相关论文: Holography of K-complexity: Switchbacks and Shockw…

Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the…

We study the complexity of the gravity dual to the confining $SU(N)\times SU(N+M)$ Klebanov-Strassler gauge theory, which is an important test case for holographic complexity in higher-dimensional and nonconformal gauge/gravity dualities.…

In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…

Recent developments in static patch holography proposed that quantum gravity in de Sitter space admits a dual description in terms of a quantum mechanical theory living on a timelike surface near the cosmological horizon. In parallel,…

We propose a tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-negative nature of singular values, bypassing the complex…

Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. We investigate the evolution of the maximally entangled state in the Krylov basis for both…

A step is made towards generalizing the method of holographic renormalization to backgrounds which are not asymptotically AdS, corresponding to a dual gauge theory which has logarithmically running couplings even in the ultraviolet. A prime…

In holography, the complexity--momentum correspondence relates the increasing momentum of a point particle falling into an eternal black hole to the rate of growth of the Krylov complexity of the dual boundary state, a conjecture…

The operator wavefunction provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature this wavefunction can acquire a phase that…

We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a $U(1)$ global symmetry. The analysis shows how to incorporate a chemical…

Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a…

We compute the Krylov Complexity of a light operator $\mathcal{O}_L$ in an eigenstate of a $2d$ CFT at large central charge $c$. The eigenstate corresponds to a primary operator $\mathcal{O}_H$ under the state-operator correspondence. We…

Schwarzian quantum mechanics describes the collective IR mode of the SYK model and captures key features of 2D black hole dynamics. Exact results for its correlation functions were obtained in JHEP {\bf 1708}, 136 (2017) [arXiv:1705.08408].…

We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm…

Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are prerogative of quantum chaotic systems and how they relate to more standard…

For large-scale discrete ill-posed problems, LSQR, a Lanczos bidiagonalization process based Krylov method, is most often used. It is well known that LSQR has natural regularizing properties, where the number of iterations plays the role of…

Spindle and disc solutions have received significant attention in recent literature. However, it is not entirely clear what these supergravity solutions represent in the dual SCFT. In this work we elucidate this issue by considering a…

We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the…

We adapt the Hamilton-Jacobi method of holographic renormalization to scalar field theories in Minkowski spacetime with scattering boundary conditions. The approach yields a flat-space holographic dictionary in which the expectation value…

We establish a holographic gravitational dual for the fundamental dynamical equations governing operator growth in Krylov subspace. Specifically, we show that the deep interior of the Krylov subspace maps directly to the near-horizon regime…