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Symmetric Exclusion Process under Power-law Stochastic Resetting

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dc.contributor.advisor Basu, Urna en_US
dc.contributor.author MISHRA, SEEMANT en_US
dc.date.accessioned 2022-05-04T07:09:51Z
dc.date.available 2022-05-04T07:09:51Z
dc.date.issued 2022-05
dc.identifier.citation 72 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6793
dc.description.abstract We study the behaviour of the Symmetric Exclusion Process in the presence of a non- Markovian stochastic resetting, where the system’s configuration is reset to a step-like profile at power-law waiting times with an exponent α. We find that power-law resetting leads to a rich behaviour for the diffusive and total currents, as well as the density profile. For α < 1, we show that, in the limit of large system size L → ∞, the density profile eventually becomes uniform while the average diffusive current grows sub-linearly with time t, with an exponent that lies between 1/2 and 1. For any finite L, however, the current grows ∼ t^α at late-times t ≫ L2. We develop a perturbative approach to get the distributions of the diffusive current and explain the origins of certain peculiar ‘peaks’ in them. Furthermore, we find that the average total current grows ∼√t. Using a renewal approach, we also compute the total current distributions, which turn out to be strongly non-Gaussian and bimodal for α ≃ 1/2. For α > 1, the system relaxes to an eventual non-trivial stationary density profile, which we compute exactly. In this regime, the average diffusive current grows ∼ t. The total current, on the other hand, reaches a stationary distribution with typical non-Gaussian fluctuations and a diverging average for α ≤ 3/2, while for α > 3/2 the average total current reaches a stationary value. en_US
dc.language.iso en en_US
dc.subject Statistical Physics en_US
dc.subject Stochastic Resetting en_US
dc.subject Symmetric Exclusion Process en_US
dc.subject Non-Markovian en_US
dc.title Symmetric Exclusion Process under Power-law Stochastic Resetting en_US
dc.type Thesis en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Physics en_US
dc.contributor.registration 20161094 en_US


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  • MS THESES [1705]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the BS-MS Dual Degree Programme/MSc. Programme/MS-Exit Programme

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