A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle. (English) Zbl 1457.82251
J. Stat. Mech. Theory Exp. 2019, No. 5, Article ID 053206, 34 p. (2019); erratum ibid. 2020, No. 4, Article ID 049901, 9 p. (2020).
Summary: We study the probability distribution \(P(X_N = X,N)\) of the total displacement \(X_N\) of an \(N\)-step run and tumble particle on a line, in the presence of a constant nonzero drive \(E\). While the central limit theorem predicts a standard Gaussian form for \(P(X,N)\) near its peak, we show that for large positive and negative \(X\), the distribution exhibits anomalous large deviation forms. For large positive \(X\), the associated rate function is nonanalytic at a critical value of the scaled distance from the peak where its first derivative is discontinuous. This signals a first-order dynamical phase transition from a homogeneous “fluid” phase to a “condensed” phase that is dominated by a single large run. A similar first-order transition occurs for negative large fluctuations as well. Numerical simulations are in excellent agreement with our analytical predictions.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
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