it can be used to construct a detailed picture of the low-temperature metallic state of the unconventional superconductor Sr2RuO4. We show how the normal state properties can be consistently and quantitatively explained in terms of Landau quasi-particles moving on a quasi-two-dimensional Fermi surface. Besides presenting our full and extensive data sets, we explain the details of some novel data analysis tools that can be used within the general context of quasi-two-dimensional metals. We then use the experimental Fermi surface and band dispersion to reassess several issues relevant to the unconventional superconductivity in Sr2RuO4, such as the spin-fluctuation spectrum, quasi-particle renormalization, interlayer dispersion and pressure dependence.

The loop algorithm

Abstract: A review of the loop algorithm , its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a quantum Monte Carlo procedure that employs non-local changes of worldline configurations, determined by local stochastic decisions. It is based on a formulation of quantum models of any dimension in an extended ensemble of worldlines and graphs, and is related to Swendsen-Wang algorithms. It can be represented directly on an operator level, both with a continuous imaginary time path integral and with the stochastic series expansion. It overcomes many of the difficulties of traditional worldline simulations. Autocorrelations are reduced by orders of magnitude. Grand-canonical ensembles, off-diagonal operators, and variance reduced estimators are accessible. In some cases, infinite systems can be simulated. For a restricted class of models, the fermion sign problem can be overcome. Transverse magnetic fields are handled efficiently, in contrast to strong diagonal fiel...

Description of far-from-equilibrium processes by mean-field lattice gas models

Abstract: Mean-field kinetic equations are a valuable tool to study the atomic dynamics and spin dynamics of simple lattice gas and Ising models. They can be derived from the microscopic master equation of the system and contain analytical expressions for kinetic coefficients and thermodynamic quantities which are usually introduced phenomenologically. We review several methods to obtain such equations, and discuss applications to the dynamics of order–disorder transitions, spinodal decomposition, and dendritic growth in the isothermal or chemical model. In the case of dendritic growth we show that the mean-field kinetic equations are equivalent to standard continuum equations for this problem and derive expressions for macroscopic quantities, e.g. the surface tension and kinetic coefficients, as functions of the microscopic order parameters. In spinodal decomposition, we focus our attention on the vacancy mechanism, which is a more faithful picture of diffusion in solids than the more widely examined exchange mech...

Dielectric electrorheological fluids: theory and experiment

Abstract: Electrorheological (ER) fluids are a class of materials whose rheological properties are controllable by the application of an electric field. A dielectric electrorheological (DER) fluid is the simplest type of ER fluid, in which the material components follow a linear electrostatic response. We review and discuss the progress of the studies on physics of this type of material. A first-principles theory of DER fluids, along with relevant experimental verifications, are presented in some detail. In particular, the properties presented include static equilibrium structure, shear modulus, static yield stress and its variation with applied electric field frequency, and structure-induced dielectric nonlinearity.

Charge ordering, charge fluctuations and lattice effects in strongly correlated electron systems

Abstract: Charge fluctuation and charge-ordering phenomena in compounds based on the 3d electrons of transition-metal ions and 4f electrons of rare-earth ions are reviewed with particular emphasis on the mutual coupling of charge and lattice degrees of freedom. For the description of charge ordering in inhomogeneously mixed-valence compounds of localized 3d or 4f-electron systems, we employ Landau's phenomenological theory for second-order phase transitions. By use of the group-theoretical method, the charge fluctuation mode corresponding to the active representation for the second-order transition is determined. The localization of 3d and 4f electrons makes the valence for the specific ions an integer number of charge units e in the ordered phases at low temperatures. The elastic soft mode observed by the ultrasonic method is often a useful indication for the charge fluctuation mode that is frozen below the charge-ordering point T C. The transverse c44 mode exhibiting a considerable softening in the rare-earth com...

Quantum cascade transitions in nanostructures

Abstract: In this article we review the physical characteristics of quantum cascade transitions (QCTs) in various nanoscopic systems. The quantum cascade laser which utilizes such transitions in quantum wells is a brilliant outcome of quantum engineering that has already demonstrated its usefulness in various real-world applications. After a brief introduction to the background of this transition process, we discuss the physics behind these transitions in an externally applied magnetic field. This has unravelled many intricate phenomena related to intersubband resonance and electron relaxation modes in these systems. We then discuss QCTs in a situation where the quantum wells in the active regions of a quantum cascade structure are replaced by quantum dots. The physics of quantum dots is a rapidly developing field with its roots in fundamental quantum mechanics, but at the same time, quantum dots have tremendous potential applications. We first present a brief review of those aspects of quantum dots that are likely...

How fast can cracks move? A research adventure in materials failure using millions of atoms and big computers

Abstract: During the last decade, we have been simulating the dynamic failure of brittle and ductile solids at the atomic level using some of the world's fastest computers. Computer experiments encompassing crack dynamics in brittle fracture, crack blunting in ductile failure, and multi-dislocation entanglement in work-hardening are some examples and have given new and exciting insights into the failure processes of solids. Our presentation begins at an introduction level where basic concepts are presented before their application is needed for the understanding of specific phenomena. The story is primarily based on our past experiences, and our goal is to give the reader a fundamental appreciation for how materials fail.

Magnetic domains in non-ferromagnetic metals: The non-linear de Haas-van Alphen effect

Abstract: This review is devoted to an exposition of the principles of the physics of magnetic domains in non-ferromagnetic metals and diamagnetic phase transitions, which lead to the formation of the so-called Condon domains during magnetic oscillations in a three-dimensional electron gas. One of the goals of the review is to provide a deeper insight into the nature of this instability of the electron gas in normal metals and improve the understanding of this type of non-spin magnetism. We discuss theoretical aspects of the physics underlying magnetic ordering of conduction electrons in bulk metals and in thin films, and describe the behaviour of the susceptibility, thermal expansion, specific heat, compressibility, sound velocity, magnetic induction bifurcation, the order parameter, domain formation, wetting of domain walls, nucleation and kinetics of diamagnetic phase transitions. In the vicinity of diamagnetic phase transitions the results obtained coincide with those following from the Landau theory of phase t...