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Bohmian quantum mechanical and classical Lyapunov exponents for kicked rotor

Yindong Zheng, Donald H. Kobe

Chaos Solitons & FractalsAug 11, 20062 citations

Quantum Lyapunov Exponents

Paolo Falsaperla, Giacomo Fonte, Giovanni Salesi

arXiv:quant-ph/0607133Foundations of PhysicsFeb 1, 20022 citations

Observing quantum chaos with noisy measurements and highly mixed states

Jason F. Ralph, Kurt A. Jacobs, M. J. Everitt

A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to $\ensuremath{\hbar}$. While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low-purity states and to variations in the parameters of the system.A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to $\ensuremath{\hbar}$. While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low-purity states and to variations in the parameters of the system.

arXiv:1609.07338Physical Review AJan 26, 201710 citations

On the notion of quantum Lyapunov exponent

Margo Kondratieva, T. A. Osborn

arXiv:quant-ph/0505066Journal of Mathematical SciencesApr 16, 20080 citations

Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation

Andrew Maris, Bibek Pokharel, Sharan Ganjam Seshachallam +2 more

We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial complexity metrics based on Kullback-Leibler distances between phase-space attractors and temporal complexity metrics based on the Lyapunov exponent, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. We find that a remarkable parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. We also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime and show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial complexity metrics based on Kullback-Leibler distances between phase-space attractors and temporal complexity metrics based on the Lyapunov exponent, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. We find that a remarkable parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. We also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime and show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.

arXiv:2011.00118Physical review. EAug 6, 20214 citations

Lyapunov exponent in quantum mechanics. A phase-space approach

Vladimir I. Man’ko, R. Vilela Mendes

arXiv:quant-ph/0002049Physica D Nonlinear PhenomenaNov 1, 200084 citations

Surprises In Computed Lyapunov Exponents Across The Quantum-Classical Transition

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