arXiv subjects

Gleb Oshanin

Publications and source records attributed to Gleb Oshanin.

At least 55 records · Page 3Linked to original sources

arXiv2019

Bath-Mediated Interactions between Driven Tracers in Dense Single-Files

Single-file transport, where particles cannot bypass each other, has been observed in various experimental setups. In such systems, the behaviour of a tracer particle (TP) is subdiffusive, which originates from strong correlations between particles. These correlations are especially marked when the TP is driven and leads to inhomogeneous density profiles. Determining the impact of this inhomogeneity when several TPs are driven in the system is a key question, related to the general issue of bath-mediated interactions, which are known to induce collective motion and lead to the formation of clusters or lanes in a variety of systems. Quantifying this collective behaviour, the emerging interactions and their dependence on the amplitude of forces driving the TPs, remains a challenging but largely unresolved issue. Here, considering dense single-file systems, we analytically determine the entire dynamics of the correlations and reveal out of equilibrium cooperativity and competition effects between driven TPs.

cond-mat.stat-mech↗

arXiv2019

Single-trajectory spectral analysis of scaled Brownian motion

A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, $T\to\infty$. In many experimental situations one is able to garner only relatively few stochastic time series of finite $T$, such that practically neither an ensemble average nor the asymptotic limit $T\to\infty$ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion. We demonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time $T$, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent. We also compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing single-trajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.

cond-mat.stat-mech↗

arXiv2019

Covariance of the running range of a Brownian trajectory

The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a Brownian Bridge and of a Slepian process. Here, we focus on the two-time correlations of the running range of Brownian motion - the maximal extent of a Brownian trajectory on a finite time interval. We calculate exactly the covariance function of the running range and analyse its asymptotic behaviour. Our analysis reveals non-trivial correlations between the value of the largest descent (rise) of a BM from the top to a bottom on some time interval, and the value of this property on a larger time interval.

cond-mat.stat-mech↗

arXiv2019

Polymer translocation across a corrugated channel: Fick-Jacobs approximation extended beyond the mean first passage time

Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick-Jacobs approach. Our main aim is to probe an effective broadness of the first passage time distribution (FPTD), by determining the so-called coefficient of variation $γ$ of the FPTD, defined as the ratio of the standard deviation versus the mean first passage time (MFPT). We present a systematic analysis of $γ$ as a function of a variety of system's parameters. We show that $γ$ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.

cond-mat.soft↗

arXiv2018

Towards a full quantitative description of single-molecule reaction kinetics in biological cells

The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially-reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it typically is very broad in many biological situations: thus, the mean FPT can differ from the most probable FPT by orders of magnitude. The most probable FPT is shown to strongly depend only on the starting position within the geometry and to be almost independent of the target size and reactivity. These findings demonstrate the dramatic relevance of knowing the full distribution of FPTs and thus open new perspectives for a more reliable description of many intracellular processes initiated by the arrival of one or few biomolecules to a small, spatially localised region inside the cell.

q-bio.SC↗

arXiv2018

Asymmetry relations and effective temperatures for biased Brownian gyrators

We focus on a paradigmatic two-dimensional model of a nanoscale heat engine, - the so-called Brownian gyrator - whose stochastic dynamics is described by a pair of coupled Langevin equations with different temperature noise terms. This model is known to produce a curl-carrying non-equilibrium steady-state with persistent angular rotations. We generalize the original model introducing constant forces doing work on the gyrator, for which we derive exact asymmetry relations, that are reminiscent of the standard fluctuation relations. Unlike the latter, our relations concern instantaneous and not time averaged values of the observables of interest. We investigate the full two-dimensional dynamics as well as the dynamics projected on the $x$- and $y$-axes, so that information about the state of the system can be obtained from just a part of its degrees of freedom. Such a state is characterized by effective "temperatures" that can be measured in nanoscale devices, but do not have a thermodynamic nature. Remarkably, the effective temperatures appearing in full dynamics are distinctly different from the ones emerging in its projections, confirming that they are not thermodynamic quantities, although they precisely characterize the state of the system.

cond-mat.stat-mech↗

arXiv2018

Spectral content of fractional Brownian motion with stochastic reset

We analyse the power spectral density (PSD) $S_T(f)$ (with $T$ being the observation time and $f$ is the frequency) of a fractional Brownian motion (fBm), with an arbitrary Hurst index $H \in (0,1)$, undergoing a stochastic resetting to the origin at a constant rate $r$ - the resetting process introduced some time ago as an example of an efficient, optimisable search algorithm. To this end, we first derive an exact expression for the covariance function of an arbitrary (not necessarily a fBm) process with a reset, expressing it through the covariance function of the parental process without a reset, which yields the desired result for the fBm in a particular case. We then use this result to compute exactly the power spectral density for fBM for all frequency $f$. The asymptotic, large frequency $f$ behaviour of the PSD turns out to be distinctly different for sub- $(H < 1/2)$ and super-diffusive $(H > 1/2)$ fBms. We show that for large $f$, the PSD has a power law tail: $S_T(f) \sim 1/f^γ$ where the exponent $γ= 2H+1$ for $0 1/2$ sticks to its Brownian value and does not depend on $H$.

