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The basic idea of the CAM theory has been briefly explained. In the present lecture, many applications have been demonstrated explicitly to show how useful the CAM is. The present work is partially supported by the Society of Non-Traditional Technology. [ABSTRACT FROM AUTHOR]

The inherent linearity of quantum mechanics is one of the difficulties in developing a fully quantum theory of dissipative processes. Several microscopic and more or less phenomenological descriptions of quantum dissipative dynamics have been proposed in the past. Following the successful development of classical metriplectic dynamics — a systematic description of dissipative systems using a natural extension of symplectic dynamics — we discuss the possibility of a similar formulation for quantum dissipative systems. Particular attention is paid to the Madelung representation of quantum mechanics. [ABSTRACT FROM AUTHOR]

Recent investigations of the exchange-correlation potential of the Kohn-Sham (KS) scheme, making use of three equations satisfied by density matrices, are summarized and systematized. They lead to three exact expressions for the potential in terms of low-order density matrices of the interacting system and the KS system, and three approximations for the exchange-only potential in terms of the KS matrices. The application of the perturbation theory of Görling and Levy permits the formulation of a computational scheme in which the exact exchange potential and consecutive terms of the expanded correlation potential can be obtained within an extended KS approach. [ABSTRACT FROM AUTHOR]

The Peierls instability and the flux phase problem are treated in a unified way for certain models of strong electronic correlations. The treatment relies on an adaptation of the reflection positivity technique valid for certain models of itinerant fermions. We discuss three applications: the dia- or paramagnetic behavior of annulenes, the instability in a two dimensional Peierls-Hubbard model and some properties of coupled polyacetylene chains. [ABSTRACT FROM AUTHOR]

A method for studying critical behaviour in non-integer space dimensions is discussed. The critical exponents of several models commonly used in the theory of phase transitions are calculated for the case of non-integer space dimension. The calculations are performed using a fixed-dimension field theoretical approach. The renormalization group functions in the Callan—Symanzik scheme are considered directly in non-integer dimensions. Perturbation theory expansions are resummed with the use of Padé-Borel transformation. [ABSTRACT FROM AUTHOR]

The critical behaviour of two-dimensional (2D) anisotropic systems with weak quenched disorder described by an Ising model (IM) with random bonds, the N-colour Ashkin-Teller model (ATM) and some of its generalizations is studied. In the critical region, these models are shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behaviour of the two-spin correlation function. The equation of state at criticality is also obtained within this framework. We find that the random models under consideration belong to the same universality class as that of the two-dimensional IM. The critical behaviour of the 3- and 4-state random-bond Potts models is also briefly discussed. [ABSTRACT FROM AUTHOR]

A one-dimensional fermion model with bond charge-interactions as well as Hubbard-type interactions is investigated exactly. The large distance asymptotics of the density-density and pair correlations are calculated. The system shows Luther-Emery liquid behaviour with a crossover from a density-density dominated regime to one with dominant pair correlations. Furthermore, the integrable tJ chain is studied at finite temperatures. Some concepts for this analysis are introduced, notably the Trotter-Suzuki mapping and the quantum transfer matrix. Finally, the specific heat is presented and its structure discussed. [ABSTRACT FROM AUTHOR]

A growing crystal or any other object is said to have an instability when its surface does not remain planar but instead develops patterns such as dendrites. After a short outline of the instabilities in growth from the melt or solution or vapour, a detailed analysis is given of the instabilities in molecular beam epitaxy (MBE). [ABSTRACT FROM AUTHOR]

Condon's theory, predicting the periodic formation and disappearance of dia- and paramagnetic domains in non-magnetic metals under the conditions of a strong de Haas-van Alphen effect, is reviewed. Earlier experiments, evincing domains in silver and supporting the conjecture of domains in Be are discussed, and the recently obtained first spectroscopical evidence for the domain phase in beryllium is presented. The principle of muon spin rotation spectroscopy, used in these investigations, is described in some detail. [ABSTRACT FROM AUTHOR]

