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SUMMARY:Phase transitions in persistent and run-and-tumble walks - Raúl T
 oral (Universitat de les Illes Balears)
DTSTART:20231106T100000Z
DTEND:20231106T110000Z
UID:TALK203194@talks.cam.ac.uk
DESCRIPTION:The motion of active matter\, like bacteria and other tiny par
 ticles\, has been studied extensively using mathematical models such as pe
 rsistent and run-and-tumble random walks. These models incorporate a memor
 y element\, making it more likely for the walker to move in the same direc
 tion as their previous step. In this talk\, I will explore various random-
 walk models\, with a specific focus on calculating the large-deviation fun
 ction. This function helps us understand how the end-to-end distance scale
 s with the number of steps taken. Additionally\, I will consider its Lapla
 ce transform\, the so-called Langevin function providing insight into the 
 relationship between force and extension. When persistence is present\, th
 ere are some unexpected phenomena that are absent in walks without memory.
  Firstly\, in on-lattice random walks with persistence in spatial dimensio
 n three or larger\, two new inflexion points appear in the Langevin functi
 on. This suggests an initial softening phase before the usual stiffening\,
  which occurs beyond a critical force level. For off-lattice random walks 
 with persistence and run-and-tumble walks in spatial dimension larger than
  four\, the large deviation function undergoes a first-order phase transit
 ion. In the corresponding force-versus-extension relation\, this transitio
 n manifests as the attainment of complete extension at a finite force magn
 itude. Analytically\, the origin of this phenomenology bears many similari
 ties with the calculation of the partition function of an ideal quantum bo
 son gas\, and the phase transitions found have the same mathematical origi
 n than the Bose-Einstein condensation.
LOCATION:Seminar Room 1\, Newton Institute
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