IPM

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.