arXiv subjects

M. N. Najafi

Publications and source records attributed to M. N. Najafi.

At least 19 recordsLinked to original sources

arXiv2026

Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory

We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.

cond-mat.stat-mech↗

arXiv2025

Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems

Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being attracted to the trails left by one another. This system is inspired by, but not limited to, pheromone-guided insect navigation. The coupling of self-avoidance and attraction generates rich emergent behavior, including distinct anomalous diffusion regimes, non-Gaussian position distributions, and compressed exponential encounter statistics. Most notably, we identify new universality classes for coupled random walks, characterized by unique scaling laws and distributional properties that, to our knowledge, have not been previously reported. These findings advance the theoretical understanding of coupled stochastic processes with memory and interaction feedback, providing a framework for exploring transport phenomena in a broad range of multi-agent systems beyond biological contexts.

q-bio.PE↗

arXiv2025

Stylized Facts of High-Frequency Bitcoin Time Series

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an anomalous diffusion process, transitioning from subdiffusion for short intervals to weak superdiffusion over longer time intervals. The characteristic features related to this anomalous behavior studied in the present paper include heavy tails, which can be described using a $q$-Gaussian distribution and correlations. When we sample the autocorrelation of absolute returns, we observe a power-law relationship, indicating time dependence in both periods initially. The ensemble autocorrelation of the returns decays rapidly. We fitted the autocorrelation with a power law to capture the decay and found that the second period experienced a slightly higher decay rate. The further study involves the analysis of endogenous effects within the Bitcoin time series, which are examined through detrending analysis. We found that both periods are multifractal and present self-similarity in the detrended probability density function (PDF). The Hurst exponent over short time intervals shifts from less than 0.5 ($\sim$ 0.42) in Period 1 to closer to 0.5 in Period 2 ($\sim$ 0.49), indicating that the market has gained efficiency over time.

q-fin.ST↗

arXiv2024

Statistical analysis of the drying pattern of coffee

In this study, we experimentally study the dried pattern droplets of coffee with and without sugar. We statistically analyze the rough surface formed after the stain becomes dried. The amount of sugar is controlled by the mass $m$. Along with the formation of the coffee ring, we discuss the Marangoni effect, in the system, and also analyzed the statistics of the cracks. For large enough $m$ values, the exponents approach to the ones for the Gaussian free field (GFF) (the loop fractal dimension $\frac{3}{2}$, loop and gyration radius distribution exponents $τ_l=\frac{7}{3}$ and $τ_r=3$ respectively). Using the multifractal analysis (MA) for the mass configuration of the dried pattern, we numerically show that, the mass-fractal dimension is $1.76\pm 0.04$ for the case without sugar, which decreases increasing the sugar. This is explained by the fact that the droplet becomes more hydrophilic, resulting in more sparse spatial patterns, in agreement compatible with the contact angle analysis.

cond-mat.stat-mech↗

arXiv2024

Centrality and Universality in Scale-Free Networks

We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter $0\le p\le 1$) shapes the structure of the evolving network. We reveal the ability to seamlessly explore a vast landscape of scale-free networks, unlocking an entirely new class of complex networks that we call \textit{stars-with-filament} structure. Remarkably, the average degree $\bar k$ of these networks grows like $\log t$ to some power, where $t$ is time and the average shortest path length grows logarithmically with the system size for intermediate $p$ values, offering fresh insights into the structural dynamics of scale-free systems. Our approach is backed by a robust mean-field theory, which nicely captures the dynamics of $\bar{k}$. We further unveil a rich, $p$-dependent phase diagram, encompassing 47 real-world scale-free networks, shedding light on previously hidden patterns. This work opens exciting new avenues for understanding the universal properties of complex networks.

physics.soc-ph↗

arXiv2024

Closed-form solutions for the Salpeter equation

We propose integral representations and analytical solutions for the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. We explore the exact Green function and an exact solution for a given initial condition, and also find the asymptotic solutions in some limiting cases. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent stochastic problem, namely the Bäumer equation. This equation describes \textit{relativistic} stochastic processes with time-changing anomalous diffusion. This Bäumer propagator corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy distributions for small times and Gaussian diffusion for large times, providing a framework for stochastic processes where anomalous diffusion is time-dependent.

quant-ph↗

arXiv2024

A field theory representation of sum of powers of principal minors and physical applications

