Fano Factor Research Articles

Current cross correlations in a quantum Hall collider at filling factor two

We use the nonequilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall edge states at filling factor $\ensuremath{\nu}=2$. The current cross correlations and Fano factor, which carry the information about the exclusion statistics, are calculated. It is shown that both these quantities have a nonanalytical dependence on the source transparency, which scales as $log(1/{T}_{s})$ at small ${T}_{s}\ensuremath{\ll}1$. This is a consequence of electron-electron interactions in the outgoing nonequilibrium states of the collider.

Waiting time distribution and current correlations via a Majorana single-charge transistor

We investigate the electron transport and the waiting time distribution (WTD) in a topological superconducting Coulomb island system weakly coupled to two metallic leads. A pair of Majorana bound states are hosted in the island with a finite charging energy. By employing the Markovian master equation, we study the effect of interplay between Majorana energy splitting and the charging energy on the current correlations and the relevant electron WTDs. It is found that the super-Poissonian shot noise could be induced when the Majorana energy splitting is larger than the charging energy. The reason is that the degeneracy of the ground states in the island could be lifted by a finite Majorana energy splitting, which produces the asymmetry between tunneling channels and leads to the dynamical channel blockade effect. We show that the WTD for electron tunneling through two Majorana bound states is equivalent to the WTD in a single-resonant-level device. For comparison, we also discuss the WTD for electron tunneling through a non-Majorana device. It is found that the WTD sensitively depends on the length of the island and indicates oscillation behaviors in the absence of Majorana bound states. The particular behaviors of the WTDs in a Majorana island device can be useful in identifying the existence of Majorana bound states. Furthermore, we study the randomness parameter of the waiting time to describe the fluctuations of waiting times. It is shown that the randomness parameter indicates behavior similar to that indicated by the noise Fano factor, and both of them reflect the information of tunneling dynamics.

Certain Aspects of Quantum Transport in Zigzag Graphene Nanoribbons

We have investigated the Fano factor and shot noise theoretically in the confined region of the potential well of zigzag graphene nanoribbon (ZGNR). We have found that the Fano factor is approximately 1, corresponding to the minimum conductivity (σ) for both symmetrical and asymmetrical potential wells. The conductivity plot with respect to Fermi energy appears as symmetrical plateaus on both sides of zero Fermi energy. Moreover, a peak observed at zero Fermi energy in the local density of states (LDOS) confirms the edge states in the system. The transmission properties of ZGNR in the confined region of the potential well are examined using the standard tight-binding Green’s function approach. The perfect transmission observed in the confined region of the potential well shows that pnp type transistors can be made with ZGNR. We have discussed the Fano factor, shot noise, conductivity, and nanohub results in the continuation of previous results. Our results show that the presence of van-Hove singularities in the density of states (DOS) matters in the presence of edge states. The existence of these edge states is sensitive to the number of atoms considered and the nature of the potential wells. We have compared our numerical results with the results obtained from the nanohub software (CNTbands) of Purdue University.

Stimulus presentation can enhance spiking irregularity across subcortical and cortical regions.

Stimulus presentation is believed to quench neural response variability as measured by fano-factor (FF). However, the relative contributions of within-trial spike irregularity and trial-to-trial rate variability to FF fluctuations have remained elusive. Here, we introduce a principled approach for accurate estimation of spiking irregularity and rate variability in time for doubly stochastic point processes. Consistent with previous evidence, analysis showed stimulus-induced reduction in rate variability across multiple cortical and subcortical areas. However, unlike what was previously thought, spiking irregularity, was not constant in time but could be enhanced due to factors such as bursting abating the quench in the post-stimulus FF. Simulations confirmed plausibility of a time varying spiking irregularity arising from within and between pool correlations of excitatory and inhibitory neural inputs. By accurate parsing of neural variability, our approach reveals previously unnoticed changes in neural response variability and constrains candidate mechanisms that give rise to observed rate variability and spiking irregularity within brain regions.

