Logarithmic Behavior Research Articles

Measurement-driven entanglement transition in hybrid quantum circuits

In this paper we continue to explore "hybrid" quantum circuit models in one-dimension with both unitary and measurement gates, focussing on the entanglement properties of wavefunction trajectories at long times, in the steady state. We simulate a large class of Clifford circuits, including models with or without randomness in the unitary gates, and with or without randomness in the locations of measurement gates, using stabilizer techniques to access the long time dynamics of systems up to 512 qubits. In all models we find a volume law entangled phase for low measurement rates, which exhibits a sub-dominant logarithmic behavior in the entanglement entropy, S_A = {\alpha} ln |A| + s|A|, with sub-system size |A|. With increasing measurement rate the volume law phase is unstable to a disentangled area law phase, passing through a single entanglement transition at a critical rate of measurement. At criticality we find a purely logarithmic entanglement entropy, S_A = {\alpha}(p_c) ln|A|, a power law decay and conformal symmetry of the mutual information, with exponential decay off criticality. Various spin-spin correlation functions also show slow decay at criticality. Critical exponents are consistent across all models, indicative of a single universality class. These results suggest the existence of an effective underlying statistical mechanical model for the entanglement transition. Beyond Clifford circuit models, numerical simulations of up to 20 qubits give consistent results.

Curvature Sensor Based on a Long-Period Grating in a Fiber Ring Resonator Interrogated by an OTDR

The proposed technique demonstrates a fiber ring resonator interrogated by an optical time domain reflectometer (OTDR), for intensity sensing. By using this methodology, a cavity round trip time of 2.85 μs was obtained. For a proof of concept, a long-period grating was inserted in the resonant cavity operating as a curvature sensing device. A novel signal processing approach was outlined, regarding to the logarithmic behavior of the OTDR. Through analyzing the experimental results, an increase in the measured sensitivities was obtained by increasing applied bending. With curvatures performed from 1.8 m−1 to 4.5 m−1, the sensitivity values ranged from 2.94 dB·km−1 to 5.15 dB·km−1. In its turn, the sensitivities obtained presented a linear behavior when studied as a function of the applied curvature, following a slope of 0.86×10−3 dB. The advantages of applying this technique were also discussed, demonstrating two similar fiber rings multiplexed in a series of configurations.

A universal velocity profile for smooth wall pipe flow

The most important unanswered questions in turbulence regard the nature of turbulent flow in the limit of infinite Reynolds number. The Princeton superpipe (PSP) data comprise 26 velocity profiles that cover three orders of magnitude in the Reynolds number from $Re=19\,639$, to $Re=20\,088\,000$ based on pipe radius and pipe centreline velocity. In this paper classical mixing length theory is combined with a new mixing length model of the turbulent shear stress to solve the streamwise momentum equation and the solution is used to approximate the PSP velocity profiles. The model velocity profile is uniformly valid from the wall to the pipe centreline and comprises five free parameters that are selected through a minimization process to provide an accurate approximation to each of the 26 profiles. The model profile is grounded in the momentum equation and allows the velocity derivative, Reynolds shear stress and turbulent kinetic energy production to be studied. The results support the conclusion that logarithmic velocity behaviour near the wall is not present in the data below a pipe Reynolds number somewhere between $Re=59\,872$, and $Re=87\,150$. Above $Re=87\,150$, the data show a very clear, nearly logarithmic, region. But even at the highest Reynolds numbers there is still a weak algebraic dependence of the intermediate portion of the velocity profile on both the near-wall and outer flow length scales. One of the five parameters in the model profile is equivalent to the well-known Kármán constant, $k$. The parameter $k$ increases almost monotonically from $k=0.4034$ at $Re=87\,150$ to $k=0.4190$ at $Re=20\,088\,000$, with an average value, $k=0.4092$. The variation of the remaining four model parameters is relatively small and, with all five parameters fixed at average values, the model profile reproduces the entire velocity data set and the wall friction reasonably well. With optimal values of the parameters used for each model profile, the fit to the PSP survey data is very good. Transforming the model velocity profile using the group, $u/u_{0}\rightarrow ku/u_{0}$, $y^{+}\rightarrow ky^{+}$ and $R_{\unicode[STIX]{x1D70F}}\rightarrow kR_{\unicode[STIX]{x1D70F}}$ where $R_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, leads to a reduced expression for the velocity profile. When the reduced profile is cast in outer variables, the physical velocity profile is expressed in terms of $\ln (y/\unicode[STIX]{x1D6FF})$ and a new shape function $\unicode[STIX]{x1D719}(y/\unicode[STIX]{x1D6FF})$. In the limit of infinite Reynolds number, the velocity profile asymptotes to plug flow with a vanishingly thin viscous wall layer and a continuous derivative everywhere. The shape function evaluated at the pipe centreline is used to produce a new friction law with an additive constant that depends on the Kármán constant and a wall damping length scale.

