arXiv subjects

Igor M. Sokolov

Publications and source records attributed to Igor M. Sokolov.

At least 19 recordsLinked to original sources

arXiv2026

Formal Fluctuation-Response Relations for Non-Stationary Systems: The Dynamic Conjugate Variable

Fluctuation-response relations (FRRs) connect the linear response of a system to an external perturbation with properties of spontaneous fluctuations in the unperturbed system. We provide a simple derivation of FRRs for non-stationary dynamics following an almost standard way based on introducing a variable conjugated to perturbation (a dynamic conjugate). The derivation relies solely on the Markovianity of the underlying dynamics, with the only additional assumption that the transition PDF of the process is differentiable with respect to the strength of a constant, time- independent perturbation. The structure of this conjugate variable is however unusual: it is a two-time one, and reduces to a usual single-time conjugate in stationary situations. We show how several known results follow from this approach.

cond-mat.stat-mech↗

arXiv2026

Genuine and spurious (non-)ergodicity in single particle tracking

In single-particle tracking experiments measuring anomalous diffusion dynamics, understanding ergodicity is crucial, as it ensures that the time average of an observable matches the ensemble average, and can thus be fitted with known ensemble-averaged observables. A commonly used criterion for assessing the ergodicity of a stochastic process is based on the comparison of the mean-squared displacement (MSD) with the time-averaged MSD (TAMSD). This approach has been widely applied and proves effective in cases of weak ergodicity breaking across various systems in both theoretical and experimental studies. However, there is relatively little discussion regarding the theoretical justification and limitations of this definition. Here, we demonstrate that this widely accepted criterion to some extent contradicts the classical definition of ergodicity as well as physical intuition, leading to spurious (non-)ergodicity results when applied to several well-known stochastic models. To address this limitation, we propose using the mean-squared increment (MSI) instead of the MSD for comparison of ensemble- and time-averaged observables. Several well-established examples demonstrate that our MSI-TAMSD criterion not only effectively reveals weak ergodicity breaking, equivalent to the MSD-TAMSD approach, but also provides a more accurate characterization of the genuine (non-)ergodicity of systems where the MSD-TAMSD method fails. Additionally, for systems exhibiting "ultraweak" ergodicity breaking, the MSI can reveal the asymptotic stationarity and ergodic nature of the process' increments. Our findings emphasize the important role of the MSI observable for SPT experiments and anomalous diffusion studies.

cond-mat.stat-mech↗

arXiv2026

Hitting the blinking target under stochastic resetting

The first hitting times of a stochastic process, i.e., the first time a process reaches a particular level, are of significant interest across various scientific disciplines, including biology, chemistry, and economics. We modify the standard setup by allowing the target to spontaneously switch between two states, either active or inactive, and investigate the distribution of first hitting times accrued while the target is active. For this setup, we provide closed formulas for the distribution of the first hitting time. Additionally, we can introduce stochastic resetting to the underlying process and, utilizing our results, derive the formulas for the first time the active target is hit by the process under stochastic resetting. Interestingly, we show that resetting in this setup still leaves some memory; the system is no longer Markovian, which prevents a straightforward application of standard techniques. The analytical results are accompanied by computer simulations of Langevin dynamics.

cond-mat.stat-mech↗

arXiv2026

Light propagation in atomic stratified media: breakdown of the transfer-matrix method at high density

The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole-dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.

physics.atom-ph↗

arXiv2025

Heterogeneous diffusion in an harmonic potential: the role of the interpretation

Diffusion in heterogeneous energy and diffusivity landscapes is widespread in biological systems. However, solving the Langevin equation in such environments introduces ambiguity due to the interpretation parameter $α$, which depends on the underlying physics and can take values in the range $0<α<1$. The typical interpretations are Itô ($α=0$), Stratonovich ($α=1/2$), and Hänggi-Klimontovich ($α=1$). Here, we analyse the motion of a particle in an harmonic potential -- modelled as an Ornstein-Uhlenbeck process -- with diffusivity that varies in space. Our focus is on two-phase systems with a discontinuity in environmental properties at $x=0$. We derive the probability density of the particle position for the process, and consider two paradigmatic situations. In the first one, the damping coefficient remains constant, and fluctuation-dissipation relations are not satisfied. In the second one, these relations are enforced, leading to a position-dependent damping coefficient. In both cases, we provide solutions as a function of the interpretation parameter $α$, with particular attention to the Itô, Stratonovich, and Hänggi-Klimontovich interpretations, revealing fundamentally different behaviours, in particular with respect to an interface located at the potential minimum.