Shot noise of photonic heat transport through an oscillation device modulated by Majorana fermions

The photonic heat transport through an oscillation device under the modulation of Majorana bound states (MBSs) is investigated by using nonequilibrium Green’s function method. The photonic heat current correlation and shot noise formulas are derived. The overall behavior of heat shot noise is governed by terminal temperatures, while its detailed construction is modulated by the attached MBSs and oscillation device. The maximum values of heat current and shot noise are located at integer n times quantum flux Φ0, while they are modulated to zero at half integer of quantum flux (n+12)Φ0 due to changing magnetic flux. The Fano factor presents explicit nonlinear behavior by decreasing firstly to the minimum value and then increasing as the increase of temperature difference. The minimum value of Fano factor is raised up, while its position shifts towards zero temperature difference due to increasing terminal photon frequency. The monotonous enhancement of Fano factor valley is presented due to increasing the coupling constant λ between oscillation device and MBSs, while nonmonotonous variation of Fano factor valley is generated by adjusting the coupling energy ɛM of MBSs.

Conductance and shot noise in a silicene-based superconducting superlattice with two ferromagnetic electrodes

Using the scattering matrix method and the Blonder–Tinkham–Klapwijk formalism, we theoretically study the transport properties and the shot noise in a silicene-based superconducting superlattice (SCSL) with two ferromagnetic electrodes . It is found that for the antiparallel (AP) magnetization configuration, the crossed Andreev reflection (CAR) probability for spin-up electron from the K valley shows the nearly perfect transmission peak at the superconducting energy gap. With increasing the exchange splitting energy, the transmission probabilities of the elastic cotunneling and CAR processes for spin-up electron from the K valley around zero incident angle show the valley–peak–valley transitions. For the AP magnetization configuration, the local Fano factor shows the super-Poissonian value and the nonlocal Fano factor forms a Poissonian value plateau with weak oscillation within a suitable parameter regime. Compared to the local Fano factor, the nonlocal Fano factor is always sub-Poissonian for the parallel magnetization configuration, but for the AP magnetization configuration its maximum value increases and becomes super-Poissonian as the number of layers in the SCSL increases. • The crossed Andreev reflection probability shows nearly perfect transmission peak. • The transmission probabilities are symmetric about the incident angle of electron. • The super-Poissonian Fano factor is found. • The Poissonian value plateaus of the local and nonlocal Fano factors are formed. • The energy range with pure crossed Andreev reflection is robust to layer number.

Stochastic gene transcription with non-competitive transcription regulatory architecture.

The transcription factors, such as activators and repressors, can interact with the promoter of gene either in a competitive or non-competitive way. In this paper, we construct a stochastic model with non-competitive transcriptional regulatory architecture and develop an analytical theory that re-establishes the experimental results with an improved data fitting. The analytical expressions in the theory allow us to study the nature of the system corresponding to any of its parameters and hence, enable us to find out the factors that govern the regulation of gene expression for that architecture. We notice that, along with transcriptional reinitiation and repressors, there are other parameters that can control the noisiness of this network. We also observe that, the Fano factor (at mRNA level) varies from sub-Poissonian regime to super-Poissonian regime. In addition to the aforementioned properties, we observe some anomalous characteristics of the Fano factor (at mRNA level) and that of the variance of protein at lower activator concentrations in the presence of repressor molecules. This model is useful to understand the architecture of interactions which may buffer the stochasticity inherent to gene transcription.

Detecting Spontaneous Neural Oscillation Events in Primate Auditory Cortex.

Electrophysiological oscillations in the brain have been shown to occur as multicycle events, with onset and offset dependent on behavioral and cognitive state. To provide a baseline for state-related and task-related events, we quantified oscillation features in resting-state recordings. We developed an open-source wavelet-based tool to detect and characterize such oscillation events (OEvents) and exemplify the use of this tool in both simulations and two invasively-recorded electrophysiology datasets: one from human, and one from nonhuman primate (NHP) auditory system. After removing incidentally occurring event-related potentials (ERPs), we used OEvents to quantify oscillation features. We identified ∼2 million oscillation events, classified within traditional frequency bands: δ, θ, α, β, low γ, γ, and high γ. Oscillation events of 1–44 cycles could be identified in at least one frequency band 90% of the time in human and NHP recordings. Individual oscillation events were characterized by nonconstant frequency and amplitude. This result necessarily contrasts with prior studies which assumed frequency constancy, but is consistent with evidence from event-associated oscillations. We measured oscillation event duration, frequency span, and waveform shape. Oscillations tended to exhibit multiple cycles per event, verifiable by comparing filtered to unfiltered waveforms. In addition to the clear intraevent rhythmicity, there was also evidence of interevent rhythmicity within bands, demonstrated by finding that coefficient of variation of interval distributions and Fano factor (FF) measures differed significantly from a Poisson distribution assumption. Overall, our study provides an easy-to-use tool to study oscillation events at the single-trial level or in ongoing recordings, and demonstrates that rhythmic, multicycle oscillation events dominate auditory cortical dynamics.