Prior physicochemical stress exposures and subsequent UV-C resistance of E. coli O157:H7 in coconut liquid endosperm

This study determined the effects of prior exposures to individual acid, desiccation, and heat stress, and all their possible simultaneous combinations, on the subsequent ultraviolet-C (UV-C) inactivation kinetics of E. coli O157:H7 in a coconut liquid endosperm suspending medium. Sublethal injury rates determined in the cells after stress exposure and acclimation in the suspending medium ranged from 0.00% (acid stressed) to 84.24% (desiccation+heat stressed). Regardless of the previous stress to which cells were exposed, a logarithmic linear inactivation behavior was observed in the cells. The decimal reduction energy (DUV-C) of the stressed cells ranged from 152.17mJ/cm2 (acid+desiccation+heat stressed) to 209.81mJ/cm2 (acid+heat stressed). No apparent relationship was observed between % injury and DUV-C values possibly because the nature of the injury the cells incurred after exposures to the stresses was not determined. Cells previously exposed to the combined acid and heat stress exhibited the highest D ratio (DUV-C stressed/ DUV-C control), indicative of heterologous adaptation that resulted in cells 30% more resistant towards UV-C. The results established in this study contribute in further understanding the utility and limitations of UV-C radiation as an alternative nonthermal processing technique for fruit juices.

Memory Distance for Interfacial Chemical Bond-Induced Friction at the Nanoscale.

Macroscale rate and state friction (RSF) laws include a memory distance, Dc, which is considered to be the distance required for a population of frictional contacts to renew itself via slip, counteracting the effects of aging in slow or static contact. This concept connects static friction and kinetic friction. Here, we use atomic force microscopy to study interfacial chemical bond-induced kinetic friction and the memory distance at the nanoscale for single silica-silica nanocontacts. We observe a logarithmic trend of decreasing friction with sliding velocity (i.e., velocity-weakening) at low velocities and a transition to increasing friction with velocity at higher velocities (i.e., velocity-strengthening). We propose a physically based kinetic model for the nanoscale memory effect, the "activation-passivation loop" model, which accounts for the activation and passivation of chemical reaction sites and the formation of new chemical bonds from dangling bonds during sliding. In the model, we define the memory distance to be the average sliding distance that accrues before an activated reaction site becomes passivated. Results from numerical simulations based on this model match experimental friction data well in the velocity-weakening regime and show that Dc is sensitive to the surface chemistry, and nearly independent of sliding velocity. The simulations also show values of Dc that are consistent with those obtained from the experiments. We propose a semiquantitative physical explanation of the observed logarithmic velocity-weakening behavior based on the conservation of the number of interfacial bonds during sliding. We also extract from the experimental data physically reasonable values of the energy barriers to the activation of reaction sites. Our results provide one possible physical mechanism for the nanoscale memory distance.

