Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

Pilatowsky-Cameo, Saúl; Chávez-Carlos, Jorge; Bastarrachea-Magnani, Miguel A.; Stránský, Pavel; Lerma-Hernández, Sergio; Santos, Lea F.; Hirsch, Jorge G.

doi:10.1103/physreve.101.010202

Cited by 135 publications

(113 citation statements)

References 95 publications

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“…We now show that the same result applies to the semi-classical limit of the echo observable (35). This has been already discussed in Ref.…”

Section: Discussionsupporting

confidence: 82%

“…Substituting the Bopp representation forÂ(0) =â 2 (0) andB(t) =â † (t) into Eq. (35), and using the chain rule for the second-order derivatives, one gets…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, one anticipates that at least near the classical limit, the square commutator should grow exponentially fast in time with a rate given by the maximal Lyapunov exponent (similar considerations apply to the echo). Indeed, examples of quantum exponential sensitivity have been found only in models of fewparticle systems near well-defined semi-classical limits [30][31][32][33][34][35][36][37][38][39] and in the large-N limit of a Sachdev-Ye-Kitaev (SYK) model, a solvable model of all-to-all interacting fermions [15,29,40]. On the other hand, following the initial observation of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020

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Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

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“…We now show that the same result applies to the semi-classical limit of the echo observable (35). This has been already discussed in Ref.…”

Section: Discussionsupporting

confidence: 82%

“…Substituting the Bopp representation forÂ(0) =â 2 (0) andB(t) =â † (t) into Eq. (35), and using the chain rule for the second-order derivatives, one gets…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020

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“…Level statistics as in random matrices are found also in some integrable models, but they are caused by finite-size effects [11,12] or change abruptly upon tiny variations of the Hamiltonian parameters [13,14]. Other definitions of quantum chaos include the short-time exponential growth of out-of-time order correlators [15][16][17][18][19][20] and diffusive transport [21][22][23], although exponential behaviors of fourpoint correlation functions appear also near critical points of integrable models [24][25][26][27][28] and ballistic transport has been observed in the chaotic single-defect X X Z model [29].…”

Section: Introductionmentioning

confidence: 99%

Speck of chaos

Santos

Pérez‐Bernal

Torres-Herrera

2020

Phys. Rev. Research

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It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional X X Z model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

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“…It is interesting to generalize our scheme to higher-dimensional systems [3] and complex geometries [1]. An open fundamental question is connecting out-of-time-ordered correlator [64,65] and LE in our STIRAP setup especially because STIRAP is a unique platform to access both chaotic and nonchaotic regimes.…”

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confidence: 99%

Emergence of chaos and controlled photon transfer in a cavity-QED network

Dey

Kulkarni

2020

Phys. Rev. Research

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We develop optimal protocols for efficient photon transfer in a cavity-QED network. This is executed through stimulated Raman adiabatic passage scheme where time-varying inductive or capacitive couplings (with carefully chosen sweep rate) play a key role. We work in a regime where the semiclassical limit is valid, and we investigate the dynamical chaos caused by the light-matter coupling. We show that this plays a crucial role in estimating the lower bound on the sweep rate for ensuring efficient photon transfer. We present Hermitian as well as an open quantum system extension of the model. Without loss of generality, we study the three cavity and four cavity cases and our results can be adapted to larger networks. Our analysis is also significant in designing transport protocols aimed for nonlinear open quantum systems, in general.

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Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

Cited by 135 publications

References 95 publications

Quantum echo dynamics in the Sherrington-Kirkpatrick model

Quantum echo dynamics in the Sherrington-Kirkpatrick model

Speck of chaos

Emergence of chaos and controlled photon transfer in a cavity-QED network

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