cond-mat.stat-mech↗

arXiv2018

Nonequilibrium fluctuations and enhanced diffusion of a driven particle in a dense environment

We study the diffusion of a tracer particle driven out-of-equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced both by the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

cond-mat.stat-mech↗

arXiv2018

Order-disorder transitions in lattice gases with annealed reactive constraints

We study equilibrium properties of catalytically-activated $A + A \to \oslash$ reactions taking place on a lattice of adsorption sites. The particles undergo continuous exchanges with a reservoir maintained at a constant chemical potential $μ$ and react when they appear at the neighbouring sites, provided that some reactive conditions are fulfilled. We model the latter in two different ways: In the Model I some fraction $p$ of the {\em bonds} connecting neighbouring sites possesses special catalytic properties such that any two $A$s appearing on the sites connected by such a bond instantaneously react and desorb. In the Model II some fraction $p$ of the adsorption {\em sites} possesses such properties and neighbouring particles react if at least one of them resides on a catalytic site. For the case of \textit{annealed} disorder in the distribution of the catalyst, which is tantamount to the situation when the reaction may take place at any point on the lattice but happens with a finite probability $p$, we provide an exact solution for both models for the interior of an infinitely large Cayley tree - the so-called Bethe lattice. We show that both models exhibit a rich critical behaviour: For the annealed Model I it is characterised by a transition into an ordered state and a re-entrant transition into a disordered phase, which both are continuous. For the annealed Model II, which represents a rather exotic model of statistical mechanics in which interactions of any particle with its environment have a peculiar Boolean form, the transition to an ordered state is always continuous, while the re-entrant transition into the disordered phase may be either continuous or discontinuous, depending on the value of $p$.

cond-mat.stat-mech↗

arXiv2018

$N$-tag Probability Law of the Symmetric Exclusion Process

The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognised qualitatively for a long time, up to now there is no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically the large time limit of all cumulants for an arbitrary density of particles, and their full dynamics in the high density limit. In this limit, we unveil a universal scaling form shared by the cumulants and obtain the time-dependent large deviation function of the problem.

cond-mat.stat-mech↗

arXiv2018

Power spectral density of a single Brownian trajectory: What one can and cannot learn from it

The power spectral density (PSD) of any time-dependent stochastic processes $X_t$ is a meaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of $X_t$ over an infinitely large observation time $T$, that is, it is defined as an ensemble-averaged property taken in the limit $T \to \infty$. A legitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a \textit{single} trajectory recorded for a \textit{finite} observation time $T$. In quest for this answer, for a $d$-dimensional Brownian motion we calculate the probability density function of a single-trajectory PSD for arbitrary frequency $f$, finite observation time $T$ and arbitrary number $k$ of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of Brownian motion trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is a fluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of Brownian motion, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for Brownian motion and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.

cond-mat.stat-mech↗

arXiv2017

Universal Long Ranged Correlations in Driven Binary Mixtures

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

cond-mat.stat-mech↗

arXiv2016

Diffusive escape through a narrow opening: new insights into a classic problem

We study the mean first exit time $T_{\ve}$ of a particle diffusing in a circular or a spherical micro-domain with an impenetrable confining boundary containing a small escape window (EW) of an angular size $\ve$. Focusing on the effects of an energy/entropy barrier at the EW, and of the long-range interactions (LRI) with the boundary on the diffusive search for the EW, we develop a self-consistent approximation to derive for $T_{\ve}$ a general expression, akin to the celebrated Collins-Kimball relation in chemical kinetics and accounting for both rate-controlling factors in an explicit way. Our analysis reveals that the barrier-induced contribution to $T_{\ve}$ is the dominant one in the limit $\ve \to 0$, implying that the narrow escape problem is not "diffusion-limited" but rather "barrier-limited". We present the small-$\ve$ expansion for $T_{\ve}$, in which the coefficients in front of the leading terms are expressed via some integrals and derivatives of the LRI potential. On example of a triangular-well potential, we show that $T_{\ve}$ is non-monotonic with respect to the extent of the attractive LRI, being minimal for the ones having an intermediate extent, neither too concentrated on the boundary nor penetrating too deeply into the bulk. Our analytical predictions are in a good agreement with the numerical simulations.

