A bstract We study a notion of operator growth known as Krylov complexity in free and
interacting massive scalar quantum field theories in d-dimensions at finite temperature. We …

The dynamics of quantum systems unfolds within a subspace of the state space or operator
space, known as the Krylov space. This review presents the use of Krylov subspace …

We consider proposals for the cost of holographic path integrals. Gravitational path integrals
within finite radial cutoff surfaces have a precise map to path integrals in $ T\overline {T} …

We explore spread and spectral complexity in quantum systems that exhibit a transition from
integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor …

In this paper, we investigate the complexity growth of the tensionless limit of string in the
neutral BTZ black hole horizon in massive gravity. When the string approaches the horizon …

In this paper, we investigate the second-order normal quantum fluctuation on the world-
sheet of a probe string in the Ba\~ nados-Teitelboim-Zanelli (BTZ) black hole. These …

A bstract Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of
a log-correlated real scalar field with a background charge and an exponential potential. We …

In this thesis, I establish new relations between quantum information measures in a two-
dimensional CFT and geometric objects in a three-dimensional AdS space employing the …