cond-mat.stat-mech↗

arXiv2024

Langevin equation in heterogeneous landscapes: how to choose the interpretation

The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases, the solution to a Langevin equation is not unique unless the interpretation of stochastic integrals involved is selected. We analyze the diffusion of particles in such systems and evaluate the mean, the mean square displacement, and the distribution of particles, as well as the variance of the time-averaged mean-squared displacements. Our analytical results provide a method to choose the interpretation parameter from single particle tracking experiments.

cond-mat.stat-mech↗

arXiv2023

Random walks in correlated diffusivity landscapes

In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows linearly in time, like in a normal diffusion, but the distribution of displacements is non-Gaussian. In situations when the convergence to Gaussian still takes place at longer times, the probability density of the displacements may show a persisting peak around the distribution's mode, and the pathway of convergence to the Gaussian is unusual. One of the theoretical models showing such a behavior corresponds to a disordered system with local diffusion coefficients slowly varying in space. While the standard pathway to Gaussian, as proposed by the Central Limit Theorem, would assume that the peak, under the corresponding rescaling, smoothens and lowers in course of the time; in the model discussed, the peak, under rescaling, narrows and stays sharp. In the present work, we discuss the nature of this peak. On a coarse-grained level, the motion of the particles in the diffusivity landscape is described by continuous time random walks with correlations between waiting times and positions. The peak is due to strong spatiotemporal correlations along the trajectories of diffusing particles. Destroying these correlations while keeping the temporal structure of the process intact leads to the decay of the peak. We also note that the correlated CTRW model reproducing serial correlations between the waiting times along the trajectory fails to quantitatively reproduce the shape of the peak even for the decorrelated motion, while being quite accurate in the wings of the PDF. This shows the importance of high-order temporal correlations for the peak's formation.

cond-mat.stat-mech↗

arXiv2023

Synchronization transitions in Kuramoto networks with higher-mode interaction

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function and hence going beyond the Kuromoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling-modes. We describe the multistability induced by the presence of a second coupling-mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that in essence the two-mode coupling gives rise to states that are characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems including complex interaction functions beyond the Kuramoto-type.

nlin.AO↗

arXiv2023

Vulnerability analysis in Complex Networks under a Flood Risk Reduction point of view

The measurement and mapping of transportation network vulnerability to natural hazards constitute subjects of global interest, especially due to climate change, and for a sustainable development agenda. During a flood, some elements of a transportation network can be affected, causing loss of life of people and damage to vehicles, streets/roads, and other logistics services, sometimes with severe economic impacts. The Network Science approach may offer a valuable perspective considering one type of vulnerability related to network type critical infrastructures: the topological vulnerability. The topological vulnerability index associated with an element is defined as the reduction in the network's average efficiency due to the removal of the set of edges related to that element. We present a topological vulnerability index analysis for the highways in the state of Santa Catarina, Brazil, and produce a map considering that index and the areas susceptible to urban floods and landslides. The risk knowledge, combining hazard and vulnerability, is the first pillar of an Early Warning System, and represent an important tool for stakeholders from the transportation sector in a disaster risk reduction agenda.

physics.soc-ph↗

arXiv2022

Heterogeneous nucleation in finite size adaptive dynamical networks

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, co-evolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multi-step transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.

nlin.AO↗

arXiv2022

Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like illness

After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia, Legionella pneumophila etc and viruses such as influenza, coronavirus, rhinovirus/enterovirus, parainfluenza, metapneumovirus, influenza B virus etc are identified as co-pathogens. In our current effort, we develop and analysed a compartmental based Ordinary Differential Equation (ODE) type mathematical model to understand the co-infection dynamics of Covid-19 and other influenza type illness. In this work we have incorporated the saturated treatment rate to take account of the impact of limited treatment resources to control the possible Covid-19 cases. As results, we formulate the basic reproduction number of the model system. Finally, we have performed numerical simulations of the co-infection model to examine the solutions in different zones of parameter space.

q-bio.PE↗

arXiv2022

Beyond the shortest path: the path length index as a distribution

The traditional complex network approach considers only the shortest paths from one node to another, not taking into account several other possible paths. This limitation is significant, for example, in urban mobility studies. In this short report, as the first steps, we present an exhaustive approach to address that problem and show we can go beyond the shortest path, but we do not need to go so far: we present an interactive procedure and an early stop possibility. After presenting some fundamental concepts in graph theory, we presented an analytical solution for the problem of counting the number of possible paths between two nodes in complete graphs, and a depth-limited approach to get all possible paths between each pair of nodes in a general graph (an NP-hard problem). We do not collapse the distribution of path lengths between a pair of nodes into a scalar number, we look at the distribution itself - taking all paths up to a pre-defined path length (considering a truncated distribution), and show the impact of that approach on the most straightforward distance-based graph index: the walk/path length.