Revisión y análisis de la corrosión a largo plazo de recubrimientos basados en aleaciones de Zinc-Aluminio-Magnesio, como alternativa a los recubrimientos tradicionales basados en cinc, para canalizaciones eléctricas

Se presenta una revisión del estado del arte en lo que se refiere a recubrimientos metálicos basados en aleaciones de cinc-aluminio-magnesio, para la protección frente a la corrosión, de sistemas metálicos de canalización eléctrica, como alternativa a los tradicionales recubrimientos metálicos basados en cinc. Esta revisión contempla su evolución en el tiempo, las distintas calidades y designaciones existentes en el mercado, su estructura y composición, la normativa internacional que los regula, las principales marcas comercializadas y sus características, los principales fabricantes de canalización eléctrica que ofrecen dichas aleaciones, y finalmente, un análisis de la resistencia a la corrosión sobre la base de ensayos de campo y ensayos de corrosión acelerada, los cuales han formado igualmente parte de esta investigación. A partir de dicho análisis, se ha determinado un modelo matemático para la estimación de la corrosión a largo plazo, en el que se evidencia el comportamiento logarítmico de la función corrosión-tiempo. Con todo y con ello, el artículo pretende, por una parte, ser un compendio de los aspectos clave a considerar en este tipo de aleaciones y por otra, dar soporte al ingeniero de proyectos en la toma de decisión, que supone la elección de este tipo de recubrimiento frente a los recubrimientos basados en zinc, proporcionándole los aspectos más relevantes a considerar, de tal forma que se asegure el cumplimiento de las especificaciones del proyecto en lo que a resistencia a la corrosión se refiere.

One Dimensional Phase-Ordering in the Ising Model with Space Decaying Interactions

The study of the phase ordering kinetics of the ferromagnetic one-dimensional Ising model dates back to 1963 for non conserved order parameter (NCOP) and to 1991 for conserved order parameter (COP). The case of long range interactions $J(r)$ has been widely studied at equilibrium but their effect on relaxation is a much less investigated field. Here we make a detailed numerical and analytical study of both cases, NCOP and COP. Many results are valid for any positive, decreasing coupling $J(r)$, but we focus specifically on the exponential case, $J_{exp}(r)=e^{-r/R}$ with varying $R>0$, and on the integrable power law case, $J_{pow}(r) =1/r^{1+\sigma}$ with $\sigma > 0$. We find that the {\it asymptotic} growth law $L(t)$ is the usual algebraic one, $L(t)\sim t^{1/z}$, of the corresponding model with nearest neighborg interaction ($z_{NCOP}=2$ and $z_{COP}=3$) for all models except $J_{pow}$ for small $\sigma$: in the non conserved case when $\sigma\le 1$ ($z_{NCOP}=\sigma+1$) and in the conserved case when $\sigma\to 0^+$ ($z_{COP}=4\beta+3$, where $\beta=1/T$ is the inverse of the absolute temperature). The models with space decaying interactions also differ markedly from the ones with nearest neighbors due to the presence of many long-lasting preasymptotic regimes, such as an exponential mean-field behavior with $L(t)\sim e^{t}$, a ballistic one with $L(t)\sim t$, a slow (logarithmic) behavior $L(t)\sim \ln t$ and one with $L(t)\sim t^{1/\sigma+1}$. All these regimes and their validity ranges have been found analytically and verified in numerical simulations. Our results show that the main effect of the conservation law is a strong slowdown of COP dynamics if interactions have an extended range. Finally, we compare the Ising model at hand with continuum approaches based on a Ginzburg-Landau free energy.

Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow

The logarithmic law of the mean velocity is considered a fundamental feature of wall-bounded turbulent flows. The logarithmic velocity law is used widely to model the near-wall turbulence and to predict skin friction. Although classical scaling theory has been used to verify that the velocity profile in the overlap region follows the logarithmic behavior asymptotically, and thus recent experiments have attempted to assess the logarithmic law in large-scale facilities, there is a lack of understanding of the structural basis for the logarithmic law. Here, we show the logarithmic law by extracting the wall-attached structures of the streamwise velocity fluctuations through direct numerical simulation of turbulent pipe flow. The wall-attached structures exhibit self-similar behavior according to their height and have an inverse-scale population density, reminiscent of Townsend’s attached-eddy hypothesis. The wall-normal distributions of the streamwise velocity within the identified structures are conditionally averaged with respect to their height. The velocity profile is reconstructed by superimposing the velocity distributions of the objects that follow the inverse-scale population density. The indicator function of the resulting velocity profile shows a complete plateau for the high-speed structures due to their higher local Reynolds number. These findings provide strong evidence that the identified coherent structures are directly related to the logarithmic velocity law and serve as the structural basis for the inertial layer.

Surface behavior of α-chymotrypsinogen A in aqueous solutions at 298.15 K

In this work, a systematic study concerning the surface properties of α-chymotrypsinogen A in water and aqueous solutions of ethylene glycol, glycerol, meso-erythritol, D-sorbitol and myo-inositol at 298.15 K is developed to obtain a further insight of the stabilizing effect of polyols on the conformation of proteins.The results were used to establish if there is a general correlation between the surface tension of the solvent and the change in the denaturation temperature. Evolution of surface tension with time was used to obtain information on the adsorption process of the protein on the air-liquid interface in water and in the polyol solutions.The results show that there is a clear correlation between the surface tension of the solvent and the change in the denaturation temperature of the protein.The experimental adsorption isotherms of α-chymotrypsinogen in the air-liquid interface in water and in the presence of polyols were determined from surface tension measurements. Experimental data were fitted to semiempirical models that describe the adsorption process. They show that the adsorption process is well represented by a semi-empirical model that describes the process using three steps: a first step controlled by diffusion, a second step that presents a logarithmic behavior and represents the penetration rate of the protein at the air-water interface and a last step that also follows a logarithmic behavior and corresponds to the rate of rearrangement of the protein at the air-water interface.

Pressure and spanwise velocity fluctuations in turbulent channel flows: Logarithmic behavior of moments and coherent structures

We study the logarithmic behavior of the pressure variance (p+2) from the datasets obtained from direct numerical simulations of turbulent channel flow for friction Reynolds number Reτ up to 4000. The higher-order moments of p were found to follow logarithmic behaviors at the same distances from the wall where (p+2) shows its log profile. The same results have been confirmed for the spanwise velocity fluctuations w at the same Reynolds numbers, with both p and w following a super-Gaussian behavior. The minimum Reynolds number for (p+2) and (w+2) log profiles to appear is Reτ≈500, where flow structures O(h) or less were found to significantly contribute to these profiles. The configuration of the hairpin eddy structures obtained from the conditional sampling at different wall-normal locations showed a strong link between p and w fluctuations. Positive pressure fluctuations are located between the legs of the hairpin eddy, while the negative pressure fluctuations are consistent with the head part of the hairpin eddy. Positive and negative spanwise velocity fluctuations are strongly positioned with the legs of the hairpin eddy, consistent with the counter-rotating motion resulting from the eddy legs. The structures were also found to be geometrically self-similar such that their length and their width increase linearly with the distance from the wall.

Finite-temperature entanglement negativity of free fermions

The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper (Shapourian et al 2017 Phys. Rev. B 95 165101). In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.

Area law and universality in the statistics of subsystem energy

We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in its ground state and then, take a subdomain of this system with natural truncated Hamiltonian. Since the total Hamiltonian does not commute with the truncated Hamiltonian, the subsystem can be in one of its eigenenergies with different probabilities. Using the fact that the global energy eigenstates are locally close to diagonal in the local energy eigenbasis, we argue that the R\'enyi entropy of these probabilities follows an area law for the gapped systems. When the system is at the critical point, the R\'enyi entropy follows a logarithmic behavior with a universal coefficient. Consequently, our quantity not only detects the phase transition but also determines the universality class of the critical point. Moreover we show that the largest defined probabilities are very close to the biggest Schmidt coefficients. We quantify this by defining a {\it{truncated}} Shannon entropy which its value is almost indistinguishable from the {\it{truncated}} von Neumann entanglement entropy. Compare to the entanglement entropy, our quantity has the advantage of being associated to a natural observable (subsystem Hamiltonian) that can be defined (and probably measured) easily for all the short-range interacting systems. We support our arguments by detailed numerical calculations performed on the transverse field XY-chain.