For a better appreciation of the revolutionary aspect of the discovery in 1986 of the first high-temperature superconductor, the main stations in the 80 years old history of superconductivity are revisited. It is emphasized that the first breakthrough in this history came only in its 5th decade when Bardeen, Cooper and Schrieffer succeded in formulating a microscopic theory of this phenomenon. The progress made in the following 3 decades then is described mentioning the names of Little, Ginzburg, Bednorz and Müller who were among the few physicists who had the optimism to consider another breakthrough possible. After Bednorz and Müller's discovery, progress leaped forward and produced an avalanche of publications which can be faced only by being selective. Thus after presenting the main characteristics of the different cuprate families of the new superconductors the main theoretical models are presented, which all make explicit use of the fact that the strongly correlated mobile holes in the copper-oxygen layers carry most of the interesting physics. Some of the new ideas like the separation of spin and charge of the holes and the possible existence of a "spin liquid" instead of a Fermi liquid are considered. Also discussed are the main pairing mechanisms proposed to describe the superconducting state and, in particular, the alternative of s- versus d-wave symmetry. Finally, possible explanations of the strange linear resistivity as function of the temperature observed parallel to the layers in the normal state and the technical applications in the form of wires, squids and filters for medicine and the communications industry are reviewed. [ABSTRACT FROM AUTHOR]

In this lecture we present some interesting issues that arise when the dynamics of the charge carriers in the CuO2 planes of high temperature superconductors is considered. Based on the qualitative picture of doping, set by experiments and some previous calculations, we consider the strength of the various inter- and intra-cell charge transfer susceptibilities, the question of Coulomb screening and charge collective-modes. The starting point is the usual p-d model extended by the long-range Coulomb (LRC) interaction. Within this model it is possible to examine the case in which the LRC forces frustrate the electronic phase separation, the instability which is present in the model without a LRC interaction. While the static dielectric function in such systems is negative down to arbitrarily small wavevectors, the system is not unstable. We consider the dominant electronic charge susceptibilities and possible consequences for the lattice properties. [ABSTRACT FROM AUTHOR]

As a first approximation, a metal can be modelled as an electron gas. A non-interacting electron gas has a continuous spectrum of electron-hole pair excitations. At each wavevector Q with Q less than the maximum Fermi surface spanning vector (2kF) there is a continuous set of electron-hole pair states, with a maximum energy but no gap (the minimum energy is zero.) Once the Coulomb interaction is taken into account, a new collective mode, the plasmon, is built from the electron-hole pair spectrum. The plasmon captures most of the spectral weight in the scattering cross-section, yet the particle-hole pairs remain practically unchanged, as can be seen from the success of the Landau Fermi-liquid picture. This article explores how even an isolated electron-hole pair in non-interacting approximation is a form of charge density wave excitation, and how the Coulomb interaction totally alters the charge properties, without affecting many other properties of the electron-hole pairs. [ABSTRACT FROM AUTHOR]

A brief review is given of the present understanding of the transitions between integer quantized plateaus of the Hall conductivity in two-dimensional disordered systems in a strong magnetic field. The similarity to continuous thermodynamic phase transitions is emphasized. Results of numerical simulations for non-interacting electrons are presented and compared to experiment. The role of the Coulomb interactions at the integer quantum Hall transitions is studied. [ABSTRACT FROM AUTHOR]

A new type of electron confinement in modulated semiconductor systems is proposed. The confinement occurs when the effective mass of electrons in the central region of the structure is higher than that in the outside regions. This results in a ‘kinetic well' produced by the transverse free motion. The calculated density of confined states is similar but not identical to that of the potentially bound 2D states. It is shown that the presence of an external magnetic field parallel to the growth direction stabilizes and controls the kinetically confined states. The resulting levels are strongly nonlinear functions of magnetic field intensity. We discuss specific structures in which the kinetic confinement of electrons would be possible. [ABSTRACT FROM AUTHOR]

