Out-of-time-order correlator in coupled harmonic oscillators

Akutagawa, Tetsuya; Hashimoto, Koji; Sasaki, Toshiaki; Watanabe, Ryota

doi:10.1007/jhep08(2020)013

Cited by 48 publications

(35 citation statements)

References 54 publications

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“…This was a motivation for the model of[18], and string theory matrix models in similar spirit are found in[47][48][49][50] 4. For related chaos analyses, see[52][53][54] 5.…”

mentioning

confidence: 74%

“…This could be due to the fact that our analyses are not semiclassical but fully quantum, and/or the fact that the Hilbert space of our system is infinite dimensional. Pinning down the reason would help us when we generalize the analyses to quantum field theories which have much bigger Hilbert spaces, 18 in view of the holographic principle. Numerical investigation of the semiclassical limits of our system, and comparison to the general semiclassical analyses [68], may provide a path to a resolution.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…With the OTOC as the novel indicator of quantum chaos, quantum chaotic few-body systems have been probed to see whether the OTOC grows exponentially in time. The way to calculate microcanonical/thermal OTOCs in generic quantum mechanics was provided [12], and major examples of chaotic systems with the exponentially growing OTOCs include a kicked rotor [13], a stadium billiard [12,14], the Dicke model [15], bipartite systems [16,17], and coupled harmonic oscillators [18]. 1 In particular, in the coupled harmonic oscillator system [18] (which is reminiscent of Yang-Mills theory [36][37][38]), the thermal OTOC is a better indicator of quantum chaos compared to the conventional energy level statistics.…”

Section: Introductionmentioning

confidence: 99%

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Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Hashimoto

Huh

Kim

et al. 2020

J. High Energ. Phys.

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We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

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“…This was a motivation for the model of[18], and string theory matrix models in similar spirit are found in[47][48][49][50] 4. For related chaos analyses, see[52][53][54] 5.…”

mentioning

confidence: 74%

Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Hashimoto

Huh

Kim

et al. 2020

J. High Energ. Phys.

Self Cite

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show abstract

“…where the subscript T denotes calculation of the expectation value in a heat bath of temperature T = 1 β . Specifically, introducing the microcanonical OTOC c n (t) as the OTOC for a fixed energy eigenstate |n as in [1] c n (t) = − n|[x(t), p(0)] 2 and if the Hamiltonian is of the form 5) it was shown in ref. [1] that this leads to…”

Section: Jhep01(2021)030mentioning

confidence: 99%

“…Early-time exponential growth of OTOCs has been found in a system of non-linearly coupled oscillators [2], which is expected to exhibit quantum chaos. More recently, however, it has been found that OTOCs show exponential growth in systems that do not possess quantum chaos, such as the inverted harmonic oscillator [3,4].…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator

Romatschke

2021

J. High Energ. Phys.

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Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy-level distribution. For low temperature, OTOCs are periodic in time, similar to results for the harmonic oscillator and the particle in a box. For high temperature, OTOCs exhibit a rapid (but power-like) rise at early times, followed by saturation consistent with 2〈x2〉T〈p2〉T at late times. At high temperature, the spectral form factor decreases at early times, bounces back and then reaches a plateau with strong fluctuations.

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C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Choudhury

2022

Fortschritte der Physik

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In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations, (1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region (−kτ≫1$-k\tau \gg 1$), super Hubble region (−kτ≪1$-k\tau \ll 1$) and at the horizon crossing point (−kτ=1$-k\tau = 1$) for massless field (m/scriptH≪1$m/{\cal H}\ll 1$), partially massless field (m/scriptH∼1$m/{\cal H}\sim 1$) and massive/heavy field (m/scriptH≫1$m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum (nζ$n_{\zeta }$) and tensor‐to‐scalar ratio (r). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

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Out-of-time-order correlator in coupled harmonic oscillators

Cited by 48 publications

References 54 publications

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

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