The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics well beyond the short-time regime of narrow states. We find that quantum-classical differences initially grow exponentially with a characteristic exponent consistently larger than the largest Lyapunov exponent. We provide numerical evidence that the time of the break between the quantum and classical predictions scales as $\mathrm{log}(\mathcal{J}/\ensuremath{\Elzxh}),$ where $\mathcal{J}$ is a characteristic system action. However, this logarithmic break-time rule applies only while the quantum-classical deviations are smaller than $O(\ensuremath{\Elzxh}).$ We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics well beyond the short-time regime of narrow states. We find that quantum-classical differences initially grow exponentially with a characteristic exponent consistently larger than the largest Lyapunov exponent. We provide numerical evidence that the time of the break between the quantum and classical predictions scales as $\mathrm{log}(\mathcal{J}/\ensuremath{\Elzxh}),$ where $\mathcal{J}$ is a characteristic system action. However, this logarithmic break-time rule applies only while the quantum-classical deviations are smaller than $O(\ensuremath{\Elzxh}).$ We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.

arXiv:quant-ph/0011020Physical Review AApr 13, 200130 citations

Quantum Chaos and Quantum Fractals With Atoms and Photons in a Microcavity

Michael Yu. Uleysky, Sergei V Prants

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical egrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. It manifest itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with a prominent fractal-like behavior and in the quantum atom-filed degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom-field resonance correlate strongly. This result provides a quantum-classical correspondence in a closed physical system.Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical egrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. It manifest itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with a prominent fractal-like behavior and in the quantum atom-filed degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom-field resonance correlate strongly. This result provides a quantum-classical correspondence in a closed physical system.

ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)Jan 1, 20050 citations

Systems of coupled quantum and classical degrees of freedom

Gunaretnam Rajagopal

Aug 1, 19910 citations

QUANTUM-CLASSICAL CORRESPONDENCE

Karolinum Press eBooksJun 1, 20150 citations

Quantum control and quantum chaos in cavity QED

Michael Yu. Uleysky, Sergei V Prants

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. It is shown that at given initial conditions the regime of atomic motion is governed mainly by the detuning of the atom-field resonance /spl delta/. We show that, even in the absence of any other interaction with environment, the interaction of a purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics (QED). It manifest itself in the classical degree of freedom as a random walking of an atom inside the cavity and in the quantum degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependence of variance of entanglement on /spl delta/, correlates strongly with the dependence of maximum Lyapunov exponent on /spl delta/. This result provides a quantum-classical correspondence in a closed physical system.Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. It is shown that at given initial conditions the regime of atomic motion is governed mainly by the detuning of the atom-field resonance /spl delta/. We show that, even in the absence of any other interaction with environment, the interaction of a purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics (QED). It manifest itself in the classical degree of freedom as a random walking of an atom inside the cavity and in the quantum degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependence of variance of entanglement on /spl delta/, correlates strongly with the dependence of maximum Lyapunov exponent on /spl delta/. This result provides a quantum-classical correspondence in a closed physical system.

International Conference Physics and ControlOct 4, 20060 citations

\mathcal{J}

is a characteristic system action. However, this logarithmic break-time rule applies only while the quantum-classical deviations are smaller than $O(\ensuremath{\Elzxh}).$ We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.