A Comment on "Semiquantum Chaos"

Reply to Comment on "Non-monotonicity in the Quantum-Classical Transition: Chaos Induced by Quantum Effects"

Response to comment by Finn et al.

Comment on "Stable Quantum Computation of Unstable Classical Chaos"

This is a 1-page comment on a wrong paper that recently appeared in PRL (Phys. Rev. Lett. 86 (23), 5393 (2001), also quant-ph/0101004). The authors claim to have shown that using a quantum computer gives an "exponential advantage" for simulating and studying classical chaotic systems.

Comment on "Non-monotonicity in the Quantum-Classical Transition: Chaos Induced by Quantum Effects"

In a recent Letter [PRL 101, 074101 (2008)], Kapulkin and Pattanayak presented evidence that a quantum Duffing oscillator, sufficiently damped so that it is not classically chaotic, becomes chaotic in the transition region between quantum and classical motion. If true, this would be a striking result. However, Kapulkin and Pattanayak did not calculate the Lyapunov exponent for the system, usually regarded as the litmus-test of chaos. Here we perform this calculation, which throws considerable doubt upon their conclusions.

Comment on "Entanglement and chaos in the kicked top"

We comment on the investigation of the connection between chaos and dynamically generated entanglement in Phys. Rev. E, \textbf{83}, 016207, (2011). While, in the referred paper, the authors give an explicit example of a state initially localized in the regular region and still has entanglement properties similar to the states localized in the chaotic region, a few clarifications related to previous works are in order. Firstly, it is crucial to point out that such a behavior can occur for states initially localized near the border between the chaotic region and regular island, which seems to b…

Comment on "Exploring chaos in the Dicke model using ground-state fidelity and the Loschmidt echo"

In [PRE \textbf{90}, 022920 (2014), arXiv:1404.6738] a study of the ground state fidelity of the Dicke model as a function of the coupling parameter is presented. Abrupt jumps of the fidelity in the superradiant phase are observed and are assumed to be related to the transition to chaos. We show that this conclusion results from a misinterpretation of the numerics. In fact, if the parity symmetry is taken into account, the unexpected jumps disappear.

Comment on "Stable Quantum Computation of Unstable Classical Chaos"

I think the title and content of the recent Letter by Georgeot and Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As long as the classical Arnold map is considered, the classical computational algorithm can be made exactly equivalent with the quantum one. The claimed advantage of the Letter's quantum algorithm disappears if we correctly restrict the statistical analysis for the classical Arnold system.

Comment on: "Solving many-body Schrödinger equations with kinetic energy partition method'', Ann. Phys. 388 (2018) 54-68 by Y-H. Chen and S. D. Chao

We discuss a recent test of the performance of the kinetic energy partition method (KEP) through its application to two separable quantum-mechanical models. We argue that one of the benchmark models is exceedingly simple for testing any realistic approximate method and that almost any reasonable approach yields better results. In the second example our exact benchmark eigenvalues disagree considerably with those chosen by the authors for comparison, which casts doubts on the accuracy of their KEP approach.

Comments on `Stable Quantum Computation of Unstable Classical Chaos,' `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum Computer Inverting Time Arrow for Macroscopic Systems'

Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_, 5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi, quant-ph/0110026]. The Letter claims an exponential speedup and reduction in error sensitivity, when phase-space density evolution under the Arnold cat map is performed on a quantum computer. On the one hand, some points have not yet been made by previous respondents. On the other, the authors' reaction [quant-ph/0110142] raises new issues. The present note addresses both.

非马尔可夫开放量子系统中的量子混沌：干涉 OTOC、Loschmidt 回波与对易子算符范数

Quantum Chaos in Non-Markovian Open Quantum Systems: Interferometric OTOC, Loschmidt Echo and Commutator Operator Norm

本文在两类非马尔可夫开放量子相互作用模型中计算 OTOC、分析量子信息置乱，并结合 Loschmidt 回波与受 Lieb-Robinson 界约束的对易子增长刻画其混沌特征。

Onset of many-body chaos in the $O(N)$ model

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with $N$ components in the $(2+1)$-dimensional $O(N)$ nonlinear sigma model to leading order in $1/N$. The system is taken to be in thermal equilibrium at a temperature $T$ above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted $λ_L$. At large $N$ the growth of chaos as measured by $λ_L$ is slow because the mode…