The dynamics of disordered systems and the motion of vortices in disordered type-II superconductors

We develop a field theoretical method which permits us to study the dynamics of interacting particles in disordered systems. In particular, making use of a Hartree-type approximation, we obtain a self-consistent system of equations for disorder averaged quantities. The method is first applied to a single particle on a rough surface. Then, we calculate the current-voltage (I-V) characteristics of a type-II superconductor in the flux flow regime. Finally, the structure of the steps is discussed which arise in the I-V-characteristics when a small ac field is superimposed on the constant voltage. These may serve as a probe for incipient melting of the vortex lattice.     

Kinetic roughening and pinning of two coupled interfaces in disordered media

We studied the kinetic roughening dynamic of two coupled interfaces formed in paper wetting experiments at low evaporation rate. We observed three different regimes of impregnation in which kinetic roughening dynamics of coupled precursor and main fronts belong to different universality classes; nevertheless both interfaces are pinned in the same configuration. Reported experimental observations provide a novel insight into the nature of kinetic roughening phenomena occurring in the vast variety of systems far from equilibrium.     

Numerical approaches on driven elastic interfaces in random media

We discuss the universal dynamics of elastic interfaces in quenched random media. We focus on the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined.     

The shapes of bowed interfaces in the two-dimensional Ising model

We show that properly normalized net energy fluctuations associated with interfaces in two-dimensional Ising models are described, asymptotically, by random walk partition functions. Two examples are investigated: one is a droplet on a wall, and the other is two nearby, ideally parallel interfaces; the mean shapes of the interfaces in both cases prove to be elliptic, bowed outward from the wall or from each other, the semiminor axis of the latter ellipse being 1/2 that of the former, in accord with random walk results.     

The tensor renormalization group for pure and disordered two-dimensional lattice systems

The tensor renormalization group (TRG) is a powerful new approach for coarse-graining classical two-dimensional (2D) lattice Hamiltonians. It uses the intuitive framework of traditional position space renormalization group methods-analyzing flows in the space of Hamiltonian parameters-but can be systematically improved to yield thermodynamic properties at much higher precision. We present initial results demonstrating that the TRG can be generalized to quenched random systems, applying it to obtain the phase diagram of a bond-diluted triangular lattice Ising ferromagnet. This opens a variety of potential future applications, most prominently spin glasses.     

Driven quasi-one-dimensional classical electron gas in the presence of a constriction: Pinning and depinning

We studied the properties of a quasi-one-dimensional system of charged particles in the presence of a local Lorentzian-shaped constriction. We investigated the response of the system when a time-independent external driving force is applied in the unconfined direction. Langevin molecular dynamics simulations for different values of the drive and temperature are performed. We found that the particles are pinned unless a threshold value of the driving force is reached. We investigated in detail the depinning phenomenon. The system can depin “elastically”, with particles moving together and keeping their neighbors, or “quasi-elastically”, with particles moving together through a complex net of conducting channels without keeping their neighbors. In the case of elastic depinning the velocity vs applied drive curves is characterized by a critical exponent β consistent with the value , while in the case of quasi-elastic depinning the critical exponent β has on average the value 0.94. The model is relevant e.g. for electrons on liquid helium, colloids and dusty plasma.     

Localization in disordered systems with interactions

We present an improved numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to disorder and interacting problems respectively. The method is applied to spinless fermions in 1D and a generalization to finite cross-sections is outlined.      

