Tagged Particle in Single-File Diffusion

Krapivsky, P. L.; Mallick, Kirone; Sadhu, Tridib

doi:10.1007/s10955-015-1291-0

Cited by 52 publications

(97 citation statements)

References 86 publications

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“…For the uniform annealed case where the average densities are ̺ ± (x) = ρ, the large deviation function associated to this probability density function for Brownian particles has been obtained earlier using macroscopic fluctuation theory [12,37]. For general propagators of the form (8), the full probability distribution has also been derived in [34,35] for this case.…”

Section: B Annealed Casementioning

confidence: 99%

“…While there are many results available for hard-core inter-particle interaction, very less theoretical results are available for more general interactions. These include: the simple exclusion process where the MSD and the fourth cumulant is known [11,12], and the colloidal systems where the MSD is known in terms of isothermal compressibility [13]. Several experiments have recently been able to observe TP diffusion, for example, in passive microrehology in zeolites, transport of colloidal particles or charged spheres in narrow circular channels [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Tagged particle in single-file diffusion with arbitrary initial conditions

Cividini¹,

Kundu²

2017

J. Stat. Mech.

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We compute the full probability distribution of the positions of a tagged particle exactly for given arbitrary initial positions of the particles and for general single-particle propagators. We consider the thermodynamic limit of our exact expressions in quenched and annealed settings. For a particular class of single-particle propagators, the exact formula is expressed in a simple integral form in the quenched case whereas in the annealed case, it is expressed as a simple combination of Bessel functions. In particular, we focus on the step and the power-law initial configurations. In the former case, a drift is induced even when the one-particle propagators are symmetric. On the other hand, in the later case the scaling of the cumulants of the position of the tracer becomes different than the uniform case. We provide numerical verifications of our results.

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Section: B Annealed Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tagged particle in single-file diffusion with arbitrary initial conditions

Cividini¹,

Kundu²

2017

J. Stat. Mech.

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“…(1) defines it. Such processes appear in a broad range of contexts: Anomalous diffusion [3], diffusion of a marked monomer inside a polymer [4,5], polymer translocation through a pore [5][6][7][8], singlefile diffusion [9][10][11] observable experimentally in ion channels [12,13], the dynamics of a tagged monomer [14,15], finance (fractional Black-Scholes, fractional stochastic volatility models, and their limitations) [16][17][18], hydrology [19,20], and many more. Their extreme-value statistics has been stud-FIG.…”

Section: Introductionmentioning

confidence: 99%

“…ied in many referenes [9][10][11][21][22][23][24][25][26]. When studying random processes in a time interval [0, T ], quite generally the initial value X 0 is known, and the endpoint X T is itself a random variable determined by the random process.…”

Section: Introductionmentioning

confidence: 99%

Extreme-value statistics of fractional Brownian motion bridges

Delorme

Wiese

2016

Phys. Rev. E

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Fractional Brownian motion is a self-affine, non-Markovian and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t+ the process is positive, the maximum m it achieves, and the time tmax when this maximum is taken. Using a perturbative expansion around Brownian motion (H = 1 2 ), we give the first-order result for the probability distribution of these three variables, and the joint distribution of m and tmax. Our analytical results are tested, and found in excellent agreement, with extensive numerical simulations, both for H > . This precision is achieved by sampling processes with a free endpoint, and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

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“…This system can be viewed as independent Brownian motions that exchange their labels when they collide and has been solved exactly using various techniques [16,41,43,44,55]. Retaining only the first order terms in ρ ± in the formula (6), and using (5), we obtain the large deviation of a tracer in the reflecting Brownian limit:…”

mentioning

confidence: 99%

Large Deviations of a Tracer in the Symmetric Exclusion Process

2017

Self Cite

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The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite lattice with a step initial profile with average densities ρ+ and ρ− on the right and on the left of the origin. When ρ+ = ρ−, the gas is at equilibrium and undergoes stationary fluctuations. When these densities are unequal, the gas is out of equilibrium and will remain so forever. A tracer, or a tagged particle, is initially located at the boundary between the two domains; its position Xt is a random observable in time, that carries information on the nonequilibrium dynamics of the whole system. We derive an exact formula for the cumulant generating function and the large deviation function of Xt, in the long time limit, and deduce the full statistical properties of the tracer's position. The equilibrium fluctuations of the tracer's position, when the density is uniform, are obtained as an important special case.

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Tagged Particle in Single-File Diffusion

Cited by 52 publications

References 86 publications

Tagged particle in single-file diffusion with arbitrary initial conditions

Tagged particle in single-file diffusion with arbitrary initial conditions

Extreme-value statistics of fractional Brownian motion bridges

Large Deviations of a Tracer in the Symmetric Exclusion Process

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