RESEARCH

Areas of Research

Shamik Gupta has worked on a wide variety of problems in nonlinear dynamics and statistical physics, including stochastic processes, stochastic thermodynamics, equilibrium and nonequilibrium dynamics of long-range interacting systems, synchronization, quantum dynamics. He has worked extensively in the areas of long-range interactions (a total of 24 papers) and synchronization (a total of 15 papers and a book). 

Synchronization

A remarkable phenomenon abound in nature is spontaneous synchronization in which a large population of coupled oscillating units of diverse frequencies operate in unison. Such cooperative effects occur in physical and biological systems pervading length and time scales of several orders of magnitude, e.g., flashing of fireflies, rhythmic applause in a concert hall, animal flocking behaviour, etc. Besides its obvious necessity in firings of cardiac cells that keep the heart beating and life going, synchrony is desired in man-made systems, e.g., in parallel computing in computer science, whereby processors must coordinate to finish a task on time, and in electrical power-grids, where generators must run in synchrony to be locked in frequency to that of the grid. However, synchrony could also be hazardous, e.g., in neurons, leading to impaired brain functions in Parkinson's disease and epilepsy. From its first documented observation by Christiaan Huygens in the 17th century, spontaneous synchronization has witnessed an enormous growth in terms of development of ideas and applications. Collective synchrony in oscillator networks has attracted immensely the attention of physicists and applied mathematicians, and has found applications in diverse fields, from quantum electronics to electrochemistry, from bridge engineering to social science.

His main overall achievement in the field of synchronization has been that while this area has traditionally been mostly studied from dynamical systems perspectives, he has shown how including weak stochasticity in the dynamics allows to treat analytically the observed phenomena by borrowing tools from statistical mechanics, and to interpret them to be of thermodynamic origin. In the half a century following Winfree’s landmark work in the field, studies in this area have almost exclusively been approached through nonlinear dynamics and computer simulations, and connection to statistical physics has had a subordinate role. Shamik Gupta’s work in this area, pursued together with collaborators and students, has served to enlarge the scope of such studies by bringing in valuable insights of statistical physics, using concepts like H-theorems, Fokker-Planck equations and the breakdown of detailed balance. The approach allowed to tackle analytically problems that are difficult and fascinating, both from the standpoint of nonlinear dynamics and from that of statistical physics because of their nonequilibrium and many-body character. In particular, his work was the first one to explore and emphasize the role of inertia and that of the nonequilibrium character of the dynamics, themes that have important implications both in terms of theory and applications but which have been given relatively little attention in the whole of the nonlinear dynamics literature. His work in the field of synchronization has been summarized in a book “Statistical Physics of Synchronization," coauthored with Alessandro Campa (INFN, Roma) and Stefano Ruffo (SISSA, Trieste) and published by Springer in 2018.

Long-range Interactions

Long-range interacting (LRI) systems are encountered across disciplines, for example, in hydrodynamics, astrophysics, plasmas, atomic and nuclear physics. These systems  are non-additive, that is, unlike systems with short-range interactions, they cannot be trivially divided into independent macroscopic sub-parts so that macroscopic observables for the entire system are obtained by summing over contributions from independent subparts. as is possible with short-range systems. This lack of additivity challenges several important results of equilibrium statistical physics found in classical textbooks and developed for short-range interactions, e.g., inequivalence of statistical ensembles, different ensembles yielding, e.g., different phase diagrams. Other striking effects are breaking of ergodicity: the phase space is broken up into subspaces not connected by local dynamics. 

A very interesting dynamical feature of LRI systems is the occurrence of quasistationary states (QSSs) during relaxation to equilibrium. These states involve a slow relaxation of macroscopic observables over times that diverge algebraically with the system size, so that in the thermodynamic limit, the system remains trapped in them and never attains the Boltzmann-Gibbs equilibrium. An important consequence is that large systems may essentially remain trapped in out-of-equilibrium states for times accessible to experiments. All of aforementioned features of long-range systems require an analytical approach for their understanding that derives directly from the dynamical equations of the system under study, e.g., a kinetic theory approach that describes the time evolution of the distribution in the phase space of the system. The long-time state of the system is then obtained from a knowledge of the fate of the distribution in the limit of long times. Such an approach may be contrasted with the one adopted for short-range systems for which the long-time state, which is typically the equilibrium state, is generically given by the Gibbs-Boltzmann distribution: Once the underlying Hamiltonian is known, the form of the distribution is given for free, and the dynamics that would lead to such a state is constructed only a posteriori, in a way that it satisfies the principle of detailed balance. Even for simple LRI systems, obtaining the steady-state distribution is often a tour de force, while in many cases, analytical characterization of the steady state has so far been elusive, thereby requiring one to resort to numerical simulations.

In the field of long-range interactions, some of his main achievements are

1.  Showing for the first time that long-lived non-equilibrium quasistationary states, observed under deterministic Hamilton dynamics of long-range systems and known to have lifetimes diverging with the system size, have a finite lifetime on including stochastic noise in the dynamics,

2.  Exploring the ubiquity of occurrence of non-equilibrium quasistationary states under deterministic dynamics of long-range systems, by considering very different dynamical settings than the ones known in the literature, 

3.  Treating for the first time the question of response of non-equilibrium quasistationary states in long-range systems to external perturbations, 

4. Studying for the first time non-equilibrium stationary states in systems with non-integrable potentials, by considering long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system, and developing a novel kinetic theory approach to describe the dynamics of this non-equilibrium problem, and others.

Research Funding

• Alexander von Humboldt Research Fellowship for Experienced Researchers, 2021 -- 2024

• CEFIPRA/IFCAR (Indo-French Centre for the Promotion of Advanced Scientific Research) Grant with Professor Julien Barré, University of Orleans, France, 2021 -- 2024

• Core Research Grant (CRG) scheme of Science and Engineering Research Board (SERB), Government of India; Project period: 2020 -- 2023

• MATRICS scheme of Science and Engineering Research Board (SERB), Government of India; Project period: 2020 -- 2023

• TARE scheme of Science and Engineering Research Board (SERB), Government of India; Project period: 2019 -- 2022