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Title:
Euclidean operator growth and quantum chaos
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Abstract:
Operator growth in Euclidean time differs substantially from its Minkowski counterpart. While the latter is known to conform to Lieb-Robinson bound, much less is known about the Euclidean case. We will introduce a new bound which establishes Euclidean version of the Lieb-Robinson result and discuss how euclidean growth is related to quantum chaos and plays interpolating role connecting out of time ordered correlators and eigenstate thermalization hypothesis. We will also show that the rate of Euclidean growth can be formulated in the language of Lancsoz coefficients, which were recently proposed to encode chaotic behavior. Using this relation we establish a new bound on Lyapunov exponents, which is valid for high temperatures. We also show that Lancsoz coefficients in full generality satisfy integrable Toda chain equations.
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