Scientific Series

 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. 

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.

It has been realized that anomalies can be classified by topological phases in one higher dimension. Previous studies focus on ’t Hooft anomalies of a theory with a global symmetry that correspond to invertible topological orders and/or symmetry protected topological orders in one higher dimension. In this talk, I will introduce an anomaly that appears on the boundaries of (non-invertible) topological order with anyonic excitations [1]. The anomalous boundary theory is no longer invariant under a re-parametrization of the same spacetime manifold. The anomaly is matched by simple universal topological data in the bulk, essentially the statistics of anyons. The study of non-invertible anomalies opens a systematic way to determine all gapped and gapless boundaries of topological orders, by solving simple eigenvector problems. As an example, we find all conformal field theories (CFT) of so-called ``minimal models’’, except four cases, can be the critical boundary theories of Z_2 topological order (toric code). The matching of non-invertible anomaly have wide applications. For example, we show that the gapless boundary of double-semion topological order must have central charge c_L=c_R >= 25/28. And the gapless boundary of the non-Abelian topological order described by S_3 topological quantum field theory can be three-state Potts CFT, su(2)_4 CFT, etc. [1] WJ, Xiao-Gang Wen, arXiv: 1905.13279, Phys. Rev. Research 1,033054

VisIt (https://wci.llnl.gov/simulation/computer-codes/visit/) is an interactive, powerful visualization, animation, and analysis tool.

VisIt is an open source and available for Unix, Windows or Mac users.

In this tutorial, after a brief introduction of VisIt, we will walk through several basic plotting/animation functions by using some toy data.

Neutrinos are established to be massive and the mass differences have been measured, but the absolute neutrino mass values remain unknown. Cosmic neutrinos with finite mass slightly suppress the matter power spectrum below their free-streaming scale and this effect can be applied to constrain neutrino masses. However, the challenge of this method is to disentangle the complex and poorly understood baryonic effects and to obtain better optical depth measurements from the cosmic microwave background experiments. In this talk, I will discuss the effects of the relative velocity between dark matter and neutrino fluids and how to use them to constrain neutrino masses with nonlinear reconstruction methods. The new method is not affected by most systematics which are parity even and not limited by the knowledge of optical depth to the cosmic microwave background, rendering it a new promising probe of neutrino properties.

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus break unitarity. Here we show that these expectations can be made precise in loop quantum cosmology. Concretely, even when loop quantum cosmology is unitary at the fundamental level, when microscopic degrees of freedom, irrelevant to low-energy cosmological observers, are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. When extrapolated to black hole formation and evaporation, this concrete example provides a key physical insight for a natural resolution of Hawking's information paradox.

Cosmological perturbation theory has a long tradition for describing the early phases of the Universe. As the observations of the CMB radiation suggest, it is reasonable, at least as a first approximation, to implement cosmological inhomogeneities as small perturbations around homogeneous and isotropic FRW solutions. In these approaches, backreactions between the inhomogeneities and the background are usually neglected. There is an ongoing debate about how and to which extend these backreactions affect the large scale structure of the Universe. Even at a purely classical level, there is no conclusive answer to this question yet.

In my talk, I am going to present a new systematic formalism for implementing backreactions in cosmological perturbation theory, in which both, the perturbations and the homogeneous degrees of freedom are considered as quantum degrees of freedom. As a more realistic theory of quantum fields on quantum cosmological space times, it can help to close the gap between a full theory of quantum gravity and symmetry-reduced models of quantum cosmology, and to confront these theories with observations. Our results show that quantum backreactions imply non-trivial corrections that are potentially phenomenologically significant.

Bergman's Diamond Lemma for ring theory gives an algorithm to produce a (non-canonical) basis for a ring presented by generators and relations. After demonstrating this algorithm in concrete, geometrically-minded examples, I'll turn to preprojective algebras and their multiplicative counterparts. Using the Diamond Lemma, I'll reprove a few classical results for preprojective algebras. Then I'll propose a conjectural basis for multiplicative preprojective algebras. Finally I'll explain why the set is a basis in the case of multiplicative preprojective algebras for quivers containing a cycle, the subject of joint work with Travis Schedler.

Results from the first digital quantum simulation of an SU(2) gauge theory are presented. This was done by analytically constructing gauge-invariant states and implementing a Trotterized time evolution operator for that basis on superconducting hardware. By using error mitigation techniques, electric energy measurements could be reliably extracted following one Trotter-Suzuki time step. This work is a small but important step toward determining what field-theoretic calculations will be possible using near-term devices.

In quantum spin systems, the existence of a spectral gap above the ground state has strong implications for the low-energy physics. We survey recent results establishing spectral gaps in various frustration-free spin systems by verifying finite-size criteria. The talk is based on collaborations with Abdul-Rahman, Lucia, Mozgunov, Nachtergaele, Sandvik, Yang, Young, and Wang.