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Register a new userLevy ratchets with dichotomic random flashing
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Added by
Alejandro B. Kolton
Publication date
2011
fields
Physics
and research's language is
English
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Additive symmetric Levy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such Levy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the Levy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static Levy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive Levy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.
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We consider a randomly flashing ratchet, where the potential acting can be switched to another at random. Using coupled Fokker-Planck equations, we formulate the expressions of quantities measuring dynamics and thermodynamics. Extended numerical calculations present how the potential landscapes and the transitions affect the motility and energetics. Load-dependent velocity and energetic efficiency of motor proteins, kinesin and dynein, further exemplify the randomly flashing ratchet model. We also discuss the system with two shifted sawtooth potentials.
We develop a novel method based in the sparse random graph to account the interplay between geometric frustration and disorder in cluster magnetism. Our theory allows to introduce the cluster network connectivity as a controllable parameter. Two types of inner cluster geometry are considered: triangular and tetrahedral. The theory was developed for a general, non-uniform intra-cluster interactions, but in the present paper the results presented correspond to uniform, anti-ferromagnetic (AF) intra-clusters interactions $J_{0}/J$. The clusters are represented by nodes on a finite connectivity random graph, and the inter-cluster interactions are random Gaussian distributed. The graph realizations are treated in replica theory using the formalism of order parameter functions, which allows to calculate the distribution of local fields and, as a consequence, the relevant observable. In the case of triangular cluster geometry, there is the onset of a classical Spin Liquid state at a temperature $T^{*}/J$ and then, a Cluster Spin Glass (CSG) phase at a temperature $T_{f}/J$. The CSG ground state is robust even for very weak disorder or large negative $J_{0}/J$. These results does not depend on the network connectivity. Nevertheless, variations in the connectivity strongly affect the level of frustration $f_{p}=-Theta_{CW}/T_{f}$ for large $J_{0}/J$. In contrast, for the non-frustrated tetrahedral cluster geometry, the CSG ground state is suppressed for weak disorder or large negative $J_{0}/J$. The CSG boundary phase presents a re-entrance which is dependent on the network connectivity.
We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial ``sign transition using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments $<J^n>$ always determine, uniquely, the probability distribution $P(J)$. We also derive, exactly, the moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations ($nto 0$) to obtain $<ln J>$ for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting ``solitonic structures that propagate as a function of $p$. Finally, we derive the exact probability distribution for path sums $J$ up to length L=64 for all sign probabilities.
Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a sub-thermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. Here we quantify these notions by identifying a universal, subleading logarithmic contribution to the volume law entanglement entropy: $S^{(2)}(A)=kappa L_A+frac{3}{2}log L_A$ which bounds the mutual information between a qudit inside region $A$ and the rest of the system. Specifically, we find the power law decay of the mutual information $I({x}:bar{A})propto x^{-3/2}$ with distance $x$ from the regions boundary, which implies that measuring a qudit deep inside $A$ will have negligible effect on the entanglement of $A$. We obtain these results by mapping the entanglement dynamics to the imaginary time evolution of an Ising model, to which we can apply field-theoretic and matrix-product-state techniques. Finally, exploiting the error-correction viewpoint, we assume that the volume-law state is an encoding of a Page state in a quantum error-correcting code to obtain a bound on the critical measurement strength $p_{c}$ as a function of the qudit dimension $d$: $p_{c}log[(d^{2}-1)({p_{c}^{-1}-1})]le log[(1-p_{c})d]$. The bound is saturated at $p_c(drightarrowinfty)=1/2$ and provides a reasonable estimate for the qubit transition: $p_c(d=2) le 0.1893$.
We provide a simple and predictive random-matrix framework that naturally generalizes Pages law for ergodic many-body systems by incorporating a finite entanglement localization length. By comparing a highly structured one-dimensional model to a completely unstructured model and a physical system, we uncover a remarkable degree of universality, suggesting that the effective localization length is a universal combination of model parameters up until it drops down to the microscopic scale.
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