#### Alladi Ramakrishnan Hall

#### Fluctuation-Dissipation in de-Sitter Universe and Black Hole Spacetime

#### Ashmita Das

##### IIT Guwahati

*In the studies of quantum field theory in curved spacetime, the ambiguous concept of vacuum state and the particle content, is a long standing debatable aspect. So far it is well known to us that in the background of the curved spacetime, some privileged class of observers detect particle production in the suitably chosen vacuum states of the quantum matter fields. In this work we aim to study the characteristics behaviour of these produced particles in the back- ground of the de-Sitter (dS) Friedmann-Lamaître-Robertson-Walker (FLRW) Universe and (1 + 1) dimensional Schwarzschild spacetime, from the point of view of the respective privileged class of observers. Here the analysis is confined to the observers who perceive particle excitations in the conformal vacuum. We consider some test particles in the thermal bath of the produced particles and calculate the correlation function of the fluctuation of the random force as exerted by the produced quanta on the test particles. We obtain that the correlation function abide by the fluctuation-dissipation theorem which in turn signifies that the test particles execute Brownian like motion in the thermal bath of the produced quanta.*

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