English
Related papers

Related papers: Probing the localization effects in Krylov basis

200 papers

We study the intermediate statistics of the spectrum of quasi-energies and of the eigenfunctions in the kicked rotator, in the case when the corresponding system is fully chaotic while quantally localized. As for the eigenphases, we find…

Chaotic Dynamics · Physics 2013-09-03 Thanos Manos , Marko Robnik

We investigate the phase transitions from chaotic to nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder, which can be realized with a Rydberg atom array setting. As the disorder strength increases, the emergence…

Quantum Physics · Physics 2025-10-03 Yijia Zhou , Wei Xia , Lin Li , Weibin Li

Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a…

Quantum Physics · Physics 2025-03-11 Aranya Bhattacharya , Pingal Pratyush Nath , Himanshu Sahu

We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \le 3000$, which in the limit $N \rightarrow…

Chaotic Dynamics · Physics 2015-06-23 T. Manos , M. Robnik

We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit…

Krylov complexity has emerged as a new probe of operator growth in a wide range of non-equilibrium quantum dynamics. However, a fundamental issue remains in such studies: the definition of the distance between basis states in Krylov space…

Quantum Physics · Physics 2023-03-14 Chenwei Lv , Ren Zhang , Qi Zhou

We investigate the Krylov complexity of Schr\"odinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in…

High Energy Physics - Theory · Physics 2025-03-21 Peng-Zhang He , Hai-Qing Zhang

Krylov complexity has recently emerged as a useful probe of operator growth and quantum dynamics in many-body systems and holographic dualities. In this paper we study its behavior in the Veneziano--Wosiek model, a supersymmetric matrix…

High Energy Physics - Theory · Physics 2026-03-24 Eleonora Alfinito , Matteo Beccaria

Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a…

Strongly Correlated Electrons · Physics 2023-08-11 Chang Liu , Haifeng Tang , Hui Zhai

In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and…

High Energy Physics - Theory · Physics 2025-09-17 Pawel Caputa , Giuseppe Di Giulio , Tran Quang Loc

In the Wigner-Weyl phase space formulation of quantum mechanics, we analyse the problem of the spreading of an initial state or an initial operator under time evolution when described in terms of the Krylov basis. After constructing the…

Quantum Physics · Physics 2026-03-18 Kunal Pal , Kuntal Pal , Keun-Young Kim

We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to…

Quantum Physics · Physics 2025-01-30 Philippe Suchsland , Roderich Moessner , Pieter W. Claeys

The problem of Anderson localization, as well as the single particle localization-delocalizaton transition of the Aubry-Andr\'e model, is studied employing operator Krylov space methods. It is shown that even when the dynamics is generated…

Disordered Systems and Neural Networks · Physics 2026-05-26 Hsiu-Chung Yeh , Aditi Mitra

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…

High Energy Physics - Theory · Physics 2023-10-18 Arnab Kundu , Vinay Malvimat , Ritam Sinha

In this work, we investigate local quench dynamics in two-dimensional conformal field theories using Krylov space methods. We derive Lanczos coefficients, spread complexity, and Krylov entropies for local joining and splitting quenches in…

High Energy Physics - Theory · Physics 2025-10-21 Pawel Caputa , Giuseppe Di Giulio

We show that strongly localized wave functions occur around classical bifurcations. Near a saddle node bifurcation the scaling of the inverse participation ratio on Planck's constant and the dependence on the parameter is governed by an…

chao-dyn · Physics 2007-05-23 I. Varga , P. Pollner , B. Eckhardt

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric…

High Energy Physics - Theory · Physics 2023-04-27 Bao-ning Du , Min-xin Huang

We study a system of two coupled kicked rotors, both classically and quantum mechanically, for a wide range of coupling parameters. This was motivated by two published reports, one of which reported quantum localization, while the other…

Quantum Physics · Physics 2009-10-15 Borzumehr Toloui , Leslie E. Ballentine

We investigate Anderson localization in a three dimensional (3d) kicked rotor. By a finite size scaling analysis we have identified a mobility edge for a certain value of the kicking strength $k = k_c$. For $k > k_c$ dynamical localization…

Disordered Systems and Neural Networks · Physics 2010-02-17 Jiao Wang , Antonio M. Garcia-Garcia

The classical and quantum dynamics of a particle trapped in a one-dimensional infinite square well with a time periodic pulsed field is investigated. This is a two-parameter non-KAM generalization of the kicked rotor, which can be seen as…

Chaotic Dynamics · Physics 2009-11-07 R. Sankaranarayanan , A. Lakshminarayan , V. B. Sheorey