相关论文: Holography of K-complexity: Switchbacks and Shockw…
We provide the first steps towards a flat space holographic correspondence in two bulk spacetime dimensions. The gravity side is described by a conformally transformed version of the matterless Callan-Giddings-Harvey-Strominger model. The…
We develop K$\omega$, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations $(z_k I-H)x^{(k)}=b\, (k=0,1,2,...)$ for a given matrix $H$ and a vector $b$,…
In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner…
The double copy relationship between Yang-Mills theory and general relativity can be stated in terms of a field theory Kawai-Lewellen-Tye (KLT) momentum kernel, which maps two colour-ordered gluon amplitudes to a graviton amplitude at…
This thesis consists of four parts. In the first part of the thesis, we investigate the phase structure of Einstein-Maxwell-Scalar system with a negative cosmological constant. We chart out the full phase diagram, and discuss it's…
We argue that at finite energies, double-scaled SYK has a semiclassical approximation controlled by a coupling $\lambda $ in which all observables are governed by a non-trivial saddle point. The Liouville description of double-scaled SYK…
The SYK model consists of $N\gg 1$ fermions in $0+1$ dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the…
We analyse the Krylov solvability of inverse linear problems on Hilbert space $\mathcal{H}$ where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound…
Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…
In the context of a cosmological study of the bulk flows in the Universe, we present a detailed study of the statistical properties of the kinematic Sunyaev-Zel'dovich (kSZ) effect. We first compute analytically the correlation function and…
We consider the holographic dual of SQCD in the conformal phase. It is based on a higher derivative gravity theory, which ensures the correct field theory anomalies. This is then related to a six dimensional gravity theory via S^1…
In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and non-integrable…
We study the holographic complexity of noncommutative field theories. The four-dimensional $\mathcal{N}=4$ noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a…
We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent $z$. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of Krylov…
We study Krylov complexity $C_K$ and operator entropy $S_K$ in operator growth. We find that for a variety of systems, including chaotic ones and integrable theories, the two quantities always enjoy a logarithmic relation $S_K\sim…
We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics,…
Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator $T \bar T$, the product of the left- and right-moving stress tensor. We propose that…
Recent work showed holographic error correcting codes to have simple universal features at $O(1/G)$. In particular, states of fixed Ryu-Takayanagi (RT) area in such codes are associated with flat entanglement spectra indicating maximal…
We study upper bounds on the growth of operator entropy $S_K$ in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate $|\partial_t S_K|\leq 2b_1 \Delta S_K$, where $b_1$ is the first Lanczos…
We propose an algorithm which builds a concrete dual for large-radius 3d de Sitter with a timelike York boundary for both gravity and bulk effective fields. This generalizes the solvable $T\bar T+\Lambda_2$ deformation, whose finite real…