In Silico Evolution of Biochemical Log-Response.

Numerous biological systems are known to harbor a form of logarithmic behavior, from Weber's law to bacterial chemotaxis. Such a log-response allows for sensitivity to small relative variations of biochemical inputs over a large range of concentration values. Here we use a genetic algorithm to evolve biochemical networks displaying a logarithmic response. A quasi-perfect log-response implemented by the same core network evolves in a convergent way across our different in silico replications. The best network is able to fit a logarithm over 4 orders of magnitude with an accuracy of the order of 1%. At the heart of this network, we show that a logarithmic approximation may be implemented with one single nonlinear interaction, that can be interpreted either as multisite phosphorylations or as a ligand induced multimerization. We provide an analytical explanation for the effect and exhibit constraints on parameters. Biological log-response might thus be easier to implement than usually assumed.

Dynamical analogues of rank distributions

We present an equivalence between stochastic and deterministic variable approaches to represent ranked data and find the expressions obtained to be suggestive of statistical-mechanical meanings. We first reproduce size-rank distributions N(k) from real data sets by straightforward considerations based on the assumed knowledge of the background probability distribution P(N) that generates samples of random variable values similar to real data. The choice of different functional expressions for P(N): power law, exponential, Gaussian, etc., leads to different classes of distributions N(k) for which we find examples in nature. Then we show that all of these types of functions can be alternatively obtained from deterministic dynamical systems. These correspond to one-dimensional nonlinear iterated maps near a tangent bifurcation whose trajectories are proved to be precise analogues of the N(k). We provide explicit expressions for the maps and their trajectories and find they operate under conditions of vanishing or small Lyapunov exponent, therefore at or near a transition to or out of chaos. We give explicit examples ranging from exponential to logarithmic behavior, including Zipf’s law. Adoption of the nonlinear map as the formalism central character is a useful viewpoint, as variation of its few parameters, that modify its tangency property, translate into the different classes for N(k).

Radial symmetry of non-maximal entire solutions of a bi-harmonic equation with exponential nonlinearity

AbstractWe study radial symmetry of entire solutions of the equation0.1$$\Delta ^2u = 8(N-2)(N-4)e^u\quad {\rm in}\;R^N\;\;(N \ges 5).$$It is known that (0.1) admits infinitely many radially symmetric entire solutions. These solutions may have either a (negative) logarithmic behaviour or a (negative) quadratic behaviour at infinity. Up to translations, we know that there is only one radial entire solution with the former behaviour, which is called ‘maximal radial entire solution’, and infinitely many radial entire solutions with the latter behaviour, which are called ‘non-maximal radial entire solutions’. The necessary and sufficient conditions for an entire solutionuof (0.1) to be the maximal radial entire solution are presented in [7] recently. In this paper, we will give the necessary and sufficient conditions for an entire solutionuof (0.1) to be a non-maximal radial entire solution.

Nanocomposite membrane based on SPEEK as a perspectives application in electrochemical hydrogen compressor

