Coulomb blockade of tunneling between disordered conductors

We determine the zero-bias anomaly of the conductance of tunnel junctions by an approach unifying the conventional Coulomb blockade theory for ultrasmall junctions with the diffusive anomalies in disordered conductors. Both electron-electron interactions within the electrodes and electron-hole interactions between the electrodes are taken into account nonperturbatively. Explicit results are given for one- and two-dimensional junctions, and the crossover to ultrasmall junctions is discussed.     

Nuclear spin relaxation in disordered conductors

The relaxation timesT ₁ andT ₂ for nuclear spins interacting with the conduction electrons of disordered metals are calculated. An explicite expression for Warren's relaxation enhancement in terms of electron spectra is obtained, showing in particular that the proportionality ofT ₁ and the conductivity is a universal feature of high resistivity conductors. A formula for an inhomogeneous line width contribution due to disorder induced static Knight shift fluctuations is found. Two dimensional electron spin diffusion is shown to imply various logarithmic line width corrections.     

Low-temperature resistance fluctuation in disordered conductors

At low temperatures the electron elastic mean free path in a disordered conductor can become much smaller than the inelastic mean free path (or more precisely the Thouless length) which in turn may be comparable with, or even larger than the sample size. In this quantum regime, the electrical resistance is dominated by the coherence effects that eventually lead to the now well-known weak or strong localization. Yet another remarkable manifestation of the quantum coherence is that it makes the resistance non-additive in series and, more importantly, non-self averaging, thus replacing the classical Ohm’s law with a quantum Ohm’s law describing statistical fluctuations. In this paper, we report on some of our recent work on the statistics of these “Sinai” fluctuations of residual resistance for one and higher space dimensions (d). In particular we show that the physics at the mobility edge may be dominated by these fluctuations. We also show that an external electric field tends to harness these fluctuations. Some observational consequences such as 1/f-noise at low temperatures are discussed. Our approach is based on invariant imbedding extended by us for this purpose.     

Crossover dynamics in bond disordered lattices

The asymptotic dynamics of the percolation model for a bond disordered lattice is studied. The velocity autocorrelation function (VACF) is investigated for arbitrary concentration of disorder in two and three dimensions using an effective medium approximation (EMA). Corrections to the long time tails away from the percolation threshold and to the percolation tails at the threshold are calculated. A characteristic time scale for the long time tails is identified and found to diverge at the threshold. Sufficiently close to the threshold the two types of asymptotic dynamics can be identified clearly for times greater than and less than this characteristic time, respectively. An approximate scaling of the EMA equation is obtained near the threshold for investigation of the crossover region. More generally, the EMA equation is solved numerically for arbitrary concentration in two dimensions to exhibit the complete time dependence of the VACF in all domains near and far from the threshold.     

On the universality classes of the Henon map

Within an appropriate renormalization framework, we discuss a¹(b) and δ associated with the bifurcation road to chaos of a Hénon-like map generalized as follows: (x_t+1, y_t+1) = (1?a|x_t|^z + y_t, ?bx_t); (b?0, z?1). For fixed z, we obtained (i) only two universality classes, namely the conservative (b = 1) and non-conservative (b≠1) ones and (ii) $\text{a}{}^1\text{(}\text{1}\text{b}\text{) =}\text{a}{}^1\text{(b)}\text{b}{}^{\mathrm{z}}$. For b = 1, δ(z) presents a minimum, and diverges for z → 1 and z → ∞ (this contrasts with the b≠1 case).     

Scaling and universality in the optics of disordered exciton chains

The joint probability distribution of exciton energies and transition dipole moments determines a variety of optical observables in disordered exciton systems. We demonstrate numerically that this distribution obeys a one-parameter scaling, originating from the fact that both the energy and the dipole moment are determined by the number of coherently bound molecules. A universal underlying distribution is found, which is identical for uncorrelated Gaussian disorder in the molecular transition energies or in the intermolecular transfer interactions. The universality breaks down for disorder in the transfer interactions resulting from variations in the molecular positions. We suggest the possibility to probe the joint distribution by means of single-molecule spectroscopy.     

New universality classes in “Percolative” dynamics

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.     

Residual conductance fluctuations of tiny disordered conductors

Conductances of the equivalent samples differ randomly (Stone 1985). At zero temperature these fluctuations were found to be of the order ofe ²/h for samples of arbitrary size and form (Altshuler 1985; Lee and Stone 1985). Experimentally such fluctuations manifest themselves as e.g. the reproducible aperiodic oscillations of the given sample conductance in magnetic field (Webbet al 1985; Stone 1985). These oscillations can be understood in terms of the correlation function (Lee and Stone 1985; Altshuler and Khmel’nitskii 1985) of the conductances in different fields. The characteristic field scale of the aperiodic oscillations corresponds to the unit magnetic flux through the sample. Conductance fluctuations decrease with the growth of temperature if the sample size is larger than the diffusion length within the timeh/T (Stone 1985; Lee and Stone 1985; Webbet al 1984, 1985; Altshuler and Khmel’nitskii 1985). These fluctuations are proportional toT ^?1/4,T ^?1/2 logT, andT ^?1/2 in the 3-d, 2-d and 1-d cases, respectively (Altshuler and Khmel’nitskii 1985) (the experiments of Webbet al 1984, 1985 correspond to the latter case). Random potential in tiny samples breaks all space symmetries. All effects which are forbidden in the average by these symmetries should manifest themselves by (i) conductance anisotropy, (ii) its dependence on the electric field direction and (iii) giant generation of the second harmonic in the granular sample under light radiation (Altshuler and Khmel’nitskii 1985). Conductance changes aperiodically with variation of the chemical potential (Lee and Stone 1985). Because of this thermopower fluctuations are much larger than its average value (Altshuler and Khmel’nitskii 1985). Conductance fluctuations are very sensitive to the random impurity potential variations (Altshuler and Spivak 1985). For instance, the change of the film conductance due to the shift ofone impurity isfinite for any film size. This effect can be used for the super flow impurity diffusion investigations. Variations of the localized spins realization in spin glasses change the conductance. This can explain (Altshuler and Spivak 1985) the conductance dependence on the magnetic field direction observed by Webbet al (1984, 1985).     

The dynamical origin of the universality classes of spatiotemporal intermittency

Two universality classes of spatiotemporal intermittency are seen in the spreading and non-spreading regimes of the sine circle map lattice, spatiotemporal intermittency of the directed percolation class, and spatial intermittency, not of the DP class, where the temporal behavior is regular. The transition between the two classes maps to a probabilistic to deterministic transition of the equivalent cellular automaton of the model, and is seen to have its dynamic origin in an attractor-widening crisis.