Quantum tunneling in graphene Corbino disk in a solenoid magnetic potential with wedge disclination

We investigate the wedge disclination effect on quantum tunneling of a Corbino disk in gapped-graphene of inner R1 and outer R2 radii in the presence of magnetic flux Φi. We solve Dirac equation for different regions and obtain the solutions of energy spectrum in terms of Hankel functions. The asymptotic behaviors for large arguments allow us to determine the transmission, Fano factor and conductance. We establish the case where the crystal symmetry is modified locally by replacing a hexagon by pentagon, square, heptagon or octagon. We show that the wedge disclination n modifies the amplitude of transmission oscillations. We find that the period of Fano factor oscillations is of the Aharonov–Bohm type, which strongly depends on n where intense peaks are observed. As another result, n changes the minimum and period of conductance oscillations of the Aharonov–Bohm type. We show that n minimizes the effect of resonance and decreases the amplitude of conductance magnitude ΔG oscillations.

Study the mixed valence problem in asymmetric Anderson model: Fano–Kondo resonance around Fermi level

We numerically calculate the local density of states (LDOS) in asymmetric Anderson model in mixed valence regime using hierarchical equations of motion approach. Based on the idea that the asymmetric line shape of LDOS around Fermi level stems from the interference between the single particle resonance and the Kondo resonance, we perform a fitting. From the fitting results, we obtain the Kondo temperatures and the Fano factors with changing the single particle energy. The tendency of Kondo temperature agrees with the previous analytic expressions and the Fano factors are in an expected variation of Fano resonance. Our study shows that the Fano–Kondo resonance can reasonably explain the asymmetric line shape of the LDOS around the Fermi level.

Quantification of Microbial Robustness in Yeast.

Stable cell performance in a fluctuating environment is essential for sustainable bioproduction and synthetic cell functionality; however, microbial robustness is rarely quantified. Here, we describe a high-throughput strategy for quantifying robustness of multiple cellular functions and strains in a perturbation space. We evaluated quantification theory on experimental data and concluded that the mean-normalized Fano factor allowed accurate, reliable, and standardized quantification. Our methodology applied to perturbations related to lignocellulosic bioethanol production showed that the industrial bioethanol producing strain Saccharomyces cerevisiae Ethanol Red exhibited both higher and more robust growth rates than the laboratory strain CEN.PK and industrial strain PE-2, while a more robust product yield traded off for lower mean levels. The methodology validated that robustness is function-specific and characterized by positive and negative function-specific trade-offs. Systematic quantification of robustness to end-use perturbations will be important to analyze and construct robust strains with more predictable functions.

Dynamics of a semiconductor laser with feedback and modulation: experiments and model comparison.

We study experimentally and numerically the dynamics of a semiconductor laser near threshold, subject to optical feedback and sinusoidal current modulation. The laser operates in the low frequency fluctuation (LFF) regime where, without modulation, the intensity shows sudden spikes at irregular times. Under particular modulation conditions the spikes lock to the modulation and their timing becomes highly regular. While the modulated LFF dynamics has received a lot of attention, an in-depth comparison with the predictions of the Lang-Kobayashi (LK) model has not yet been performed. Here we use the LK model to simulate the laser dynamics and use the Fano factor to quantify the regularity of the timing of the spikes. The Fano factor is calculated by counting the number of spikes in successive segments of the intensity time-series and keeps information about temporal order in the spike sequence that is lost when the analysis is based on the distribution of inter-spike intervals. Here we compare the spike timing regularity in experimental and in simulated spike sequences as a function of the modulation amplitude and frequency and find a good qualitative agreement. We find that in both experiments and simulation for appropriate conditions the spike timing can be highly regular, as revealed by very small values of the Fano factor.

A physical mechanism of heterogeneity and micro-metastasis in stem cells, cancer cells, and cancer stem cells.

Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer SC (CSC). This heterogeneity manifests in the form of diverse sub-populations of SC, CS, and CSC with self-renewal and unique regeneration capacity. Moreover, the progeny of CSC possess multiple plasticity and cancerous characteristics. Many studies have demonstrated that cancer heterogeneity is among the greatest obstacles to successful anti-cancer therapy. This leads to incomplete therapy and transitory efficacy. Furthermore, numerous micro-metastases lead to the spread of tumor cells widely across the body; this is the beginning of metastasis. Epigenetic processes (DNA methylation and histone remodification) represent sources of heterogeneity. In this study, we develop a mathematical model to quantify the heterogeneity of SC, CS, and CSC, taking into consideration both genetic and epigenetic effects. We reveal the roles and physical mechanisms of heterogeneity in SC, CSC, and cancer cells. Under the adiabatic regime (relatively fast regulatory binding and effective coupling among genes), seven native states (SC, CSC, cancer, premalignant, normal, lesion, and hyperplasia) emerge. Under the non-adiabatic regime (relatively slow regulatory binding and effective weak coupling among genes), SC, CS, CSC, and differentiated states emerge and become diffusive, partially explaining the origin of heterogeneity. In other words, slow regulatory binding that mimics epigenetic effects can give rise to heterogeneity. Moreover, we calculated the entropy production rate and Fano factor, which can be used to quantify the thermodynamic cost and the degrees of the variations or the fluctuations as the parameter ω (representing the speed of regulatory binding/unbinding relative to the synthesis/degradation) changes. Elucidating the origins of heterogeneity and the dynamical relationships between intra-tumoral cells has a clear clinical significance and will improve the understanding of the cellular basis of treatment response, therapeutic resistance, and cancer metastasis.

Magnetization dynamics in the YIG/Au/YIG magnon valve

The magnetization dynamics of an yttrium iron garnet (YIG)/Au/YIG magnon valve was investigated using broadband ferromagnetic resonance. The material characterizations of YIG/Au/YIG were performed using cross-sectional scanning transmission electron microscopy, x-ray diffraction spectroscopy, x-ray photoemission spectroscopy, Raman spectroscopy, and UV–visible spectroscopy. Asymmetric Fano resonance in the YIG/Au (60 nm)/YIG magnon valve structure was observed experimentally, and the two coupled oscillators model was used to describe the source of the Fano resonance qualitatively. We also provide a quantitative description of the Fano resonance and extract the Fano factor, which is an important feature that can be used to define the interaction sign. This represents the first attempt to apply the Fano resonance to magnetization dynamics. The spin wave resonance modes excited by the Au nanoparticles (NPs) surface plasmons were also observed in a YIG/Au NPs/YIG structure. Our findings confirm the occurrence of magnetic Fano resonance in the YIG/Au/YIG magnon valve and pave the way toward the development of quantum information devices based on magnon valves.

Critical current for giant Fano factor in neural models with bistable firing dynamics and implications for signal transmission.

Bistability in the firing rate is a prominent feature in different types of neurons as well as in neural networks. We show that for a constant input below a critical value, such bistability can lead to a giant spike-count diffusion. We study the transmission of a periodic signal and demonstrate that close to the critical bias current, the signal-to-noise ratio suffers a sharp increase, an effect that can be traced back to the giant diffusion and large Fano factor.

Fano factor in self-similar multibarrier structure based on graphene monolayer

In this paper, we investigated the Fano factor in two types of self-similar potential structures in a graphene monolayer. These structures are substrate-based potential and electrostatic-based potential. However, in order to determine the Fano factor in such structures, we solved the Dirac Hamiltonian by using the transfer matrix method. We found that the self-similar substrate-based potential structure manifests a self-similar behavior in the Fano factor and conductance. Therefore, we proposed scaling rules that represent a scale invariance between generations, main barrier heights, and total lengths of the structures. In particular, the maximum Fano factor value was reported for the self-similar electrostatic-based potentials. More analysis was given in terms of the generation, main barrier heights, and structure’s total lengths. These kinds of structures could be used to control the Fano factor.

Estimation of Fano factor for oversquare HPGe detector

Fano factor is a quantity used to measure the departure of the observed variance in the number of charge carriers produced from that predicted using poison statistics. Fano factor varies with the detector type. In case of proportional counters and semiconductor detectors, it is substantially less than unity, whereas, for scintillator detectors, it would be unity. Even in case of semiconductor detectors, it varies with the type and the shape of the detector. Another source of fluctuations that gives the overall resolution of the detector is preamplifier noise. Oversquare coaxial HPGe detectors are a recent development in the field. Literature on the Fano factor of oversquare large volume coaxial detector is not available. In this work, the Fano factor and the electronic noise of an oversquare HPGe coaxial detector are estimated after optimizing the shaping parameters. The Fano factor for the oversquare HPGe detector is estimated as 0.1291 keV, which agrees with the ideal value of 0.13 by 99.98%. The preamplifier noise was found to be 0.048 keV which is 35% lesser than the reported value.