We introduce a novel field theory representation for the Sum of Powers of Principal Minors (SPPM), a mathematical construct with profound implications in quantum mechanics and statistical physics. We begin by establishing a Berezin integral formulation of the SPPM problem, showcasing its versatility through various symmetries including $SU(n)$, its subgroups, and particle-hole symmetry. This representation not only facilitates new analytical approaches but also offers deeper insights into the symmetries of complex quantum systems. For instance, it enables the representation of the Hubbard model's partition function in terms of the SPPM problem. We further develop three mean field techniques to approximate SPPM, each providing unique perspectives and utilities: the first method focuses on the evolution of symmetries post-mean field approximation, the second, based on the bosonic representation, enhances our understanding of the stability of mean field results, and the third employs a variational approach to establish a lower bound for SPPM. These methods converge to identical consistency relations and values for SPPM, illustrating their robustness. The practical applications of our theoretical advancements are demonstrated through two compelling case studies. First, we exactly solve the SPPM problem for the Laplacian matrix of a chain, a symmetric tridiagonal matrix, allowing for precise benchmarking of mean-field theory results. Second, we present the first analytical calculation of the Shannon-Rényi entropy for the transverse field Ising chain, revealing critical insights into phase transitions and symmetry breaking in the ferromagnetic phase. This work not only bridges theoretical gaps in understanding principal minors within quantum systems but also sets the stage for future explorations in more complex quantum and statistical physics models.

quant-ph↗

arXiv2023

Variable order porous media equations: Application on modeling the S&P500 and Bitcoin price return

This article reveals a specific category of solutions for the $1+1$ Variable Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO $q$-Gaussian functions, granting them significant versatility in their application to various real-world systems, such as financial economy areas spanning from conventional stock markets to cryptocurrencies. The VO $q$-Gaussian functions provide a more robust expression for the distribution function of price returns in real-world systems. Additionally, we analyzed the temporal evolution of the anomalous characteristic exponents derived from our study, which are associated with the long-range memory in time series data and autocorrelation patterns.

cond-mat.stat-mech↗

arXiv2022

Simulating Cumulus Clouds based on Self-Organized Criticality

Recently it was shown that self-organized criticality is an important ingredient of the dynamics of cumulus clouds (Physical Review E, 103(5), p.052106, 2021). Here we introduce a new algorithm to simulate cumulus clouds in two-dimensional square lattices, based on two important facts: the cohesive energy of wet air parcels and a sandpile-type diffusion of cloud segments. The latter is realized by considering the evaporation/condensation of air parcels in various regions of the cloud, which enables them to diffuse to the neighboring regions. The results stemming from this model are in excellent agreement with the observational results reported in the above-cited paper, where the exponents have been obtained for the two-dimensional earth-to-sky RGB images of clouds. The exponents that are obtained at the lowest condensation level in our model are consistent with the observational exponents. We observed that the cloud fields that we obtain from our model are fractal, with the outer perimeter having a fractal dimension of $D_f = 1.25 \pm 0.01$. Furthermore, the distributions of the radius of gyration and the loop length follow a power-law function with exponents $τ_r = 2.3 \pm 0.1$ and $τ_l = 2.1 \pm 0.1$, respectively. The loop Green function is found to be logarithmic with the radius of gyration of the loops following the observational results. The winding angle statistic of the external perimeter of the cloud field is also analyzed, showing an exponent in agreement with the fractal dimension, which may serve as the conformal invariance of the system.

cond-mat.stat-mech↗

arXiv2022

Sandpiles Subjected to Sinusoidal Drive

This paper considers a sandpile model subjected to a sinusoidal external drive with the time period $T$. We develop a theoretical model for the Green function in a large $T$ limit, which predicts that the avalanches are anisotropic and elongated in the oscillation direction. We track the problem numerically and show that the system shows additionally a regime where the avalanches are elongated in the perpendicular direction with respect to the oscillations. We find a transition point between these two regimes. The power spectrum of avalanche size and the grains wasted from the parallel and perpendicular directions are studied. These functions show power-law behaviour in terms of the frequency with exponents, which run with $T$.

