Galaxies are the visible building blocks of the Universe where everything happens, from stars to planets to life itself. Interestingly, while some galaxies appear beautiful and orderly, others appear completely distorted, twisted, and chaotic. These irregular galaxies arise due to galaxy collisions -- one of the most spectacular events in the Universe. In this talk, we will explore galaxy collisions, and understand: how do they occur? why do they occur? Do galaxy collisions lead to complete destruction of galaxies or creation of something new? and, How our own Milky Way is currently undergoing a collision with another galaxy intruder? In essence, galaxy collisions and mergers are among the most important drivers of galaxy evolution across the cosmos.

Quantum statistics is traditionally viewed as a kinematic property that determines how particles occupy available states. In this talk, I will show that quantum statistics can itself serve as a powerful resource for energy conversion in a transport setting. Focusing on particles obeying Haldane exclusion statistics, we demonstrate that statistical interactions generate an intrinsic breaking of particle-hole symmetry, even in the absence of interactions, band asymmetry, or external symmetry-breaking mechanisms. The consequences for transport are profound. The symmetry breaking produces strong thermoelectric response and large deviations from the Wiedemann-Franz law. In particular, exclusion statistics can substantially enhance the thermoelectric figure of merit, establishing a new route toward efficient energy harvesting driven purely by quantum statistics. Building on this insight, I will show that exclusion statistics can be elevated to the status of a genuine thermodynamic resource. Within a nonlinear Landauer framework, quantum heat engines employing fractional-statistics carriers can surpass performance bounds previously regarded as universal for fermionic systems. Bosonic and fractional-statistics working media exhibit enhanced power output, improved efficiency-power trade-offs, and superior refrigeration capabilities. Finally, I will discuss a realistic realization based on thermally driven magnon transport, where the predicted advantages emerge in an experimentally accessible spin-caloritronic setting. These results suggest a new paradigm for quantum thermodynamics in which statistical correlation and not interactions, topology, or coherence alone become the fundamental resource governing transport, refrigeration, and energy conversion.

The Non-Hermitian Skin Effect (NHSE) represents a foundational shift in non-Hermitian wave physics, traditionally characterized by robust, single-edge localization driven by non-reciprocal coupling mechanisms or active bulk gain and loss. This talk explores the conceptual evolution from this established conventional paradigm toward a novel 'mesoscopic' regime, where non-Hermiticity emerges exclusively through radiative boundary leakage within an otherwise lossless photonic crystal structure. In this mesoscopic landscape, the system deviates from conventional singular edge-pinning, instead demonstrating symmetric, dual-edge localization governed by distinct size-dependent properties linked to the total system dimension. To characterize this behavior, Von Neumann entanglement entropy is utilized as a diagnostic tool, providing a quantitative measure of boundary interactions. The observed logarithmic growth patterns in this entropy offer rigorous verification of long-range, non-local correlations connecting the physical boundaries, effectively capturing the transition from isolated modes to an interconnected boundary state. In addition to this theoretical framework, the talk will outline experimental plans to map the phase transition from the mesoscopic regime to the conventional NHSE, utilizing high-precision microwave photonic crystal architectures and controlled bulk loss modulation. By establishing a unified physical framework for boundary-engineered wave trapping, this research outlines a passive, highly tunable pathway for next-generation technological integration, particularly in the fields of on-chip AI acceleration, quantum information processing, and advanced non-reciprocal photonic circuitry.

We have been using swift heavy ion beams, lasers and gamma radiations to synthesize and modify nanostructures of elemental as well as compound semiconductors and subsequently characterizing them using XRD, Raman and TEM. The dependence of the resulting new class of nano-materials on energy and fluence of the initial swift heavy ions, is being investigated in detail. These external probe radiations modify the electronic and optical properties of nano-structures (quantum wells, quantum dots and nanowires). Some applications of these studies in Nano-Science and Nanotechnology will be presented.

