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Related papers: Krylov complexity in inverted harmonic oscillator

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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…

High Energy Physics - Theory · Physics 2023-12-27 Cameron Beetar , Nitin Gupta , S. Shajidul Haque , Jeff Murugan , Hendrik J R Van Zyl

The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems and thus the OTOC is widely used as a measure of chaos. For…

Quantum Physics · Physics 2023-06-12 Tomás Notenson , Ignacio García-Mata , Augusto J. Roncaglia , Diego A. Wisniacki

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 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…

High Energy Physics - Theory · Physics 2025-04-11 Matteo Baggioli , Kyoung-Bum Huh , Hyun-Sik Jeong , Keun-Young Kim , Juan F. Pedraza

Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has…

Strongly Correlated Electrons · Physics 2021-03-24 Anna Keselman , Laimei Nie , Erez Berg

Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic…

High Energy Physics - Theory · Physics 2024-01-22 Koji Hashimoto , Keiju Murata , Norihiro Tanahashi , Ryota Watanabe

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…

High Energy Physics - Theory · Physics 2023-06-09 Kiran Adhikari , Sayantan Choudhury

Out-of-time order correlators (OTOCs) are crucial tools for studying quantum chaos as they show distinct scrambling behavior for chaotic Hamiltonians. We calculate OTOC and analyze the quantum information scrambling in atom-field and…

Quantum Physics · Physics 2025-10-07 Baibhab Bose , Devvrat Tiwari , Subhashish Banerjee

The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is…

Quantum Physics · Physics 2024-04-15 Liangyu Chen , Baoyuan Mu , Huajia Wang , Pengfei Zhang

The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends…

High Energy Physics - Theory · Physics 2021-02-10 Arpan Bhattacharyya , Wissam Chemissany , S. Shajidul Haque , Jeff Murugan , Bin Yan

Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $\mathcal{K}_M(\mathcal{H},\eta)$ spanned by the…

Quantum Physics · Physics 2024-06-21 Ryu Sasaki

In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an…

Quantum Physics · Physics 2026-02-03 Jeff Murugan , Hendrik J. R. van Zyl

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…

Strongly Correlated Electrons · Physics 2019-09-19 Shenglong Xu , Brian Swingle

In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…

High Energy Physics - Theory · Physics 2026-02-12 Matteo Baggioli , Kyoung-Bum Huh , Hyun-Sik Jeong , Xuhao Jiang , Keun-Young Kim , Juan F. Pedraza

Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos, and has recently been much studied for various time-independent systems. We initiate the study of K-complexity in…

Quantum Physics · Physics 2023-12-22 Amin A. Nizami , Ankit W. Shrestha

Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state…

High Energy Physics - Theory · Physics 2024-05-27 Kyoung-Bum Huh , Hyun-Sik Jeong , Juan F. Pedraza

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…

High Energy Physics - Theory · Physics 2023-09-06 Johanna Erdmenger , Shao-Kai Jian , Zhuo-Yu Xian

The dynamic region of out-of-time-ordered correlators (OTOCs) serves as a powerful indicator of chaos in classical and semiclassical systems, capturing the characteristic exponential growth. In contrast, this signature fails to appear in…

Quantum Physics · Physics 2025-08-05 Rohit Kumar Shukla , Gaurav Rudra Malik , S. Aravinda , Sunil Kumar Mishra

In this article, we explore dynamical aspects of Out-of-Time-Order correlators (OTOCs) for critical quenches, in which an initial non-trivial state evolves with a CFT-Hamiltonian. At sufficiently large time, global critical quenches exhibit…

High Energy Physics - Theory · Physics 2021-08-31 Suchetan Das , Bobby Ezhuthachan , Arnab Kundu , Somnath Porey , Baishali Roy

We use Krylov complexity to study operator growth in the $q$-body dissipative SYK model, where the dissipation is modeled by linear and random $p$-body Lindblad operators. In the large $q$ limit, we analytically establish the linear growth…

Quantum Physics · Physics 2024-01-18 Budhaditya Bhattacharjee , Pratik Nandy , Tanay Pathak