TY - JOUR
T1 - Toward the full short-time statistics of an active Brownian particle on the plane
AU - Majumdar, Satya N.
AU - Meerson, Baruch
N1 - Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/8
Y1 - 2020/8
N2 - We study the position distribution of a single active Brownian particle (ABP) on the plane. We show that this distribution has a compact support, the boundary of which is an expanding circle. We focus on a short-time regime and employ the optimal fluctuation method to study large deviations of the particle position coordinates x and y. We determine the optimal paths of the ABP, conditioned on reaching specified values of x and y, and the large deviation functions of the marginal distributions of x and of y. These marginal distributions match continuously with "near tails"of the x and y distributions of typical fluctuations, studied earlier. We also calculate the large deviation function of the joint x and y distribution P(x,y,t) in a vicinity of a special "zero-noise"point, and show that lnP(x,y,t) has a nontrivial self-similar structure as a function of x, y, and t. The joint distribution vanishes extremely fast at the expanding circle, exhibiting an essential singularity there. This singularity is inherited by the marginal x- A nd y-distributions. We argue that this fingerprint of the short-time dynamics remains there at all times.
AB - We study the position distribution of a single active Brownian particle (ABP) on the plane. We show that this distribution has a compact support, the boundary of which is an expanding circle. We focus on a short-time regime and employ the optimal fluctuation method to study large deviations of the particle position coordinates x and y. We determine the optimal paths of the ABP, conditioned on reaching specified values of x and y, and the large deviation functions of the marginal distributions of x and of y. These marginal distributions match continuously with "near tails"of the x and y distributions of typical fluctuations, studied earlier. We also calculate the large deviation function of the joint x and y distribution P(x,y,t) in a vicinity of a special "zero-noise"point, and show that lnP(x,y,t) has a nontrivial self-similar structure as a function of x, y, and t. The joint distribution vanishes extremely fast at the expanding circle, exhibiting an essential singularity there. This singularity is inherited by the marginal x- A nd y-distributions. We argue that this fingerprint of the short-time dynamics remains there at all times.
UR - http://www.scopus.com/inward/record.url?scp=85089889898&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.102.022113
DO - 10.1103/PhysRevE.102.022113
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C2 - 32942466
AN - SCOPUS:85089889898
SN - 2470-0045
VL - 102
JO - Physical Review E
JF - Physical Review E
IS - 2
M1 - 022113
ER -