The Boltzmann equation in the relaxation time approximation is used to calculate formal expressions for the local electrical, thermal and thermoelectric transport coefficients of a strictly 2D, elastically scattered, free electron gas. The terminal transport coefficients for the same gas confined in a quantum wire are also calculated using the Landauer-Buttiker formalism. Both calculations are valid in a quantum wire structure when its width w is much greater than the Fermi wavelength and its length l is much greater than the classical mean free path. Comparison shows that the sum of all the transmission coefficients through the system at the Fermi energy ɛ is therefore given by T(ɛ)=(w/l)ɛ/Δɛ where Δɛ=ħ/τ(ɛ) is the uncertainty in ɛ arising from the classical relaxation time τ(ɛ). A new way of calculating T(ɛ) using wave functions is outlined. Numerical results for both T(ɛ) and scattering wave functions are presented for two nanonstructures: (i) a quantum wire with one hard wall finger pushed in and (ii) a quantum wire with two hard wall fingers pushed in so as to create a quantum dot. [ABSTRACT FROM AUTHOR]

Some striking quantum phenomena discovered in small conductors, insulators and capacitors over the recent years are described. It is argued that while these phenomena may render further miniaturization of the present electronic devices difficult, they may constitute the principle of operation of the next generation of devices. [ABSTRACT FROM AUTHOR]

We describe the basic physics of a Quantum Single Electron Transistor (QSET). The QSET is a quantum dot (QD) connected to two leads and a central electrode. The effect of the central electrode, electron-electron interaction, and a magnetic field on electron droplets in the QSET is studied using the Hartree-Fock approximation and exact diagonalization techniques. In a strong magnetic field, the central electrode induces electronic spin and charge transitions in the spin-polarized droplet. We show how these spin-related transitions can be observed in transport and coherent resonant tunnelling through the QSET. [ABSTRACT FROM AUTHOR]

The electronic states of a parabolic quantum dot in a magnetic field are studied with the spin-orbit interaction included. The analytical formulae for the ground-state energy of the interacting system are derived. The spin-orbit interaction introduces a new feature into the far infra-red absorption spectrum, namely a splitting of the two principal modes. This conclusion is compared with the charging experiments of Ashoori et al. and the far infra-red absorption measurements of Demel et al. A model of an exciton confined in a quantum dot is also analyzed. At a critical dot-size, an additional strong line in the photo-luminescence spectrum appears, a consequence of the occurrence of a meta-stable weakly excited state. [ABSTRACT FROM AUTHOR]

Quantum dots are reviewed, with emphasis on the theory of electron correlation. A brief survey of dot fabrication and experimental results is also given. The theoretical model of a dot as a 2D system with parabolic confinement and Coulomb interaction is explained and numerical results for spin polarised dots are presented to illustrate the physics in a typical case. When a dot is placed in a magnetic field a series of transitions occurs in which the ground state angular momentum increases with field. The angular momentum values that are selected form a sequence of magic numbers that is characteristic of the electron number and total spin. The ground state transitions affect most physical properties of dots and generally cause magnetic field dependent oscillations. The sequence of magic numbers is related to the symmetry of the classical minimum energy configuration and an approximation technique, based on a harmonic expansion about the classical minimum, is shown to give a good account of dot physics in the high angular momentum limit. Future prospects for studies of coupled dots are briefly discussed. [ABSTRACT FROM AUTHOR]

Dense hydrogen, a dual Fermion system, possesses a Hamiltonian of high symmetry and especial simplicity. As a consequence of the latter its ground state energy satisfies general scaling conditions, independent of phase. Electron exchange is an important contributor, and its role in proton pairing (so evident at low densities) can be argued as a persistent feature. In the single particle description instabilities associated with band-gap closure can be seen as incipient charge density waves but in pair coordinates. This gives rise to a notion of higher pairing within which there can be an associated broken symmetry in electron density (consistent with the observed infrared activity). The persistence of exchange driven pairing under conditions where temperatures approach characteristic vibron energies is discussed in the context of recent reports of the metallization of hydrogen by dynamic methods. [ABSTRACT FROM AUTHOR]

