Tridib Sadhu came to the Institute in February 2015. He got his PhD from the Tata

Institute in 2011 and had done postdocs at the Weizmann Institute and at the CEA

Saclay.

He left in October 2016 since he could not postpone any further his permanent professor position at the Tata Institute in India.

Tridib Sadhu has studied systems of impenetrable particles in crowded one-dimen-

sional channels which are referred as the single file diffusion. Such crowded motion

arises in many physical systems, e.g. ion channels in cell membranes, molecular mo-

tion in porous medium or inside carbon nano-tubes, transport in ionic conductors, etc.

What makes the system interesting from a theoretical perspective is that the motion

of individual tagged particles is sub-diffusive, drastically different from a Brownian

motion. Statistics of tagged particle is a pedagogical problem in non-equilibrium

statistical physics.

In collaboration with Bernard Derrida at Laboratoire de Physique Statistique,

Kirone Mallick at IPhT-Saclay, and Paul Krapivsky at Boston university, T. Sadhu

presented a hydrodynamics formulation for a general single file system. Their formu-

lation provides a systematic approach to calculate all moments of the tagged particle

and equivalently the associated large deviation function. They confirmed old theoret-

ical as well as experimental results of the second moment and presented new results

of higher moments and multi-time correlations. As an explicit example of the frame-

work they determined the full statistics in a specific single file system and then verified

their result using an exact solution starting from microscopic dynamics. They also

demonstrated an intriguing property where the results, even at large times, depend

on the choice of initial state. This research resulted in three publications [31, 32, 33].

Another line of T. Sadhu’s research concerns the dynamical properties in a non-

equilibrium steady state. As it is well known, in contrast to equilibrium, fluctuations

in a non-equilibrium steady state typically exhibit long-range correlations at a generic

parameter value even away from criticality. In a joint work [34] with Bernard Derrida, T. Sadhu used fluctuating hydrodynamics to characterize fluctuations in the non-equilibrium steady state of general diffusive systems and demonstrated the long-range correlation.

In addition to one-time statistics, they showed how to use the hydrody-

namics framework to calculate dynamical properties, namely multi-time correlations,

spectral distributions, and linear-response. They verified their results against an exact solution of a pedagogical model : the symmetric exclusion process. Their solution also allows one to directly verify the fluctuating hydrodynamics equation which is the starting point of a recently developed macroscopic fluctuation theory.

T. Sadhu’s most recent research concerns the generalized arc-sine law in frac-

tional Brownian motion. Fractional Brownian motion is a generalization of Brownian

motion which is used to describe anomalous diffusion, e.g. tracer diffusion, polymer

trans-location, stock market, etc. It is an interesting question to ask what are the gen-

eralizations of the well-known properties of Brownian motion ? In collaboration with

Kay Wiese at the Laboratoire de Physique Théorique, T. Sadhu studied an extension

of the celebrated three Arcsine laws in Brownian motion, namely, the distribution

of the fraction time spent on the positive half, the distribution of the position of

maximum, and the distribution of the last visit to the origin. Using a perturbation

expansion they demonstrated that all three properties have different distributions in

the fractional Brownian motion. These results will be published in a forthcoming

paper.