cond-mat.stat-mech↗

arXiv2022

Persistent Homology of Fractional Gaussian Noise

In this paper, we employ the persistent homology (PH) technique to examine the topological properties of fractional Gaussian noise (fGn). We develop the weighted natural visibility graph algorithm, and the associated simplicial complexes through the filtration process are quantified by PH. The evolution of the homology group dimension represented by Betti numbers demonstrates a strong dependency on the Hurst exponent ($H$). The coefficients of the birth and death curve of the $k$-dimensional topological holes ($k$-holes) at a given threshold depend on $H$ which is almost not affected by finite sample size. We show that the distribution function of a lifetime for $k$-holes decays exponentially and the corresponding slope is an increasing function versus $H$, and more interestingly, the sample size effect completely disappears in this quantity. The persistence entropy logarithmically grows with the size of the visibility graph of a system with almost $H$-dependent prefactors. On the contrary, the local statistical features are not able to determine the corresponding Hurst exponent of fGn data, while the moments of eigenvalue distribution ($M_{n}$) for $n\ge1$ reveal a dependency on $H$, containing the sample size effect. Finally, the PH shows the correlated behavior of electroencephalography for both healthy and schizophrenic samples.

physics.data-an↗

arXiv2022

Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions

The Rényi (Shannon) entropy, i.e. $Re_α(Sh)$, of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at critical point there is an extra logarithmic subleading term with a coefficient which is universal. In this paper we study this coefficient for generic time-reversal translational invariant quadratic critical free fermions. These models can be parameterized by a complex function which has zeros on the unit circle. When the zeros on the unit circle do not have degeneracy and there is no zero outside of the unit circle we are able to classify the coefficient of the logarithm. In particular, we numerically calculate the Rényi (Shannon) entropy in configuration basis for wide variety of these models and show that there are two distinct classes. For systems with $U(1)$ symmetry the coefficient is proportional to the central charge, i.e. one half of the number of points that one can linearize the dispersion relation of the system; for all the values of $α$ with transition point at $α=4$. For systems without this symmetry, when $α>1$ this coefficient is again proportional to the central charge. However, the coefficient for $α\leq 1$ is a new universal number. Finally, by using the discrete version of Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these coefficients are universal and dependent on the underlying CFT.

cond-mat.stat-mech↗

arXiv2022

Mapping cumulus clouds to scale invariant rough surfaces

Motivated by a recent observation on the self-organized criticality of cumulus clouds (Phys. Rev E 103, 052106, 2021) we study their connection to self-similar rough surfaces, in which $f\equiv \log I$ plays the role of the main field, where $I$ is the intensity of the received visible light. By simulating the light scattering based on a coarse-grained phenomenological model in a two-dimensional cloud, we argue the possible connection of $I$ to the actual cloud thickness. Although in the vertical incident light $f$ is proportional to the cloud thickness, in the general case it is complected. We study the statistical properties of observational data for $f$ with a focus on the conventional exponents of this scale-invariant rough surface. By calculating the roughness exponents, and comparing them with other exponents like the fractal dimension of loops, the distribution function of the radius of gyration and loop lengths, and the exponent of the green function, we prove that this surface is unconventional in the sense that it is the non-Gaussian self-affine random surface which violates the Kondev hyper-scaling relations.

cond-mat.stat-mech↗

arXiv2021

The Visibility Graphs of Correlated Time Series Violate the Barthelemy's Conjecture for Degree and Betweenness Centralities

The problem of betweenness centrality remains a fundamental unsolved problem in complex networks. After a pioneering work by Barthelemy, it has been well-accepted that the maximal betweenness-degree ($b$-$k$) exponent for scale-free (SF) networks is $η_{\text{max}}=2$, belonging to scale-free trees (SFTs), based on which one concludes $δ\ge\frac{γ+1}{2}$, where $γ$ and $δ$ are the scaling exponents of the distribution functions of the degree and betweenness centrality, respectively. Here we present evidence for violation of this conjecture for SF visibility graphs (VGs). To this end, we consider the VG of three models: two-dimensional (2D) Bak-Tang-Weisenfeld (BTW) sandpile model, 1D fractional Brownian motion (FBM) and, 1D Levy walks, the two later cases are controlled by the Hurst exponent $H$ and step-index $α$, respectively. Specifically, for the BTW model and FBM with $H\lesssim 0.5$, $η$ is greater than $2$, and also $δ<\frac{γ+1}{2}$ for the BTW model, while Barthelemy's conjecture remains valid for the Levy process. We argue that this failure of Barthelemy's conjecture is due to large fluctuations in the scaling $b$-$k$ relation resulting in the violation of hyperscaling relation $η=\frac{γ-1}{δ-1}$ and emergent anomalous behaviors for the BTW model and FBM. A super-universal behavior is found for the distribution function for a generalized degree function identical to the Barabasi-Albert network model.

cond-mat.stat-mech↗

arXiv2021

Multifractal analysis of Earthquakes in Central Alborz, Iran; A phenomenological self-organized critical Model

