Bacterial chemotaxis is a well-studied system, particularly for E.coli bacteria. With the advent of single cell measurement techniques, the question arises how noise present inside the cell affects its chemotactic efficiency. For a long time, methylation reactions were believed to be the most important noise source because these are slow noises. But a new noise source has been experimentally discovered recently which comes from clustering tendency of the chemo-receptors. How does this newly found noise source affect the chemotactic performance? Using detailed theoretical models for intracellular signaling networks, we study chemotaxis motion of a single E.coli cell. We quantify chemotactic performance and show that an optimum size of the receptor clusters (i.e. an optimum noise strength) is best for chemotactic performance. We explain this performance peak as a result of sensing - adaptation interplay in the signaling network. There are many different classes of biological sensory systems where sensing an external stimulus and adaptation with the external environment are observed. Our research raises the important question whether a competition between these two modules can be a key to the most efficient sensing mechanism in this wide class of systems.

Condensed matter physics (CMP) is a rapidly growing field where novel ideas are being introduced almost regularly, including those with the potential for near (and far) term technological applications. The field, therefore, provides an excellent opportunity for studying highly diverse topics. Our group is thus interested in exploring such diverse phenomena, and has successfully explored questions related to various areas in CMP, such as strongly-correlated systems, cold-atomic physics, quantum many-body chaos, the topology of spin systems, quantum computing, Fermi and non-Fermi liquids, and others. In our research group, we often use a combination of analytical methods, namely diagrammatic field theory, variational techniques, and large-N formalism, as well as numerical techniques including variational quantum Monte Carlo (VQMC), determinantal quantum Monte Carlo (DQMC), exact diagonalization, and dynamical mean-field theory (DMFT). Apart from these techniques, our group also employs phenomenological approaches based on experimental results and first-principle calculations from density functional theory (DFT) to explore topics in CMP.

Mastering the fundamental physics behind topological phases is vital to realizing large-scale topological quantum computers. Such quantum computers will accelerate the discovery process in several technological areas, from quantum cryptography to drug design. The study of electrons in strongly interacting materials like high-Tc superconductors is crucial to the ongoing efforts to discover Room-temperature (room-T) superconductors. Realizing a room-T superconductor will have an immeasurable impact on our modern civilization. Such superconductors will allow us to transmit electrical power across vast distances without any loss and help us create highly efficient electronic devices that do not waste energy. The increased efficiency of power utilization can bring down the world's overall carbon footprint and aid in solving the climate change crisis.

Understanding the behaviour of nonequilibrium systems, which are remarkably different from their equilibrium counterparts, forms one important branch of modern day statistical physics research. Broadly, there are two different approaches used by theoretical physicists --- one is to try to formulate general principles governing and classifying nonequilibrium systems and the other is to use simple model systems to understand some specific interesting phenomena. The two approaches enhance and complement each other in advancing frontier research in nonequilibrium statistical physics. Indeed, any theoretical progress in understanding the nature of nonequilibrium systems is of immense importance since nonequilibrium processes are ubiquitous in nature. Characterizing statistical properties of active particles (like bacteria or other microorganisms) has direct application in building efficient micro and nano motors which can be used in drug delivery or bioimaging. On the other hand, characterizing non-equilibrium response is one of the essential first steps to building, say, smart materials. More generally, the statistical theoretical methods developed to study such systems are also very useful to study a diverse range of social and financial systems ranging from traffic flow to fluctuation in stock markets.

On a broad level, our aim is to understand dynamical and stationary behaviour of classical nonequilibrium systems using both analytical and numerical tools. More specifically, one of the focuses of our current research is to characterize the behaviour of active particles (from bacteria, nano-swimmers to birds), which are building blocks of active matter, using minimal statistical models. Our main interest is to understand how nonequilibrium systems respond to external perturbation, which is very different and much less understood compared to their equilibrium counterparts.

- Effective forces:The medium generated effective forces on the colloids add to the direct interaction between them, resulting in mutual effective pair interaction which controls their phase behaviour and dynamics. We study the effective colloidal forces, their tenability and consequences in phase behaviours in the presence of an external potential.
- Probing dynamics in colloids under external perturbations:Colloidal particle dynamics probed via the time dependent probability distributions of the particle displacement under a variety of external perturbations, like external potentials and confinement.
- Microscopic simulation of Thermophoretic nanoparticle
- System with temperature-dependent interaction in the presence of temperature difference.
- The cold region gets long-ranged crystalline order in the non-equilibrium steady state.

[References: Phys. Rev. E 97, 062142 (2018); Phys. Rev. E 103, 032122 (2021)]

[References: Phys. Rev. E 101, 052611 (2020); Phys. Rev. E 103, 042133 (2021); Phys. Rev. E 107, 024109 (2023)]

[References: Physical Review Letters 128, 140401 (2022); Physical Review Letters 129, 070601 (2022)]

There are major challenges between bridging the gap between molecular and relevant length scales of the system, from molecular relaxation time to large time scales of the system. There are two possible (approximate) ways to do these: (i) Mean field theory - Microscopic Hamiltonian replaced by that averaged over a large number of degrees of feedom (Liquid State Theories) and (ii) Computer simulation-Numerical calculation with the microscopic Hamiltonian for a small system. In Monte Carlo simulations, we probabilistically explore the phase space. In Molecular Dynamics simulations one performs numerical generation of the trajectories by Newton's law. We perform detailed computation and theoretical analysis on conformational changes in biomacromolecular complexes, like, protein-metal ion, protein-protein, protein-ligand structures which forms the heart of allbiochemical activities.

**Microscopic insight on protein functions:**We have developed a method for calculating the thermodynamics of conformational changes in bio-molecular complexes based on the distribution of the dihedral angles. Based on this we seek microscopic view of protein functions.**Dynamic aspects of conformational fluctuations:**We probe in detail how the time dependent fluctuations of the dihedral angles are correlated to show the connection between the structure and dynamics. In particular, we examine the long distance communication in proteins based on simulations and theoretical modeling.**Quantum Mechanical effects:**The coordination of metal ions to a protein leads to substantial electronic redistribution which governs the stability of metallo-proteins. This leads us to undertake ab-initio calculations for metal binding regions, using density functional theory.

Protein like Lactalbumin (aLA) forms molten globule state (intermediate state between protein folding and unfolding) at low pH. At low pH, the removal of Ca2+ ion reduces the overall stability of the protein, resulting the MG state. At MG state aLA bind with fatty acid like oleic acid. aLA+MG+OLA complex shows cytotoxic activity against cancer cell line. The behavior of a system comprising of bio-nacroemolecules are addressed by statistical mecahanical theories.

- The
**aggregation**behavior and dynamics of proteins is investigated by statistical mechanical theories and computer simulations. - The
**kinetics**of bio-molecular reactions are studied by theoretical modeling and computer simulations.

There are several important technological applications, like devising high sensitivity platform, bio-technology, drug design.

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