New quasiparticles hystons and coherent photoinduced dynamics of molecules in polar disordered media

Using methods of statistical thermodynamics, it is shown that after pulse excitation the evolution of a “polar luminescent probe—polar disordered medium” system is described by an equation of damping vibrations. This allows the conclusion that in the solvate shell of the probe molecule synchronous rotational vibrations (librations) of the molecules of the medium occur, whose damping is caused by dielectric friction. Such a collective synchronous motion is considered as a motion of a quasiparticle called a hyston. The moment of inertia J_n and mass M_h of a hyston are defined as J_h=2m² ₁a^-3Ω₀ ^-2(ε-1)/(2ε+1), M_h=J_hM_s/J_s, where m₁ is the dipole moment of the probe molecule in the excited S₁-stute; a is the Onsager radius; Ω₀ is the cyclic frequency of harmonic vibrations of the hyston; ε is the dielectric constant; M_s and J_s are the mass and moment of inertia of a molecule of the medium, respectively. The correlation function of the motion of the molecules c(t) is a solution of the equation of hyston motion. The fluorescence response s(t) in measurements with time resolution coincides with the correlation function: s(t)=c(t). The concepts concerning hystons make it possible to describe macroscopic photoinduced coherent motion that is manifested against a background of thermal motion of the medium molecules. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnei Spektroskopii, Vol 65, No. 2, pp. 176–183, March–April, 1998.     

Self-affinity study of nanostructured porous silicon-crystalline silicon interfaces

Self-affinity was used to analyze the roughness at the porous silicon (PS)-crystalline Si (cSi) interfaces fabricated under different conditions. Using the variable bandwidth method, the self-affinity behavior was, qualitatively and quantitatively, analyzed from the cross-section micrographs of the PS samples obtained by field emission scanning electron microscope. The results show that correlation length is related with the average pore width. Roughness exponent is found to be correlated with the interface roughness. In addition, similar experimental roughness exponents were obtained for several interfaces grown by different methods, indicating the intrinsic fractal nature of the PS-cSi interfaces. The results were confirmed through the self-affinity analysis done on the atomic force microscopy profiles.     

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.     

Electronic heat capacity in disordered graphene systems

We analyzed the electronic heat capacity of graphene systems in the presence of disorder. We consider the case of strong scatterers, working in the unitary limit. The temperature dependence of the electronic heat capacity is analyzed. Close to the clean limit we obtained the quadratic temperature dependence, corrected with a temperature and disorder dependent factor which slightly enhance the heat capacity. At very low temperatures, and in the presence of disorder, we obtained a linear temperature dependence of the electronic heat capacity. We also analyzed the temperature dependence of the electronic heat capacity in the case of extrinsic graphene.     

Dielectric resonances in disordered media

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. They present very specific properties, in particular the second-order percolation phase transition, with its fractal geometry and the multi-fractal properties of the current moments. These systems are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. The two significant parameters are the ratio h = σ ₁/σ of the complex conductances, σ and σ ₁, of the two components, and their relative abundances p (or, respectively, 1 - p). In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites constituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. In this paper, we analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (“n-legged animals”) in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain. Received 16 August 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: laurent.raymond@l2mp.fr RID="b" ID="b"e-mail: steffen.schaefer@l2mp.fr RID="c" ID="c"UMR CNRS 6137     

The dynamics of random interfaces in phase transitions

A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ _N models.Work supported by NSF grant No. DMR-8013700.     

The sub-wavelength imaging performance of disordered wire media

An analysis of the sub-wavelength imaging performance of disordered thin wire media is undertaken, in order to understand how its performance may be affected by manufacturing errors. The structure is found to be extremely robust to disorder which keeps the wires parallel. Variation in the orientation of the wires and their longitudinal position causes more significant degradation in the image quality, which is quantified numerically.     

The magnetic properties of a finite superlattice with two disordered interfaces

Within the framework of the effective field theory, based on a probability distribution technique, we examine the critical and compensation behaviors of a ferrimagnetic alternating superlattice on a simple cubic structure. The superlattice consists of k unit cells each of which consists of L layers of spin-1/2 A atoms, L layers of spin-1 B atoms and a disordered interface with two layers in between that is characterized by a random arrangement of A and B atoms A_pB_1−pA_1−pB_p with a negative coupling A − B. Considering a finite and infinite superlattices, the effect of the thickness of the film and the surface exchange coupling on the magnetic properties are studied. The obtained results show a number of characteristic phenomena.