cond-mat.other↗

arXiv2016

Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement

The ion-ion interactions become exponentially screened for ions confined in ultranarrow metallic pores. To study the phase behaviour of an assembly of such ions, called a superionic liquid, we develop a statistical theory formulated on bipartite lattices, which allows an analytical solution within the Bethe-lattice approach. Our solution predicts the existence of ordered and disordered phases in which ions form a crystal-like structure and a homogeneous mixture, respectively. The transition between these two phases can potentially be first or second order, depending on the ion diameter, degree of confinement and pore ionophobicity. We supplement our analytical results by three-dimensional off-lattice Monte Carlo simulations of an ionic liquid in slit nanopores. The simulations predict formation of ionic clusters and ordered snake-like patterns, leading to characteristic close-standing peaks in the cation-cation and anion-anion radial distribution functions.

cond-mat.soft↗

arXiv2016

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian Bridge on a finite interval $(0,L)$ and then periodically repeated over the whole real line, and study the power spectrum $S(f)$ of the diffusive process $x(t)$ in such a potential. We show that for most of realizations of $x(t)$ in a given realization of the potential, the low-frequency behavior is $S(f) \sim {\cal A}/f^2$, i.e., the same as for standard Brownian motion, and the amplitude ${\cal A}$ is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of ${\cal A}$ of arbitrary, negative or positive order $k$, and demonstrate that they exhibit a multi-fractal dependence on $k$, and a rather unusual dependence on the temperature and on the periodicity $L$, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of ${\cal A}$ has a log-normal left tail, and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process $x(t)$.

cond-mat.stat-mech↗

arXiv2016

Random pure states: quantifying bipartite entanglement beyond the linear statistics

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary $N \leq M$, a general relation between the $n$-point densities and the cross-moments of the eigenvalues of the reduced density matrix, i.e. the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite $N,M$. Then we focus on the moments $\mathbb{E}\{K^a\}$ of the Schmidt number $K$, the reciprocal of the purity. This is a random variable supported on $[1,N]$, which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for $\mathbb{E}\{K^a\}$ for $N = 2$ and $N=3$ and arbitrary $M$, and also for square $N = M$ systems by spotting for the latter a connection with the probability $P(x_{min}^{GUE} \geq \sqrt{2N}ξ)$ that the smallest eigenvalue $x_{min}^{GUE}$ of a $N\times N$ matrix belonging to the Gaussian Unitary Ensemble is larger than $\sqrt{2N}ξ$. As a byproduct, we present an exact asymptotic expansion for $P(x_{min}^{GUE} \geq \sqrt{2N}ξ)$ for finite $N$ as $ξ\to \infty$. Our results are corroborated by numerical simulations whenever possible, with excellent agreement.

cond-mat.stat-mech↗

arXiv2015

Distribution of the position of a driven tracer in a hardcore lattice gas

We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the TP position and the bath configuration and resorting to a mean-field-type approximation, we presented a computation of the fluctuations of the TP position in a previous publication [Phys. Rev. E \textbf{87}, 032164 (2013)]. Counterintuitively, on a one-dimensional lattice, the diffusion coefficient of the TP was shown to be a non-monotonic function of the density of bath particles, and reaches a maximum for a nonzero value of the density. Here, we: (i) give the details of this computation and offer a physical insight into the understanding of the non-monotonicity of the diffusion coefficient; (ii) extend the mean-field-type approximation to decouple higher-order correlation functions, and obtain the evolution equation satisfied by the cumulant generating function of the position of the TP, valid in any space dimension. In the particular case of a one-dimensional lattice, we solve this equation and obtain the probability distribution of the TP position. We show that the position rescaled by its fluctuations is asymptotically distributed accordingly to a Gaussian distribution in the long-time limit.

cond-mat.stat-mech↗

arXiv2014

Diffusion in periodic, correlated random forcing landscapes

We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in (0,1)$. While the periodicity ensures that the ultimate long-time behavior is diffusive, the generalised Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient $D_L$: Although one has the typical value $D^{\rm typ}_L \sim \exp(-βL^H)$, we show via an exact analytical approach that the positive moments ($k>0$) scale like $\langle D^k_L \rangle \sim \exp{[-c' (k βL^{H})^{1/(1+H)}]}$, and the negative ones as $\langle D^{-k}_L \rangle \sim \exp(a' (k βL^{H})^2)$, $c'$ and $a'$ being numerical constants and $β$ the inverse temperature. These results demonstrate that $D_L$ is strongly non-self-averaging. We further show that the probability distribution of $D_L$ has a log-normal left tail and a highly singular, one-sided log-stable right tail reminiscent of a Lifshitz singularity.

cond-mat.stat-mech↗