The glass transition in a hard sphere system is studied numerically, using a model free energy functional that exhibits glassy local minima at sufficiently high densities. The numerical methods used in our work include free-energy minimization, direct integration of Langevin equations and Monte Carlo simulation. At relatively low densities, the system is found to fluctuate near the uniform liquid minimum of the free energy and to exhibit mode-coupling behavior. At densities higher than a first crossover density, the dynamics is governed by thermally activated transitions between glassy free-energy minima. The typical time scale for such transitions grows very rapidly as a second crossover density is approached from below. Interpretation of existing molecular dynamics data in the light of our results is discussed. [ABSTRACT FROM AUTHOR]

In these lectures I will study some properties that are shared by many glassy systems. I will shown how some of these properties can be understood in the framework of the mean field approach based on the replica method and I will discuss which are the difficulties which we have to face when we apply the replica method to realistic short range models. We finally present a partially successfully application of the replica method to soft sphere glasses. [ABSTRACT FROM AUTHOR]

We discuss numerical experiments that allow to detect an ultrametric structure of the phase space of the 4D spin glasses with quenched random couplings J=±1. We discuss a constrained Monte Carlo method, and systematic problems like finite size effects. We compare our results to the ones we obtain for the mean field Sherrington Kirkpatrick model and by using unconstrained numerical simulations, and we exhibit a very coherent picture. [ABSTRACT FROM AUTHOR]

Some strategies to study the kinetics of disorder in Ising-like systems are reviewed. [ABSTRACT FROM AUTHOR]

Using techniques, borrowed from statistical mechanics of spin glasses, we investigate the properties of cluster algorithms applied to random and non-random data points. [ABSTRACT FROM AUTHOR]

In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by quenched disorder. These models exhibit self-organization, with critical properties developing spontaneously, without the fine tuning of external parameters. This situation is different from the usual critical phenomena, and requires the introduction of new theoretical methods. Our approach to these problems is based on two concepts, the Fixed Scale Transformation, and the quenched-stochastic transformation, or Run Time Statistics (RTS), which maps a dynamics with quenched disorder into a stochastic process. These methods, combined together, allow us to understand the self-organized nature of models with quenched disorder and to compute analytically their critical exponents. In addition, it is also possible characterize mathematically the origin of the dynamics by avalanches and compare it with the continuous growth of other fractal models. A specific application to Invasion Percolation will be discussed. Some possible relations to glasses will also be mentioned. [ABSTRACT FROM AUTHOR]

The paper discusses the size of a randomly cross-linked polymer chain. The calculations are based on an exact theorem for the characteristic function of a polydisperse phantom network that allows for treating the cross-links between pairs of randomly selected monomers as quenched variables without resorting to replica methods. By variation of the cross-linking potential from infinity (hard constraints) to zero (free chain), we have studied the cross-over of the radius of gyration from the branched polymer regime where Rg⋍O(1) to the extended regime Rg⋍O(√N). In the cross-over regime the network size Rg is found to be proportional to (N/M)1/4, where M is the total number of cross-links and N the number of monomers in the system. Our exact results can also be understood in terms of simple scaling arguments. [ABSTRACT FROM AUTHOR]

The symmetric AB block copolymer melt in a gel matrix with preferential adsorption of A monomers on the gel gives an example of a random-field system, which is described near the point of the microphase separation transition by the random field Landau-Brazovskii Hamiltonian. By using the technique of the 2-nd Legendre transform, the phase diagram of the system is calculated. We found that the preferential adsorption of the copolymer on the gel results in two effects: a) It decreases the temperature of the first order phase transition between disordered and ordered phase. b) There exists a region on the phase diagram at some small but finite value of the adsorption energy in which the replica symmetric solution for two replica correlation function is unstable with respect to replica symmetry breaking. We interpret this state as a glassy state and calculate a spinodal line of this transition. We also consider the stability of the lamellar phase in the weak segregation limit by mapping the copolymer Hamiltonian onto the Hamiltonian of the random field XY model. We suggest that the long range order is always destroyed by weak randomness. [ABSTRACT FROM AUTHOR]

