ICTS

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.

Resurgent asymptotics leads to remarkable new insights into the connection between perturbative physics and nonperturbative physics. Michael Berry has made profound contributions to the underlying ideas, as well as presenting some beautiful physical examples. I will discuss several illustrative examples of resurgent asymptotics in quantum mechanics, matrix models and quantum field theory.

Distinct phases of quantum systems, such as different symmetry-protected topological (SPT) phases, are separated by critical points. However, critical points, dubbed unnecessary quantum critical points (UQCPs),  can also appear within a single phase and do not separate two distinct phases. In this work, we investigate the geometric structure of such UQCPs in the parameter space of quantum systems and their relation to SPT phases. We show, using free-fermionic systems in various dimensions, that the locus of UQCPs arises from the phase boundaries of SPT phases. The manifold of UQCPs in the parameter space forms a geometric ``pencil'' whose axis coincides with this SPT phase boundary. This is work done in collaboration with Basudeb Mondal (IISc). 

The geometry of quantum states has drawn increasing attention in condensed matter physics, particularly in nonlinear electronic and optical responses and in adiabatic state-preparation protocols. The state space of quantum mechanics is naturally endowed with a Riemannian metric, a symplectic structure, and a complex structure, which together underlie familiar objects such as the quantum geometric tensor — whose real and imaginary parts are the quantum metric and the Berry curvature. Rather than treating these as isolated quantities that surface in individual calculations, we develop a unified geometric treatment of the dynamics of an entire congruence of flows on the curved manifold of states, described through projectors. This is precisely the setting of the Raychaudhuri equation, which characterises the evolution of geodesic congruences in curved spacetime. We identify unavoidable quantum-mechanical consequences of such flows, including caustics and tidal anisotropies. Building on this, we show that Boltzmann transport and adiabatic dynamics generate flows embedded in the full state space, with the associated responses, such as berry curvature dipole, being intricately linked to the expansion, shear, and vorticity of the congruence

We present a simple, visual proof of the spin-statistics theorem, based on the suggestion that histories of spinning particles should be represented not by worldlines but by ribbons. This suggestion is motivated and justified  by the coadjoint orbit analysis of the symmetry group. Our argument applies whenever the symmetry group topologically retracts to the Euclidean group $E(3)$, implying that neither special relativity nor even Galileian relativity is needed to prove the theorem. We also recover the Berry–Robbins geometric phase connection from this more general topological viewpoint.
 

The Event Horizon Telescope collaboration has presented remarkable images of polarised radiation from the immediate surroundings of the central black holes in M87 and in our own galaxy. These are constructed from the measured correlations between signals received by telescopes scattered over an entire hemisphere of the earth. Aberrations which modify the incoming electric fields in phase and amplitude are a major issue. One long standing solution is to construct 'closure quantities' which cancel the aberrations, using measured correlations between antenna pairs chosen to form a closed loop. The generalisation from complex scalar fields to the more realistic case of polarised EM fields is fairly recent and mathematically richer. This talk covers our joint work on this problem, which leads to a non-abelian GL(2,c) gauge theory on a graph. This has antennas as vertices and pairs with measured correlations as edges. . A complete set of gauge invariants which cancel the aberrations can be identified. The inclusion of measurement noise makes this a (Euclidean) quantum theory. Applications of this framework to real data are now emerging.

The Riemann Hypothesis has captivated mathematicians for more than a century, but its allure extends naturally to theoretical physics: the possibility that a deep arithmetic regularity may emerge from the simple logic of a physical system is hard to resist. Here we pursue this idea by recasting the Generalised Riemann Hypothesis in the language of random walks. The key ingredients are the strikingly aleatory behaviour of Möbius coefficients on square-free integers and of Dirichlet characters on prime numbers. Their statistical randomness can be tested with remarkable precision. From this viewpoint, the critical line Re s=1/2 acquires a natural physical meaning: it is the universal 1/2 scaling exponent characteristic of unbiased random walks.

The Wave and Particle nature of light is well understood in the context of double slit interference. Ascertaining the path of the photon, namely the particle nature of light, leads to the collapse of the wave function and hence resulting in no interference pattern. This wave particle duality can be precisely quantified in terms of the path predictability (P), visibility (V) and surprisingly a geometric measure of entanglement (E). In the general multislit interferometry a precise triality relationship emerges P^2 + V^2 +E^2 =1, which has found experimental verification. The geometric measure of entanglement, the so-called I-concurrence, is found to be related to the area between the constituent vectors of the Hilbert Space. This quantum mechanical treatment of the wave particle duality is in the presence of detectors to quantify the path predictability of the quanton. We illustrate the manifestation of the universal triality relation in various physical scenarios, both in optics and other multi-particle systems. Interestingly, it also manifests in Neutrino oscillations which may be verifiable in present day experience.

The complexity e.g. due to presence of disorder or complicated interactions in many realistic physical situations can lead to hamiltonians that include randomness (in physically natural bases). The latter in turn manifest in the typical eigenstate of the Hamiltonian. Quantum properties such as the quantum metric tensor G for describing distances between parameterised families of quantum states or geometric curvature C governing the geometric phase of transported quantum states are then best described by a statistical approach. In this talk, I will discuss the probability distribution of the quantum metric as well as curvature in a natural minimal model i.e an ensemble of three parameters Hamiltonians represented by standard random matrix ensembles.

In this talk, I will present a quantitative theory for the emergence of quantum many-body chaos as integrability is broken via a tunable parameter. In a circuit model of free fermions, 'doped' with a tunable density of integrability-breaking gates, we uncover the microscopic mechanisms underpinning the crossover from early-time integrable behaviour to late-time chaos through the lens of the out-of-time-ordered correlators (OTOCs). The integrability-breaking gates act as local, in spacetime, hotspots which locally amplify the OTOCs such that an accumulation of them eventually leads to fully-developed chaos. We identify the explicit characteristic time and length scales governing this crossover, as well as the dependence of the chaotic OTOC characteristics -- such as the butterfly velocity and front broadening -- on the integrability-breaking parameter. [Based on joint work with S. Biswas and R. Moessner, arXiv:2607.02506].