Talks

 In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology. In this connection, we also present a derivation of quantum corrected version of the Fokker–Planck equation without dissipation and its fourth-order corrected analytical solution for the probability distribution profile responsible for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. It is explicitly shown from our computation that quantum corrected Fokker–Planck equation describes the particle creation phenomena better for Dirac delta type of scatterer. In this connection, we additionally discuss Itô, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile. Furthermore, we extend our discussion of particle production phenomena to describe the quantum description of randomness involved in the dynamics. We also present computation to derive the expression for the measure of the stochastic nonlinearity (randomness or chaos) arising in the stochastic inflation and reheating epoch of the universe, often described by Lyapunov Exponent. Apart from that, we quantify the quantum chaos arising in a closed system by a more strong measure, commonly known as Spectral Form Factor using the principles of random matrix theory (RMT). Finally, we discuss the role of out of time order correlation function (OTOC) to describe quantum chaos in early universe cosmology. 

It has recently been shown that quenched randomness, via the phenomenon of many-body localization, can stabilize dynamical phases of matter in periodically driven (Floquet) systems, with one example being discrete time crystals. This raises the question: what is the nature of the transitions between these Floquet many-body-localized phases, and how do they differ from equilibrium? We argue that such transitions are generically controlled by infinite randomness fixed points. By introducing a real-space renormalization group procedure for Floquet systems, asymptotically exact in the strong-disorder limit, we characterize the criticality of the periodically driven interacting quantum Ising model, finding forms of (multi-)criticality novel to the Floquet setting. We validate our analysis via numerical simulations of free-fermion models sufficient to capture the critical physics.

We present a plausible counterexample to the weak cosmic censorship conjecture in four-dimensional Einstein-Scalar theory with asymptotically flat boundary conditions. Our setup stems from the analysis of the massive Klein-Gordon equation on a fixed Kerr black hole background. In particular, we construct the quasinormal spectrum numerically, and analytically in the WKB approximation, then go on to compute its backreation on the Kerr geometry. In the regime of parameters where the analytic and numerical techniques overlap we find perfect agreement. We give strong evidence for the existence of a nonlinear instability at late times.

We show that a generic many-body Hamiltonian can be uniquely reconstructed from a single pair of initial-final states under the unitary time evolution. Interesting it is, this method is not practical due to its high complexity. We then propose a practical method for Hamiltonian reconstruction from multiple pairs of initial-final states. The stability of this method is mathematically proved and numerically verified.

This work is joint with Liujun Zou and Timothy Hsieh.

Recently they have been generalized to other 3d homogeneous spaces, namely 3d anti de Sitter space and half-pipe space, a 3d homogeneous space with a degenerate metric.

We show that generalized ideal tetrahedra correspond to dual tetrahedra in 3d Minkowski, de Sitter and anti de Sitter space. They are those geodesic tetrahedra whose faces are all lightlike.

We investigate the geometrical properties of these dual tetrahedra in a unifi ed framework.  We then apply these results to obtain a volume formula for generalised ideal tetrahedra and their duals, in terms of their dihedral angles and their edge lengths.

This is joint work with Dr Carlos Scarinci, KIAS.