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Related papers: Krylov complexity from a simple quantum mechanical…

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Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm…

Quantum Physics · Physics 2023-12-15 Aranya Bhattacharya , Pratik Nandy , Pingal Pratyush Nath , Himanshu Sahu

We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional…

High Energy Physics - Theory · Physics 2025-11-04 Mohsen Alishahiha , Mohammad Javad Vasli

We investigate Krylov complexity in open quantum systems using Lindblad master equations for bosonic bath models, with particular emphasis on the Caldeira--Leggett model. Krylov complexity is computed from the moments of the two-point…

High Energy Physics - Theory · Physics 2026-04-22 Arpan Bhattacharyya , Sayed Gool , S. Shajidul Haque

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for…

Quantum Physics · Physics 2025-01-27 Kazutaka Takahashi , Adolfo del Campo

The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a pre-defined basis. It is known that this complexity is minimised by choosing the Krylov basis, thus defining…

Quantum Physics · Physics 2024-09-04 Amin A. Nizami , Ankit W. Shrestha

We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high-energy QCD. In particular, we observe that the cascade…

High Energy Physics - Phenomenology · Physics 2024-10-25 Pawel Caputa , Krzysztof Kutak

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…

High Energy Physics - Theory · Physics 2024-03-06 Hugo A. Camargo , Viktor Jahnke , Hyun-Sik Jeong , Keun-Young Kim , Mitsuhiro Nishida

Krylov complexity (K-complexity) is a measure of quantum state complexity that minimizes wavefunction spreading across all the possible bases. It serves as a key indicator of operator growth and quantum chaos. In this work, K-complexity and…

Quantum Physics · Physics 2025-10-08 J. Bharathi Kannan , Sreeram PG , Sanku Paul , S. Harshini Tekur , M. S. Santhanam

We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and…

Quantum Physics · Physics 2026-01-28 Carlo Cafaro , Emma Clements , Vishnu Vardhan Anuboyina

In this work, we have systematically investigated the Krylov complexity of curvature perturbation for the modified dispersion relation in inflation, using the algorithm in closed system and open system. Our analysis could be applied to the…

High Energy Physics - Theory · Physics 2024-05-24 Tao Li , Lei-Hua Liu

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

Spread complexity uses the distribution of support of a time-evolving state in the Krylov basis to quantify dispersal across accessible dimensions of a Hilbert space. Here, we describe how variations in initial conditions, the Hamiltonian,…

High Energy Physics - Theory · Physics 2025-11-19 Vijay Balasubramanian , Pawel Caputa , Joan Simón

We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…

High Energy Physics - Theory · Physics 2026-05-28 Ali Fatemiabhari , Carlos Nunez

While the motion of particles near a rotating, electrically-neutral (Kerr), and charged (Kerr--Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The…

High Energy Astrophysical Phenomena · Physics 2014-05-28 O. Kopáček , V. Karas

In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $\textit{Krylov subspace}$. The time evolution can be mapped onto a one-dimensional problem of a particle…

High Energy Physics - Theory · Physics 2025-09-01 Hugo A. Camargo , Yichao Fu , Viktor Jahnke , Keun-Young Kim , Kuntal Pal

Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open…

General Relativity and Quantum Cosmology · Physics 2026-02-27 Shi-Cheng Liu , Lei-Hua Liu , Bichu Li , Hai-Qing Zhang , Peng-Zhang He

This paper presents a systematic study of the chaotic dynamics of charged test particles around purely magnetically charged black holes immersed in a uniform external magnetic field within the framework of Einstein-ModMax theory. By…

General Relativity and Quantum Cosmology · Physics 2026-04-24 Zijian Liu , Wenfu Cao

In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture…

High Energy Physics - Theory · Physics 2026-04-23 Arpan Bhattacharyya , S. Shajidul Haque , Jeff Murugan , Mpho Tladi , Hendrik J. R. Van Zyl

We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds…

Quantum Physics · Physics 2025-04-29 Ankit Gill , Tapobrata Sarkar

We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…

Quantum Physics · Physics 2024-03-22 Youssef Aziz Alaoui , Bruno Laburthe-Tolra