Coulomb blockade and Non-Fermi-liquid behavior in quantum dots

The non-Fermi-liquid properties of an ultrasmall quantum dot coupled to a lead and to a quantum box are investigated. Tuning the ratio of the tunneling amplitudes to the lead and box, we find a line of two-channel Kondo fixed points for arbitrary Coulomb repulsion on the dot, governing the transition between two distinct Fermi-liquid regimes. The Fermi liquids are characterized by different values of the conductance. For an asymmetric dot, spin and charge degrees of freedom are entangled: a continuous transition from a spin to a charge two-channel Kondo effect evolves. The crossover temperature to the two-channel Kondo effect is greatly enhanced away from the local-moment regime, making this exotic effect accessible in realistic quantum-dot devices.Comment: 5 figure

Characteristics of reaction-diffusion on scale-free networks

We examine some characteristic properties of reaction-diffusion processes of the A+A->0 type on scale-free networks. Due to the inhomogeneity of the structure of the substrate, as compared to usual lattices, we focus on the characteristics of the nodes where the annihilations occur. We show that at early times the majority of these events take place on low-connectivity nodes, while as time advances the process moves towards the high-connectivity nodes, the so-called hubs. This pattern remarkably accelerates the annihilation of the particles, and it is in agreement with earlier predictions that the rates of reaction-diffusion processes on scale-free networks are much faster than the equivalent ones on lattice systems

Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents

We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for large times. However, the decay exponent varies continuously as a function of the probability of which particle, the hopping one or the target, survives in the reaction. These results suggest that diffusion-limited reactions subject to drift do not fall into a limited number of universality classes.Comment: 10 pages, tex, 3 figures, also available upon reques

Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A

Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the distribution of distances between nearest particles. However, a full characterization of a particle system is only provided by the infinite hierarchy of multiple-point density correlation functions. We derive an exact description of the full hierarchy of correlation functions for the diffusion-limited irreversible coalescence process A + A -> A.Comment: 4 pages, 2 figures (postscript). Typeset with Revte

A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings, with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some other minor changes, to conform with final for

Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation

We investigate a non-equilibrium reaction-diffusion model and equivalent ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The exact energy spectrum and the n-point hole correlations are considered with the help of the Jordan-Wigner fermionization and the inter-particle distribution function method. Although the Hamiltonian has no explicit translational symmetry, the translational invariance is recovered after long time due to the diffusion. We see the scaling relations for the concentration and the two-point function in finite size analysis.Comment: 7 pages, LaTeX file, to appear in J. Phys. A: Math. and Ge

Exactly solvable models through the empty interval method, for more-than-two-site interactions

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E_n(t)$'s, the probability that $n$ consecutive sites are empty at time $t$. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbor interaction is studied.Comment: 19 pages, LaTeX2

Time evolution of the reaction front in a subdiffusive system

Using the quasistatic approximation, we show that in a subdiffusion--reaction system the reaction front $x_{f}$ evolves in time according to the formula $x_{f} \sim t^{\alpha/2}$, with $\alpha$ being the subdiffusion parameter. The result is derived for the system where the subdiffusion coefficients of reactants differ from each other. It includes the case of one static reactant. As an application of our results, we compare the time evolution of reaction front extracted from experimental data with the theoretical formula and we find that the transport process of organic acid particles in the tooth enamel is subdiffusive.Comment: 18 pages, 3 figure

Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A->0 and A+B->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

Annihilation of Immobile Reactants on the Bethe Lattice

Two-particle annihilation reaction, A+A -> inert, for immobile reactants on the Bethe lattice is solved exactly for the initially random distribution. The process reaches an absorbing state in which no nearest-neighbor reactants are left. The approach of the concentration to the limiting value is exponential. The solution reproduces the known one-dimensional result which is further extended to the reaction A+B -> inert.Comment: 12 pp, TeX (plain