Polyampholytes (PAs) are polymers with a random sequence of positive and negative charges along their backbone. We have studied systematically the dependence of internal energy and shape of the PA on its excess charge by combining analytic arguments, Monte Carlo simulations, and exact enumeration of all configurations of short chains. The results indicate that the overall excess charge, Q, is the main determinant of the size of the PA. A polymer composed of a mixture of N positive and negative charges ±qo, is compact for Q

We summarize recent work on a frustrated periodic long-range Josephson array in a parameter regime where its dynamical behavior is identical to that of the p=4 disordered spherical model. We also discuss the physical requirements imposed by the theory on the experimental realization of this superconducting network. [ABSTRACT FROM AUTHOR]

I review several problems dealing with the equilibrium behavior of classical two dimensional Josephson junction arrays in applied magnetic fields. Specific attention is given to the cases of a uniform field with average flux density per unit cell of f=0, f=1/2, f=1/q and f=1/2−1/q. Several models incorporating the effects of randomness on the Josephson array are also reviewed. These include the case of a random vortex pinning potential and its effects on vortex lattice order, and the spin glass, gauge glass, and positionally disordered array. [ABSTRACT FROM AUTHOR]

The mixed state of High Temperature Superconductors (HTS) is a new field that allows us to study very interesting and new phenomena related with glassy behavior. There are many topics that could be addressed, but in this paper we are going to deal with two topics. The first one concerning to the single vortex dynamics, and the second one related with the dissipation mechanisms of the vortices and the so-calle d lock-in transition. The former will be studied using the anomalous behavior of the Hall effect in the mixed state with c-axis oriented 1:2:3 films the latter using as an appropriate tool the critical current, the pinning force and the resistivity (dissipation) in the m ixed state of 1:2:3 a-axis oriented superconductor / non-superconductors multilayers. [ABSTRACT FROM AUTHOR]

Small Angle Neutron Scattering (SANS) studies are an essential tool for studying vortices in the bulk of type II superconductors, providing deep understanding of their three dimensional microscopic structure in a wide range of fields and temperatures. This talk will summarize detailed studies of flux lattices in the vicinity of two critical transitions: (1) flux lattices in the vicinity of the critical current in 2H-NbSe2. We find a clear evidence for a two step depinning process: as a function of increasing driving force three regimes are observed — first, no motion; then disordered, plastic motion; and finally at high velocities a coherently moving crystal. (2) flux lattices in the vicinity of the peak effect, below the upper critical field, Hc2, in Nb. Our studies reveal drastic structural disordering, characterized by complete loss of positional and orientational correlations, whereas the lines remain well correlated along their length. [ABSTRACT FROM AUTHOR]

Columnar defects provide effective pinning centers for magnetic flux lines in high-Tc superconductors. Utilizing a mapping of the statistical mechanics of directed lines to the quantum mechanics of two-dimensional bosons, one expects an entangled flux liquid phase at high temperatures, separated by a second-order localization transition from a low-temperature "Bose glass" phase with infinite tilt modulus. Recent decoration experiments have demonstrated that below the matching field the repulsive forces between the vortices may be sufficiently large to produce strong spatial correlations in the Bose glass. This is confirmed by numerical simulations, and a remarkably wide soft "Coulomb gap" at the chemical potential is found in the distribution of pinning energies. At low currents, the dominant transport mechanism in the Bose glass phase proceeds via the formation of double kinks between not necessarily adjacent columnar pins, similar to variable-range hopping in disordered semiconductors. The strong correlation effects originating in the long-range vortex interactions drastically reduce variable-range hopping transport. [ABSTRACT FROM AUTHOR]