We develop a novel, fully unsupervised learning framework, consisting of a Convolutional autoencoder and Quantum clustering equipped with a unified evaluation score encapsulating separability and topological stability, to identify different phases and precisely locate the critical or crossover regime of quantum phase transitions using the pixilated snapshots of density profile evolution. We further illustrate, for the first time, the application of our machine learning framework in clustering distinct temporal regimes, which are characterized by critical dynamics such as sub-diffusive, super-diffusive, and diffusive dynamics. We employ transfer learning, and qualitatively show the finite size scaling of crossover region. The results demonstrate that our framework is robust to highly imbalanced heterogeneous data and multiple transitions. In this work, we have examined both single-particle and many-body systems. In single particle system, we investigated quasi-periodic Hamiltonians, specifically Aubry-Andre, Generalized Aubry-Andre, Rice-Mele models, as well as the true disorder Hamiltonian, namely the Anderson model. In the many-body system, we studied Bose-Hubbard model to capture Superfluid-Mott insulator transition and the 1D Fermi-Hubbard with quasi-periodic as well as true disorder onsite potential to capture the Ergodic-Many body localization (MBL) transition.

Over last two decades, Kitaev model established itself as a paradigmatic model in true sense. This exactly solvable model demonstrates many exotic phenomena of a frustrated magnetic system (or strongly correlated system in general) such as fractionalization, anyonic excitations, topological degeneracies in the simpler language of an effective Majorana tight binding model. Further, the material realization of Kitaev model in the presence of other non-Kitaev interaction have bought this model nearer to the broad condensed matter research community. In the first part of my talk I shall briefly present the salient features of Kitaev and Kitaev-Heisenberg model. In the second part I shall present our recent work on Kitaev-Heisenberg model in small clusters. We will argue that the salient features of Kitaev interaction allows certain features to be manifested even in small system and govern some interesting new quantum effect that might be relevant even in thermodynamic limit. In particular, we would discuss ground state, magnetization, susceptibility, correlation function, etc to establish it. Lastly, we present a possible realization of quantum Otto engine for Kitaev-Heisenberg cluster and show that certain emergent many-body effects maximize the efficiency. We also discuss the effect of negative temperature, the relative sign and magnitude of Kitaev and Heisenberg interactions and possible of role of frustration as function of magnitude of spin.

Defects are conventionally viewed as detrimental to topological phases, as they often promote localization and suppress coherent quantum phenomena. Recent studies, however, have revealed that defects can themselves become a resource for generating novel collective and topological phenomena. In this talk, I will discuss two examples that illustrate this emerging perspective. First, I will discuss the effect of realizable crystallographic defects with odd-sided plaquettes in a spin-1/2 Kitaev honeycomb model. In particular, we analyze a locally realizable 'Stone-Wales' defect which can be experimentally relevant for Kitaev materials. The emergent flux on an odd plaquette breaks time-reversal symmetry and shows a real-space chirality. We find that the chiralities of distant defects couple through an emergent long-range power-law interaction with ferromagnetic sign. While the clean Kitaev model has no  finite-temperature phase transitions, we find that introducing a dilute defect density produces a true phase transition to a non-Abelian chiral spin liquid. The critical temperature of this transition remains sizable, hence can potentially be accessed in experiments. The resulting chiral spin liquid exhibits scalar spin chirality and electron orbital magnetization even without external magnetic fields. Second, I will discuss a local time-reversal-symmetry-breaking defect in graphene modeled by imaginary next-nearest-neighbor hopping on a single hexagon. At low energies, this defect gives a topological mass term to the gapless Dirac cones and generates chirality. With increasing defect strength, surprisingly, the chirality reverses without changing the defect chirality. Such a topological transition is observed in two experimentally realizable measures of chirality: (1) electronic currents of the low-energy states and (2) orbital magnetization via a local Chern marker. We analytically compute the critical point of this chirality-reversing transition and identify that it is governed by a pair of zero-energy quasibound states appearing due to the introduction of the defect.