Tunneling effect in gapped graphene disk in magnetic flux and electrostatic potential

We investigate the tunneling effect of a Corbino disk in graphene in the presence of a variable magnetic flux Φ i created by a solenoid piercing the inner disk under the effect of a finite mass term in the disk region (R 1 < r < R 2) and an electrostatic potential. Considering different regions, we explicitly determine the associated eigenspinors in terms of Hankel functions. The use of matching conditions and asymptotic behavior of Hankel functions for large arguments, enables us to calculate transmission and other transport quantities. Our results show that the energy gap suppresses the tunneling effect by creating singularity points of zero transmission corresponding to the maximum shot noise peaks quantified by the Fano factor F. The transmission as a function of the radii ratio R 2/R 1 becomes oscillatory with a decrease in periods and amplitudes. It can even reach one (Klein tunneling) for large values of the energy gap. The appearance of the minimal conductance at the points k F R 1 = R 1 δ is observed. Finally we find that the electrostatic potential can control the effect of the band gap.

The interplay of intralead and dot-lead Coulomb electrons on shot noise in the Kondo regime

The interplay of intralead and dot-lead Coulomb interactions on shot noise of a quantum dot coupled to Luttinger-liquid leads is systematically investigated in the Kondo regime. By equation of motion and canonical transformation methods, a general shot noise formula with transmission coefficient is derived, the factors of the above two types of interactions and on-dot Coulomb interaction being taken into account. Then we study in detail the shot noise and Fano factor as a function of bias voltage. Numerical results show for weak and moderately strong intralead Coulomb interactions, the dot-lead interaction not only helps to improve the shot noise, but also narrows the zero-bias Kondo dip. A series of polaron peaks appear in the differential shot noise when the renormalized parameter Y<1, a combination effect of the intralead and dot-lead Coulomb interactions. For Y>1, a novel type of excitonic dips appear only in the case of moderately strong intralead interaction. In the very strong intralead interaction limit, all features of excitonic peaks or dips disappear, and shot noise shows power-law dependence on the voltage with the renormalized exponent Y. The Fano factor is always sub-Poisson noise no matter whether Y is greater or less than 1.

Variability of neuronal responses in the posterior superior temporal sulcus predicts choice behavior during social interactions.

Recent studies have shown that neural activity in a well-defined patch in the posterior superior temporal sulcus (the "gaze-following patch," GFP) of the primate brain is strongly modulated when the other's gaze attracts the observer's attention to locations/objects, the other is looking at. Changes of the mean discharge rate of neurons in the monkey GFP indicate that they are involved in two distinct computations: the allocation of spatial attention guided by the other's gaze vector and the suppression of gaze following if inappropriate in a given situation. Here, we asked if and how the discharge variability of neurons in the GFP is related to the task and if it carries information on behavioral performance. To this end, we calculated the Fano factor as a measure of across-trial discharge variability as a function of time. Our results show that all neurons exhibiting a task-related discharge-rate modulation also exhibit a stimulus onset-dependent drop in the Fano factor. Furthermore, the amplitude of the Fano factor reduction is modulated by task condition and the neuron's selectivity in this regard. We found that these effects are directly related to the monkeys' behavioral performance in that the Fano factor is predictive about upcoming correct or wrong decisions. Our results indicate that neuronal discharge variability as gauged by the Fano factor, hitherto primarily studied in the context of visual perception or motor control, is an informative measure also in studies of the neural underpinnings of complex social behavior.NEW & NOTEWORTHY Quenching of neural variability following stimulus onset is a widely accepted phenomenon. However, the relevance of quenching for the shaping of complex social behaviors remains to be explored. Here, we show that task selective neurons in the GFP exhibit a higher degree of variability quenching than their neighboring unselective neurons. Furthermore, we demonstrate that behavioral errors are not only associated with lower firing rates but also less variability quenching, suggesting that both facilitate optimal performance.