Extracting Classical Lyapunov Exponent from One-Dimensional Quantum Mechanics

Morita, Takeshi

doi:10.48550/arxiv.2105.09603

Cited by 3 publications

(3 citation statements)

References 61 publications

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“…This is the case when the effective motion of the particle is described by an inverse harmonic oscillator, which implies that the divergence of the close trajectories grows exponentially. This behavior is associated with chaos (e.g., see [31,[60][61][62]), and (the square of) the Lyapunov exponent is given by λ 2 . We also note that the effective motion is described by a harmonic oscillator when V eff | r=r 0 > 0, i.e., λ 2 < 0, thus, we do not have chaos.…”

Section: Jhep09(2022)026mentioning

confidence: 99%

Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

Gwak

Kan

Lee

et al. 2022

J. High Energ. Phys.

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We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bound is more easily violated compared to that in a nonextremal black hole.

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Section: Jhep09(2022)026mentioning

confidence: 99%

Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

Gwak

Kan

Lee

et al. 2022

J. High Energ. Phys.

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“…• If the inverted harmonic oscillator described by (12) in one-dimensional quantum mechanics, the Lyapunov exponent in both classical and quantum mechanics is λ = √ 2πT [23,45,46]. Therefore, the eigenvalue of Schwarzschild black hole in the thermal potential is proportional to the square of the Lyapunov exponent of the inverse harmonic oscillator [50],…”

Section: A Application 1: Schwarzschild Black Holementioning

confidence: 99%

Fokker-Planck equation for black holes in thermal potential

2021

Preprint

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We construct a kind of thermal potential and then put the black hole thermodynamic system in it. In this regard, some thermodynamic properties of the black hole are related to the geometric characteristics of the thermal potential. Driven by the intrinsic thermodynamic fluctuations, the behavior of the black hole in the thermal potential is stochastic. With the help of solving the Fokker-Planck equation analytically, we obtain the discrete energy spectrum of Schwarzschild and Banados-Teitelboim-Zanelli (BTZ) black holes in the thermal potential. For Schwarzschild black hole, the energy spectrum is proportional to the temperature of the ensemble, which is an external parameter, and the ground state is non-zero. For BTZ black hole, the energy spectrum only depends on the AdS radius, which is the intrinsic parameter. Moreover, the ground state of BTZ black hole in thermal potential is zero. This also reflects the difference between three-dimensional gravity and four-dimensional gravity.

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“…Motivated by the holographic duality, the physics of quantum circuit complexity from the sides of quantum field theory (QFTs) and quantum mechanics have attracted more and more attentions. For a quantum chaotic system, the elementary physical quantities, like the scrambling time and Lyapunov exponent, can be captured by out-of-time-order correlators (OTOCs) [19][20][21][22][23][24][25]. Some recent works, for instance [23,24], show that the evolution of quantum circuit complexity could provide equivalent information about the classical scrambling time and Lyapunov exponent in analogous to the OTOCs.…”

Section: Introductionmentioning

confidence: 99%

Complexity, chaos and the moving D3-brane

Li¹

2021

Preprint

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We use the wave-function method developed in area of quantum information to investigate the quantum circuit complexity of the small quantum fluctuations around the probe D 3 brane moving in AdS 5 × S 5 bulk. In our consideration, the reference and target states are chosen as the vacuum state and the squeezed quantum state respectively. The evolution of parameters characterizing the squeezed quantum state are governed by the time-dependent Schrödinger equation, in which the Hamiltonian operator is derived from the perturbative action of D 3 brane. For a quantum chaotic system, some recent works indicate that the evolution of quantum circuit complexity could provide equivalent information like the out-of-time-order correlators. Basing on this inference, our results show that the quantum fluctuations around the non-BPS brane manifestly evolve into the chaotic regime at the late time, while the chaotic behavior is not easy to observe in case of BPS brane. In holographic viewpoint, it implies that the thermodynamic system consist of the N = 4 supersymmetric particles in non-BPS states evolve into a chaotic system more easily than the one in BPS state.

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Extracting Classical Lyapunov Exponent from One-Dimensional Quantum Mechanics

Cited by 3 publications

References 61 publications

Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

Fokker-Planck equation for black holes in thermal potential

Complexity, chaos and the moving D3-brane

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