The winding of a single polymer in thermal equilibrium around a repulsive cylindrical obstacle is perhaps the simplest example of statistical mechanics in a multiply connected geometry. As shown by S.F. Edwards, this problem is closely related to the quantum mechanics of a charged particle interacting with a Aharonov-Bohm flux. In another development, Pollock and Ceperley have shown that boson world lines in 2+1 dimensions with periodic boundary conditions, regarded as ring polymers on a torus, have a mean square winding number given by =2nsħ2/mkBT, where m is the boson mass and ns is the superfluid number density. Here, we review the mapping of the statistical mechanics of polymers with constraints onto quantum mechanics, and show that there is an interesting generalization of the Pollock-Ceperley result to directed polymer melts interacting with a repulsive rod of radius a. When translated into boson language, the mean square winding number around the rod for a system of size R perpendicular to the rod reads $$\left\langle {W^2 } \right\rangle = \frac{{n_s \hbar ^2 }}{{2\pi mk_B T}}\ln (R/a)$$ . This result is directly applicable to vortices in Type II superconductors in the presence of columnar defects. An external current passing through the rod couples directly to the winding number in this case. [ABSTRACT FROM AUTHOR]

This article reviews recent progress of the analytical theory of quantum spin glasses (QSG). Exact results for infinite range and one loop renormalisation group calculations for finite range models of either insulating or metallic type are presented. We describe characteristics of fermionic spin glass transitions and of fermionic correlations which are affected by these transitions and by spin glass order. Connections between tricritical thermal- and T=0 QSG transitions are described. A general phase diagram with tricritical QSG transitions caused either by random chemical potential or by elastic electron scattering, and implying discontinuous T=0-transitions in weak and in strong filling regimes, is also derived. [ABSTRACT FROM AUTHOR]

Ising spin glasses in a transverse field exhibit a zero temperature quantum phase transition, which is driven by quantum rather than thermal fluctuations. They constitute a universality class that is significantly different from the classical, thermal phase transitions. Most interestingly close to the transition in finite dimensions a quantum Griffiths phase leads to drastic consequences for various physical quantities: for instance diverging magnetic susceptibilities are observable over a whole range of transverse field values in the disordered phase. [ABSTRACT FROM AUTHOR]

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>dc+=6 a mean field theory gives the exact critical exponents. For d=6−ε the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner's scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s≧2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems. [ABSTRACT FROM AUTHOR]

We give a brief review on a family of two dimensional models with continuous symmetry and possibly regular frustration or frustration-type disorder. Next we focus on the random ± J bond XY model. There are two types of variables in this system and thus two candidates for an order parameter, the continuous spin variable and the discrete chiral variable. The question is : do the chiralities order more easily than the spins ? We present an analytical approach based on correlation function studies in one dimension and on domain wall scaling analysis in two dimension. Our results contradict recent interpretation of numerical simulations. [ABSTRACT FROM AUTHOR]

We discuss the results of recent Monte Carlo simulations of a short range spin glass model with four-spin interactions, in connection with the physics of glasses. The model could be classified as a fragile glass, displaying stretched exponential relaxation with super-Arrhenius behavior of the relaxation time. The growth of this at low temperature appears to be associated to an entropy reduction according to the Adam-Gibbs equation. The correlation length appears to grow rather modestly compared with the relaxation time. [ABSTRACT FROM AUTHOR]

We discuss the large scale effective potential for elastic objects in the presence of a random pinning potential. In the static approach, converging analytical results show that the large scale, low temperature free energy landscape consists in a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined, and compared to the mean field theory of aging effects. [ABSTRACT FROM AUTHOR]

This is a short review of the current state of theory and experiment on the structure of elastic lattices weakly interacting with underlying random background. Examples are flux lattices in superconductors, magnetic bubble lattices in ferromagnetic films, charge density waves in semiconductors, and atomic monolayers physisorbed on random surfaces. We shall argue that the orientational order in these systems persists at longer scales than the translational order. The law of the decay of both types of order will be analysed, with the emphasis on its practical implications for superconductors. The depinning transition will be discussed in terms of the mobility of the lattice. [ABSTRACT FROM AUTHOR]

An analytically tractable model is introduced which exhibits both, a glass-like freezing transition, and a collection of double-well configurations in its zero-temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low-temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean-field and replica methods, we are able to compute the distribution of asymmetries and barrier-heights of the double-well configurations analytically, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier-heights as well as a collection of single-well configurations in the potential energy landscape of the glass-forming system — in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures. [ABSTRACT FROM AUTHOR]