Quasi Bernoulli fluctuations in random and disordered systems

It is shown that quasi Bernoulli fluctuations, which appear at a morphological phase transition, can be considered as a statistical basis for multifractal processes with constant multifractal specific heat in a wide class of random and disordered systems. This class contains at least following processes: percolation, diffusion-limited aggregation and corrosion, Lorenz like attractors, and mesoscopic systems with Anderson transition. Received: 14 April 1998 / Revised and Accepted: 20 April 1998     

Symmetry of Einstein - Yang - Mills systems and dimensional reduction

The following topics are discussed: G-invariant Riemannian metrics and principal connections, dimensional reduction of Einstein and Yang-Mills systems, curvature of coset spaces, dimensional reduction of spinors, geometrical interpretation of color and Higgs charges.     

Improved perturbation expansion for disordered systems: Beating Griffiths singularities

We introduce a new expansion to prove exponential clustering of connected correlations in a large class of disordered systems. Our expansion converges for values of the temperature and magnetic field where standard cluster expansions diverge, due to the presence of Griffiths type singularities. It is organized inductively over an infinite sequence of increasing distance scales. In each induction step one redefines what is means by the unperturbed system, a procedure somewhat reminiscent of K.A.M. theory. Our techniques may be useful in dealing with the so-called large-field problem in real-space renormalization group schemes.Research partially supported by the National Science Foundation under Grant PHY 82-03669Junior Fellow, Harvard Society of Fellows     

Renormalized cluster expansion for multiple scattering in disordered systems

We study wave propagation in a disordered system of scatterers and derive a renormalized cluster expansion for the optical potential or self-energy of the average wave. We show that in the problem of multiple scattering a repetitive structure of Ornstein-Zernike type may be detected. We derive exact expressions for two elementary constituents of the renormalized scattering series, called the reaction field operator and the short-range connector. These expressions involve sums of integrals of a product of a chain correlation function and a nodal connector. We expect that approximate calculation of the reaction field operator and the short-range connector allows one to find a good approximation to the self-energy, even for high density of scatterers. The theory applies to a wide variety of systems.     

On dimensional reduction of gauge theories: Symmetric fields and harmonic expansion

We compare the four-dimensional symmetric fields obtained by the coset space dimensional reduction scheme to the infinite tower of fields given by the harmonic expansion in a 4+N dimensional gauge theory coupled to fermions on a space-timeM ⁴ ×S/R.     

Nonvanishing zero temperature static conductivity in one dimensional disordered systems

We present the results of two different computer experiments for the dc-conductivity at zero temperature for a one dimensional disordered system with site energies distributed randomly over a finite energy interval. In contrast to the current assumptions an Anderson transition at a finite value of the disorder parameter is found in this model.     

On the stability of the polaron in one dimensional disordered systems

A one-dimensional disordered system of electrons described by a tight binding model interacting with vibrational degrees of freedom (in harmonic approximation) is considered. A stable configuration is determined by a numerical minimization of the total energy which is based on the adiabatic approximation. The behaviour of the electron density (charge density wave) and the density of states is analysed. The localization properties are investigated as well. In contrast to the corresponding disordered system with vanishing electron-phonon coupling the present model has an energy gap. The formation of the gap and the polaron band is shown to be quite different for both onsite and intersite types of coupling terms. For large disorder, the lattice distortion and the gap disappear if only the vibrational contribution to the intersite coupling is important. They increase, however, if only the vibrational contribution to the site energies is taken into account. In both cases the localization length decreases upon increasing the electron-phonon coupling energy. The results are discussed with respect to low dimensional organic materials and amorphous semiconductors.     

Conductivity and localization of electron states in one dimensional disordered systems: Further numerical results

The localization of the electron states and dc-conductivity of the one dimensional Anderson model are investigated with various numerical procedures. It is found that the eigenstates are always exponentially localized and that in the center of the band the localization length is proportional to the inverse square of the disorder. The dc-conductivity, as obtained by using the Kubo-Greenwood formula, obeys the central limit theorem for any finite imaginary frequency, with a variance, which is inversely proportional to the squareroot of the number of states contributing to the transport. There is no exponential length dependence of the Kubo-Greenwood conductivity within this model. The conductivity tends to zero only in the limit of vanishing imaginary frequency.     

