Lattice Magnetic Walks

Sums of walks for charged particles (e.g. Hofstadter electrons) on a square lattice in the presence of a magnetic field are evaluated. Returning loops are systematically added to directed paths to obtain the unrestricted propagators. Expressions are obtained for special values of the magnetic flux-per-plaquette commensurate with the flux quantum. For commensurate and incommensurate values of the flux, the addition of small returning loops does not affect the general features found earlier for directed paths. Lattice Green's functions are also obtained for staggered flux configurations encountered in models of high-Tc superconductors.Comment: 31 pages, Plain TeX, 2 figures (available upon request), UR-CM-93-10-1

Maximal Height Scaling of Kinetically Growing Surfaces

The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L} \sim L^{\alpha}$. For large values its distribution obeys $\log{P(h^{*}_{L})} \sim -A({h^{*}_{L}}/L^{\alpha})^{a}$, charaterized by the exponential-tail exponent $a$. In the early-time regime where the roughness grows as $t^{\beta}$, we find $h^{*}_{L} \sim t^{\beta}[\ln{L}-({\beta\over \alpha})\ln{t} + C]^{1/b}$ where either $b=a$ or $b$ is the corresponding exponent of the velocity distribution. These properties are derived from scaling and extreme-values arguments. They are corroborated by numerical simulations and supported by exact results for surfaces in 1D with the asymptotic behavior of a Brownian path.Comment: One reference added. Minor stylistic changes in the abstarct and the paper. 4 pages, 3 figure

Localization and Quantum Percolation

Electronic wave functions are studied on dilute lattices, at dimensionalities 1⩽d⩽8. Generalized average inverse participation ratios are expanded in powers of the bond concentration, p. Dlog Padé approximants indicate that these ratios diverge as (pq−p)-γq, signaling the appearance of extended states for p\u3epq. These Anderson transitions occur above classical percolation. No divergence is detected at d=2. These results are consistent with the existence of localized states at the center of the band

Fractal-Mound Growth of Pentacene Thin Films

The growth mechanism of pentacene film formation on SiO2 substrate was investigated with a combination of atomic force microscopy measurements and numerical modeling. In addition to the diffusion-limited aggregation (DLA) that has already been shown to govern the growth of the ordered pentacene thin films, it is shown here for the first time that the Schwoebel barrier effect steps in and disrupts the desired epitaxial growth for the subsequent layers, leading to mound growth. The terraces of the growing mounds have a fractal dimension of 1.6, indicating a lateral DLA shape. This novel growth morphology thus combines horizontal DLA-like growth with vertical mound growth.Comment: (5 Figures). Accepted to PR B (in print

Continuous Versus First Order Transitions in Compressible Diluted Magnets

The interplay between disorder and compressibility in Ising magnets is studied. Contrary to pure systems in which a weak compressibility drives the transition first order, we find from a renormalization group analysis that it has no effect on disordered systems which keep undergoing continuous transition with rigid random-bond Ising model critical exponents. The mean field calculation exhibits a dilution-dependent tricritical point beyond which, at stronger compressibility the transition is first order. The different behavior of XY and Heisenberg magnets is discussed.Comment: 16 pages, latex, 2 figures not include

Scaling Behavior of Cyclical Surface Growth

The scaling behavior of cyclical surface growth (e.g. deposition/desorption), with the number of cycles n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents inherited from the dominant process while the effective amplitudes are determined by both. Relevant non-linear effects in the primary processes may remain so or be rendered irrelevant. Numerical simulations for several pairs of generic primary processes confirm these conclusions. Experimental results for the surface roughness during cyclical electrodeposition/dissolution of silver show a power-law dependence on n, consistent with the scaling description.Comment: 2 figures adde

Kinetic Roughening in Surfaces of Crystals Growing on Disordered Substrates

Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature (low-noise) superrough phase with a continuously varying dynamic exponent z>2 and a non-linear response. In the presence of the KPZ nonlinearity the disorder causes the lattice efects to decay on large scales with an intermediate crossover behavior. The mobility of the rough surface hes a complex dependence on the temperature and the other physical parameters.Comment: 13 pages, 2 figures (not included). Submitted to Phys. Rev. Letts. Use Latex twic

Roughness Scaling in Cyclical Surface Growth

The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical processes by substituting the time by the number of cycles $n$. The roughness is predicted to grow as $n^{\beta}$ where $\beta$ is the cyclical growth exponent. The roughness saturates to a value which scales with the system size $L$ as $L^{\alpha}$, where $\alpha$ is the cyclical roughness exponent. The relations between the cyclical exponents and the corresponding exponents of the primary processes are studied. Exact relations are found for cycles composed of primary linear processes. An approximate renormalization group approach is introduced to analyze non-linear effects in the primary processes. The analytical results are backed by extensive numerical simulations of different pairs of primary processes, both linear and non-linear. Experimentally, silver surfaces are grown by a cyclical process composed of electrodeposition followed by 50% electrodissolution. The roughness is found to increase as a power-law of $n$, consistent with the scaling behavior anticipated theoretically. Potential applications of cyclical scaling include accelerated testing of rechargeable batteries, and improved chemotherapeutic treatment of cancerous tumors

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers

The center-bound excitonic diffusion on dendrimers subjected to several types of non-homogeneous funneling potentials, is considered. We first study the mean-first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations $g$, to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature $T$ is lowered. This is a transition from a high-$T$ regime in which all paths contribute to the MFPT to a low-$T$ regime in which only a few of them do. We further explore the funneling within a realistic non-linear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with $g$ but crosses-over, beyond a molecular-specific and $T$-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the {\it small world} model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power-law or to a logarithmic scaling with $g$, depending on the strength of the funneling force.Comment: 13 pages, 9 figure