Achieving favourable proton exchange membrane characteristics such as proton conduction, mechanical properties and hydrogen crossover is one of the main challenges in development of Electrochemical Hydrogen Compressor (EHC) systems for improving energy consumption. This work demonstrates three different in-house fabricated membranes based on Sulphonated poly (ether-ether ketone, SPEEK). The first membrane is an unmodified membrane ([S70]), second membrane ([S70/HNT15], 15 % wt/wt) was modified with a nanoclay (Halloysite Nanotubes, HNT), and last membrane is Halloysite nanotubes impregnated with Phosphotungstic Acid ([S70/(PWA/HNT30)15]). These membranes show different hydrogen crossover rate, with the [S70] membrane exhibiting 3.873 × 10−08 mol bar−1s−1cm−2 whereas the [S70/HNT15] and [S70/(PWA/HNT30)15] nanocomposite membranes show rates of 7.296 × 10−10 and 9.103 × 10−10 mol bar−1 s−1 cm−2, respectively. Furthermore, unmodified membrane presented quadratic behaviours with increased pressure in cathodic compartment, whereas nanocomposite membranes exhibit a logarithmic behaviour. For another hand, extrapolation data show that unconventional nanocomposites membranes present a low energy consumption at high pressures, which is promising for potential candidates for use in EHC systems.

Mod-Gaussian Convergence for Random Determinants

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, GOE, Laguerre, uniform Gram and Jacobi beta ensembles and random characteristic polynomials evaluated at 1 for matrices in the circular and circular Jacobi beta ensembles. We use the framework of mod-Gaussian convergence to provide quantitative estimates of their logarithmic behavior, as the size of the ensemble grows to infinity. We establish central limit theorems, Berry–Esseen bounds, moderate deviations and local limit theorems. Furthermore, we identify the scale at which the validity of the Gaussian approximation for the tails breaks. With the exception of the Gaussian ensemble, all the results are obtained for a continuous choice of the Dyson parameter, that is, for general $$\beta >0$$ . The proofs rely on explicit computations which are possible thanks to closed product formulas of the Laplace transforms.

FERTILIZATION EFFECTS ON EUCALYPTUS PELLITA F. MUELL PRODUCTIVITY IN THE COLOMBIAN ORINOCO REGION

ABSTRACT The Orinoco region, is the one with the largest area for forest development. Nonetheless, some of its soils are acid and characterized by low fertility levels, which has considerably limited plantation productivity. Therefore, this study aimed at assessing the effects of soil fertilizing and liming by using phosphorus and potassium on 34-month-old Eucalyptus pellita productivity. Tests have been carried out at: Villanueva, Casanare; Puerto Lopez, Meta and La Primavera, Vichada, under a random block design with a factor arrangement of 3x3x3, equivalent to: 0, 1 and 3 Mg ha-1 of dolomitic lime (LIME); 30, 75 and 120 kg ha-1 of P (P2O5) as well as 60, 120 and 180 kg ha-1 of K (K2O). Timber productivity volume was assessed 34 months after planting, obtaining significant differences. In Puerto Lopez, LIME effect on E. pellita growth followed a simple linear model, whereas a logarithmic behavior was observed in La Primavera and Villanueva. P2O5 effect (p<0.01) on timber volume was observed only in La Primavera, following a square-root model. K2O did not have a significant effect (p>0.05) on E. pellita growth. The results obtained indicate the positive effect on E. pellita growth in the three areas of study by using doses of approximately 1 Mg ha-1 of lime; and 120 kg ha-1 of P2O5 in La Primavera.

Wall-attached structures of velocity fluctuations in a turbulent boundary layer

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

Energy loss at zero temperature from extremal black holes

Using the AdS/CFT correspondence, we probe the extremal black holes by studying the energy loss of a moving heavy point particle in a strongly-coupled boundary field theory at zero temperature and finite charge density. We first consider the extremal AdS-Reissner-Nordström (AdSRN) background black hole in the bulk and find an analytic solution of drag force which depends on the finite charge density of the boundary field theory. By studying the near horizon geometry of trailing string in the bulk, one finds the IR divergency does not show the logarithmic behavior. This result would be a general property of extremal backgrounds. We also extend our study to the extremal backgrounds with vanishing entropy density in appropriate extremal limits. After studying the Langevin coefficients, it is shown that in the extremal black hole backgrounds the longitudinal Langevin diffusion coefficient along the semiclassical string motion is larger compared to that of the transverse direction.