Quantum Hall effect in intentionally disordered two‐dimensional electron systems

In this work intentionally disordered two‐dimensional electron systems in modulation doped GaAs/GaAlAs heterostructures are studied by magnetotransport experiments. The disorder is provided by a δ‐doped layer of negatively charged beryllium acceptors. In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic‐field‐induced delocalization. At increased magnetic fields the quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around ν_c=0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials. The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance. This is contrary to other experiments which observe a finite Hall resistance in the insulating regime and has not been observed previously. According to recent theoretical studies the divergence of the Hall resistance points to quantum coherent transport via tunneling between quantum Hall droplets. The magnetotransport experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths for far‐infrared excitations. These simulations reveal that the strong shift of the Hall plateaus and the observed critical filling factor for the insulator transition in high magnetic fields require an asymmetric density of states that can only be generated by a strongly correlated beryllium distribution. Cyclotron resonance on the same samples also indicates the possibility of correlations between the beryllium acceptors.     

Superconductivity in disordered thin films: giant mesoscopic fluctuations

We discuss the intrinsic inhomogeneities of superconductive properties of uniformly disordered thin films with a large dimensionless conductance g. It is shown that mesoscopic fluctuations, which usually contain a small factor 1/g, are crucially enhanced near the critical conductance g(cF) > 1 where superconductivity is destroyed at T = 0 due to Coulomb suppression of the Cooper attraction. This leads to strong spatial fluctuations of the local transition temperature and thus to the percolative nature of the thermal superconductive transition.     

Spin and density fluctuations in disordered narrow-band superconductors

A tight-binding theory of strong-coupling superconductivity is formulated on the basis of a random lattice model with local electron-electron and contact-type electronphonon interactions. Functional-derivative technique yields a systematic deduction of the electron self-energy in terms of Coulomb repulsion, density and spin fluctuations. A novel procedure is proposed to average disordered Berk-Schrieffer-type equations. The phonon ( ^ph)-, Coulomb ^C-, and paramagnon ( ^m)-mediated coupling parameters entering the superconductingT _c are calculated for diffusive behaviour in dirty systems or alloys. The critical reduction ofT _c due to ^m differs from the logarithmic singularity for a clean sample.     

Coherent transport in disordered metals: zero dimensional limit

We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a universal current-voltage-characteristics. The relevance of our calculation for existing experiments is discussed as well as the connection with alternative theoretical approaches. Received 2 September 2002 Published online 29 October 2002     

Localisation in disordered systems—I: The disordered spectrum

Starting from a definition of the localisation-delocalisation of electronic, wavefunctions in disordered systems based on the nature of the disordered spectrum, a delocalisation criterion identical to that of Abou-Chacraet al is recovered. The new derivation on provides a very clear picture of the mechanism of delocalisation and brings out its incompatibility with the normalisability of wavefunctions at the transition.     

Two dimensional ordering and fluctuations in alpha(')-NaV2O5

X-ray diffraction measurements of Bragg and diffuse scattering associated with charge ordering in the inorganic compound alpha(')- NaV2O5 show a continuous phase transition at a temperature of about 33.1 K. Many of this material's properties suggest a spin-Peierls transition, as established in CuGeO3 and MEM(TCNQ)(2). We compare the order parameter as well as fluctuations in the order parameter in these materials, and conclude that alpha(')- NaV2O5 is dissimilar, and that the transition is two dimensional in nature, due to charge ordering associated with the fractional average valence at the vanadium site within the orthorhombic a- b plane.     

Equivalence of dimensional reduction and dimensional regularisation

For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the -functions calculated using DRED transform into those computed in DREG. TheS-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.     

Density,phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential

We present a detailed numerical study of the dynamics of a disordered one-dimensional Bose-Einstein condensates in position and momentum space. We particularly focus on the region where non-linearity and disorder simultaneously effect the time propagation of the condensate as well as the possible interference between various parts of the matter wave. We report oscillation between spatially extended and localized behavior for the propagating condensate which dies down with increasing non-linearity. We also report intriguing behavior of the phase fluctuation and the coherence properties of the matter wave. We also briefly compare these behavior with that of a two-dimensional condensate. We mention the relevance of our results to the related experiments on Anderson localization and indicate the possibility of future experiments