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E. B. Rozenbaum, L. A. Bunimovich, and V. Galitski, Early-Time Exponential Instabilities in Nonchaotic Quantum Systems
Original
1902
Earlier work this paper cites.
T. Ali, A. Bhattacharyya, S. S. Haque, E. H. Kim, N. Moynihan, and J. Murugan, Chaos and Complexity in Quantum Mechanics
Original
1905
Earlier work this paper cites.
J. L. F. Barbón, E. Rabinovici, R. Shir, and R. Sinha, On The Evolution Of Operator Complexity Beyond Scrambling
Original
1907
Earlier work this paper cites.
S. Pilatowsky-Cameo, J. Chávez-Carlos, M. A. Bastarrachea-Magnani, P. Stránský, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
Original
1909
Earlier work this paper cites.
J. Kudler-Flam, L. Nie, and S. Ryu, Conformal field theory and the web of quantum chaos diagnostics
Original
1910
Earlier work this paper cites.
S. P. Kelly, E. Timmermans, and S. W. Tsai, Thermalization and its breakdown for a large nonlinear spin
Original
1910
Earlier work this paper cites.
A. Avdoshkin and A. Dymarsky, Euclidean operator growth and quantum chaos
Original
1911
Earlier work this paper cites.
T. Xu, T. Scaffidi, and X. Cao, Does scrambling equal chaos?
Original
1912
Earlier work this paper cites.
A. Dymarsky and A. Gorsky, Quantum chaos as delocalization in Krylov space
Original
1912
Earlier work this paper cites.
R. H. Dicke, Coherence in spontaneous radiation processes
1954
Earlier work this paper cites.
H. Lipkin, N. Meshkov, and A. Glick, Validity of many-body approximation methods for a solvable model: (i). exact solutions and perturbation theory
1965
Earlier work this paper cites.
A. Glick, H. Lipkin, and N. Meshkov, Validity of many-body approximation methods for a solvable model: (iii). diagram summations
1965
Earlier work this paper cites.
M. Feingold and A. Peres, Regular and chaotic motion of coupled rotators
1983
Earlier work this paper cites.
A. Peres, Ergodicity and mixing in quantum theory. i
1984
Earlier work this paper cites.
M. Feingold, N. Moiseyev, and A. Peres, Ergodicity and mixing in quantum theory. ii
1984
Earlier work this paper cites.
Lecture Notes in Physics Monographs. Springer Berlin Heidelberg, 1994
V. Viswanath and G. Müller, The Recursion Method: Application to Many Body Dynamics · 1994
Earlier work this paper cites.
N. Debergh and F. Stancu, On the Exact solutions of the Lipkin-Meshkov-Glick model
2001
Earlier work this paper cites.
D. A. Trunin, Pedagogical introduction to the Sachdev–Ye–Kitaev model and two-dimensional dilaton gravity
Original
2002
Earlier work this paper cites.
D. J. Yates, A. G. Abanov, and A. Mitra, Lifetime of almost strong edge-mode operators in one-dimensional, interacting, symmetry protected topological phases
Original
2002
Earlier work this paper cites.
T. Akutagawa, K. Hashimoto, T. Sasaki, and R. Watanabe, Out-of-time-order correlator in coupled harmonic oscillators
Original
2004
Earlier work this paper cites.
K. Hashimoto, K.-B. Huh, K.-Y. Kim, and R. Watanabe, Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
Original
2007
Earlier work this paper cites.
G. Styliaris, N. Anand, and P. Zanardi, Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
Original
2007
Earlier work this paper cites.

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2022

Krylov complexity in saddle-dominated scrambling

Bhattacharjee, Budhaditya, Cao, Xiangyu, Nandy, Pratik et al.

Understand

In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos.

However,on several occasions, it has been argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space.
In this work, we probe such an integrable system exhibiting saddle dominated scrambling through Krylov complexity and the associated Lanczos coefficients.
In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times.