cs.DM↗

arXiv2022

Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics

We study the effect of randomly distributed diffusivities and speeds in two models for active particle dynamics with active and passive fluctuations. We demonstrate how non-Gaussian displacement distributions emerge in these models in the long time limit, including Cauchy-type and exponential (Laplace) shapes. Notably the resulting shapes of the displacement distributions with distributed diffusivities for the active models considered here are in striking contrast to passive diffusion models. For the active motion models our discussion points out the differences between active- and passive-noise. Specifically, we demonstrate that the case with active-noise is in nice agreement with measured data for the displacement distribution of social amoeba.

cond-mat.stat-mech↗

arXiv2022

Universal fluctuations and ergodicity of generalized diffusivity on critical percolation clusters

Despite a long history and a clear overall understanding of properties of random walks on an incipient infinite cluster in percolation, some important information on it seems to be missing in the literature. In the present work, we revisit the problem by performing massive numerical simulations for (sub)diffusion of particles on such clusters. Thus, we discuss the shape of the probability density function (PDF) of particles' displacements, and the way it converges to its long-time limiting scaling form. Moreover, we discuss the properties of the mean squared displacement (MSD) of a particle diffusing on the infinite cluster at criticality. This one is known not to be self-averaging. We show that the fluctuations of the MSD in different realizations of the cluster are universal, and discuss the properties of the distribution of these fluctuations. These strong fluctuations coexist with the ergodicity of subdiffusive behavior in the time domain. The dependence of the relative strength of fluctuations in time-averaged MSD on the total trajectory length (total simulation time) is characteristic for diffusion in a percolation system and can be used as an additional test to distinguish this process with disorder-induced memory from processes with otherwise similar behavior, like fractional Brownian motion with the same value of the Hurst exponent.

cond-mat.stat-mech↗

arXiv2021

Convergence to a Gaussian by narrowing of central peak in Brownian yet non-Gaussian diffusion in disordered environments

In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g. biological, systems.

cond-mat.stat-mech↗

arXiv2021

Multiphoton resonance in a driven Kerr oscillator in presence of high-order nonlinearities

We considered the multiphoton resonance in the periodically driven quantum oscillator with Kerr nonlinearity in the presence of weak high-order nonlinearities. Multiphoton resonance leads to the emergence of peaks and dips in the dependence of the stationary occupations of the stable states on detuning. We demonstrated that due to high-order nonlinearities, these peaks and dips acquire additional fine structure and split into several closely spaced ones. Quasiclassically, multiphoton resonance is treated as tunneling between the regions of the oscillator phase portrait, and the fine structure of the multiphoton resonance is a consequence of a special quasienergy dependence of the tunneling rate between different regions of the classical phase portrait. For different values of damping and high-order nonlinearity coefficients, we identified the domain of quasienergies where tunneling strongly influences the system kinetics. The corresponding tunneling term in the Fokker-Planck equation in quasienergy space was derived directly from the quantum master equation.

quant-ph↗

arXiv2021

Large Deviation in Continuous Time Random Walks

We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting times. In the case of Gaussian distribution of steps' lengths the general expression reduces to a sequence of two Legendre transformations applied to the cumulant generating function of waiting times. The discussion of several examples (Bernoulli and Gaussian random walks with exponentially distributed waiting times, Gaussian random walks with one-sided Lévy and Pareto-distributed waiting times) reveals interesting general properties of such large deviations.

cond-mat.stat-mech↗

arXiv2021

Emergence of polarized ideological opinions in multidimensional topic spaces

Opinion polarization is on the rise, causing concerns for the openness of public debates. Additionally, extreme opinions on different topics often show significant correlations. The dynamics leading to these polarized ideological opinions pose a challenge: How can such correlations emerge, without assuming them a priori in the individual preferences or in a preexisting social structure? Here we propose a simple model that qualitatively reproduces ideological opinion states found in survey data, even between rather unrelated, but sufficiently controversial, topics. Inspired by skew coordinate systems recently proposed in natural language processing models, we solidify these intuitions in a formalism of opinions unfolding in a multidimensional space where topics form a non-orthogonal basis. Opinions evolve according to the social interactions among the agents, which are ruled by homophily: two agents sharing similar opinions are more likely to interact. The model features phase transitions between a global consensus, opinion polarization, and ideological states. Interestingly, the ideological phase emerges by relaxing the assumption of an orthogonal basis of the topic space, i.e. if topics thematically overlap. Furthermore, we analytically and numerically show that these transitions are driven by the controversialness of the topics discussed, the more controversial the topics, the more likely are opinion to be correlated. Our findings shed light upon the mechanisms driving the emergence of ideology in the formation of opinions.

physics.soc-ph↗