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A model of non-interacting particles in one dimension under resetting dynamics

Costantino Di Bello

A model of non-interacting particles in one dimension under resetting dynamics.

Rel. Alessandro Pelizzola. Politecnico di Torino, Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi), 2021

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Abstract:

In the framework of stochastic dynamics, resetting generally leads – since detailed balance is not enforced – to the existence of a non-equilibrium steady state (NESS). The model we studied here has already been treated in literature in the case of absence of resetting. We tried to understand how a resetting dynamics induces the reaching of the NESS and how resetting induces dynamical phase transitions. Specifically, we considered a one-dimensional system of noninteracting particles all located on the negative x-axis with a fixed density 𝜌. We make use of a general treatment to study the flux of particles through the origin. We also considered two cases: (i) diffusive dynamics with resetting and (ii) run-and-tumble dynamics with resetting. For simplicity, we enforced a Poissonian resetting rate r for all particles and supposed that each particle is reset to its initial position. The aim of the paper is to derive the probability 𝑃(𝑄, 𝑡) of having a net flux of particles through origin equal to Q at time t. In analogy with disordered systems, we computed the quantity 𝑃(𝑄, 𝑡) for both annealed and quenched initial conditions. In annealed case we can find the exact form of 𝑃𝑎𝑛(𝑄, 𝑡), which is a Poissonian distribution (both in diffusive and in run-and-tumble case) at any time, while in quenched case we were just able to find the large deviation form of 𝑃𝑞𝑢(𝑄, 𝑡). In particular, in case (i) we have a large deviation function for the probability quenched showing a discontinuity in the third derivative, symptomatic of a third order dynamical phase transition in 𝑃𝑞𝑢. On the contrary in case (ii) resetting does not lead to a phase transition.

Relators: Alessandro Pelizzola
Academic year: 2020/21
Publication type: Electronic
Number of Pages: 45
Subjects:
Corso di laurea: Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi)
Classe di laurea: New organization > Master science > LM-44 - MATHEMATICAL MODELLING FOR ENGINEERING
Ente in cotutela: Université Paris-Saclay (FRANCIA)
Aziende collaboratrici: CNRS LPTMS
URI: http://webthesis.biblio.polito.it/id/eprint/19141
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