Out-of-time-order correlators in quantum mechanics

We establish a direct link between the out-of-time order correlator, a recently suggested measure for probing information scrambling in quantum chaotic systems, and the Loschmidt echo, a wellappreciated diagnostic that captures the dynamical aspect of quantum chaos in the time domain. Two models has been studied to reveal the connection between these two quantities for both early growth (scrambling) regime and the intermediate decay regime. Implications to the Maldacena bound on the decay rate is also briefly discussed.

show abstract

“…This is a shifted harmonic oscillator Hamiltonian, for which the Heisenberg evolution of the position operator has been solved [59]:ŷ…”

Section: Baker-campbell-hausdorff Expansion Of the Lementioning

confidence: 99%

Information Scrambling and Loschmidt Echo

2020

View full text Add to dashboard Cite

show abstract

“…In [44] the authors demonstrate explicit calculations of OTOCs for harmonic oscillator. For our model, the OTOC for x and p operators (after reinstating the factor of ) gives [44] [x(t), p] 2 = 2 cos 2 Ω t, (33) where Ω is defined (1). When Ω is imaginary, we can write the above expression as an exponential function [x(t), p] 2 ≈ 2 e 2 |Ω| t + · · · .…”

Section: Otoc Lyapunov Exponent and Scrambling Timementioning

confidence: 99%

Chaos and complexity in quantum mechanics

et al. 2020

View full text Add to dashboard Cite

We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. Moreover, for systems that can be switched from a regular to unstable (chaotic) regime by a tuning of the coupling constant of the interaction Hamiltonian, we find that the complexity defines a new time scale. We interpret this time scale as recording when the system makes the transition from regular to chaotic behaviour.

show abstract

“…One may expect that this result could also be reproduced by using a wave packet with a small enough σ, which makes the initial wave packet narrow. However, it is not the case because the width of a free wave packet spreads as σ 2 + t 2 /σ 2 [58], i.e., an originally narrow wave packet is rapidly delocalized.…”

Section: Alternative Approachesmentioning

confidence: 99%

Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches

Lee

Yao

Fischetti

et al. 2020

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

To investigate inelastic electron scattering, which is ubiquitous in various fields of study, we carry out ab initio study of the real-time dynamics of a one-dimensional electron wave packet scattered by a hydrogen atom using different methods: the exact solution, the solution provided by timedependent density functional theory (TDDFT), and the solutions given by alternative approaches. This research not only sheds light on inelastic scattering processes but also verifies the capability of TDDFT in describing inelastic electron scattering. We revisit the adiabatic local-density approximation (ALDA) in describing the excitation of the target during the scattering process along with a self-interaction correction and spin-polarized calculations. Our results reveal that the ALDA severely underestimates the energy transferred in the regime of low incident energy particularly for a spin-singlet system. After demonstrating alternative approaches, we propose a hybrid ab initio method to deal with the kinetic correlation alongside TDDFT. This hybrid method would facilitate first-principles studies of systems in which the correlation of a few electrons among many others is of interest.

show abstract

Out-of-time-order correlators in quantum mechanics

Cited by 228 publications

References 66 publications

Information Scrambling and Loschmidt Echo

Information Scrambling and Loschmidt Echo

Chaos and complexity in quantum mechanics

Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches

Contact Info

Product

Resources

About