Talks

We derive general results relating revivals in the dynamics of quantum
many-body systems to the entanglement properties of energy eigenstates.
For a D-dimensional lattice system of N sites initialized in a
low-entangled and short-range correlated state, our results show that a
perfect revival of the state after a time at most poly(N) implies the
existence of "quantum many-body scars", whose number grows at least as
the square root of N up to poly-logarithmic factors. These are energy
eigenstates with energies placed in an equally-spaced ladder and with
Rényi entanglement entropy scaling as log(N) plus an area law term for
any region of the lattice. This shows that quantum many-body scars are a
necessary condition for revivals, independent of particularities of the
Hamiltonian leading to them. We also present results for approximate
revivals, for revivals of expectation values of observables and prove
that the duration of revivals of states has to become vanishingly short
with increasing system size.

Work in collaboration with Henrik Wilming (ETH)

I will describe how current and upcoming 21-cm measurements during cosmic dawn can probe a plethora of dark-matter and dark-energy models. This era saw the formation of the first stars, which coupled the spin temperature of hydrogen to its kinetic temperature---producing 21-cm absorption. The depth of this absorption acts as a thermostat, allowing us to constrain exotic cooling or heating due to dark matter. Additionally, the timing of the 21-cm signal strongly depends on the abundance of the small minihalos that hosted the first stars, allowing us to tightly constrain dark-matter models with suppressed power, such as warm or fuzzy dark matter. Finally, I will describe how in LCDM the acoustic physics of recombination are imprinted onto the 21-cm power spectrum during cosmic dawn, resulting in robust velocity-induced acoustic oscillations (VAOs). These act as a new standard ruler at z~20, opening up searches for early dark energy and perhaps resolving the H0 tension.

 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.