This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely weight function, quality factor, and velocity model in this region, we develop a phenomenological dissipative sandpile-like model which captures the main features of the system, especially the average activity field over the region of study. The model is based on external stimuli, the location of which are chosen (\textbf{I}) randomly, (\textbf{II}) on the faults, (\textbf{III}) on the highly active points in the region. We analyze all these cases and show some universal behaviors of the system depending slightly on the method of external stimuli. The multi-fractal analysis is exploited to extract the spectrum of the Hurst exponent of time series obtained by each of these schemes. Although the average Hurst exponent depends on the method of stimuli (the three cases mentioned above), we numerically show that in all cases it is lower than $0.5$, reflecting the anti-correlated nature of the system. The lowest average Hurst exponent is for the case (\textbf{III}), in such a way that the more active the stimulated sites are the lower the value for the average Hurst exponent is obtained, i.e. the larger earthquakes are more anticorrelated. However, the different activity fields in this study provide the depth of the basement, the depth variation (topography) of the basement, and an area that can be the location of the future probability event.

cond-mat.stat-mech↗

arXiv2021

Self-Repelling Bi-Exploration Process

Self-repelling two-leg (biped) spider walk is considered where the local stochastic movements are governed by two independent control parameters $ β_d$ and $ β_h $, so that the former controls the distance ($ d $) between the legs positions, and the latter controls the statistics of self-crossing of the traversed paths. The probability measure for local movements is supposed to be the one for the "true self-avoiding walk" multiplied by a factor exponentially decaying with $ d $. After a transient behavior for short times, a variety of behaviors have been observed for large times depending on the value of $β_d$ and $β_h$. Our statistical analysis reveals that the system undergoes a crossover between two (small and large $β_d$) regimes identified in large times ($t$). In the small $β_d$ regime, the random walkers (identified by the position of the legs of the spider) remain on average in a fixed non-zero distance in the large time limit, whereas in the second regime (large $β_d$s), the absorbing force between the walkers dominates the other stochastic forces. In the latter regime, $ d $ decays in a power-law fashion with the logarithm of time. When the system is mapped to a growth process (represented by a height field which is identified by the number of visits for each point), the roughness and the average height show different behaviors in two regimes, i.e., they show power-law with respect to $t$ in the first regime, and $\log t$ in the second regime. The fractal dimension of the random walker traces and the winding angle are shown to consistently undergo a similar crossover.

cond-mat.stat-mech↗

arXiv2021

Edwards-Wilkinson Depinning Transition in the Background of Random Coulomb Potential

The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a critical driving force $F_c\approx 0.37$ in the vicinity of which the final velocity of the interface varies linearly with time. Our data collapse analysis for the velocity shows a crossover time $t^*$ at which the velocity is size independent. Based on a two-variable scaling analysis, we extract the exponents, which are different from all universality classes we are aware of. Especially noting that the dynamic and roughness exponents are $z_w=1.55\pm 0.05$, and $α_w=1.05\pm 0.05$ at the criticality, we conclude that the system is different from both EW and KPZ universality classes. Our analysis shows therefore that making the noise long-range-correlated, drives the system out of EW universality class. The simulations on the tilted lattice shows that the non-linearity term ($λ$ term in the KPZ equations) goes to zero in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2021

Invasion percolation in short-range and long-range disorder background

In this paper, we investigate the invasion percolation (IP) in imperfect support in which the configuration of imperfections is considered to be correlated. Three lattice models were engaged to realize this pattern: site percolation, Ising model and random Coulomb potential (RCP). The first two models are short range interaction (SRI), whereas the last one includes coulomb like interactions which is pretty long range (long-range interactions, LRI). By examining various dynamical observables we show that the critical exponents of SRI IP are robust against the control parameters (temperature in the Ising model and occupation probability in site percolation), whereas its properties in the LRI (RCP) supports are completely different from the normal IP (i.e. on the regular lattice). Especially the fractal dimension of the external frontier of the largest hole converges to $1.099\pm 0.008$ for RCP IP, whereas it is nearly $\frac{4}{3}$ for SRI IP being compatible with normal IP. Additionally a novel dynamical crossover is seen in the RCP IP according to which the time dependence of all of the observables is divided to three parts: the power-law (small times), the logarithmic (mid time), and the linear (long time) regimes. The second crossover time is shown to go to infinity in the thermodynamic limit, whereas the first crossover time is nearly unchanged, signaling the dominance of the logarithmic regime. The observables become nearly constant in the thermodynamic limit for the long time, showing that it is a stationary phase.

cond-mat.stat-mech↗