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Quantum signature of the classical chaos in the field-induced barrier crossing in a quartic potential

Pratim Kumar Chattaraj, S. Sengupta, Arpita Poddar

Published May 25, 1999• 4 citations
OpenAlex

Abstract

The quantum domain behaviour of a classical double-well oscillator which exhibits chaos in the presence of an external monochromatic field has been studied using Bohmian mechanics. The classical Kolmogorov-Arnol'd-Moser (KAM) tori break down in the presence of an external perturbation for which the corresponding quantal phase portrait exhibits regular islands owing to the quantum suppression of the classical chaos. It has also been observed that the classical chaos generally enhances the quantum fluctuations.

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Chaos An Interdisciplinary Journal of Nonlinear Science•Nov 5, 2014•9 citations
The quantum domain behaviour of a classical double-well oscillator which exhibits chaos in the presence of an external monochromatic field has been studied using Bohmian mechanics. The classical Kolmogorov-Arnol'd-Moser (KAM) tori break down in the presence of an external perturbation for which the corresponding quantal phase portrait exhibits regular islands owing to the quantum suppression of the classical chaos. It has also been observed that the classical chaos generally enhances the quantum fluctuations.
Both quantum and classical analyses are performed to study the barrier crossing dynamics in a driven quartic oscillator. The regions of phase space with regular classical motion are found to be smaller than the size of a quantum state. However, coherent tunnelling is still possible due to the existence of Floquet states localized on two small regular islands. The quantum evolution of localized wavepackets and the classical evolution of the corresponding distributions show similar coherence properties although the degree of coherence is quantally enhanced.
In this work we study the non-Markovian behavior of a qubit coupled to an environment in which the corresponding classical dynamics change from integrable to chaotic. We show that in the transition region, where the dynamics has both regular islands and chaotic areas, the average non-Markovian behavior is enhanced to values even larger than those in the regular regime. This effect can be related to the non-Markovian behavior as a function of the initial state of the environment, where maxima are attained at the regions dividing separate areas in classical phase space, particularly at the borders between chaotic and regular regions. Moreover, we show that the fluctuations of the fidelity of the environment—which determine the non-Markovianity measure—give a precise image of the classical phase portrait.
In this work we study the non-Markovian behavior of a qubit coupled to an environment in which the corresponding classical dynamics change from integrable to chaotic. We show that in the transition region, where the dynamics has both regular islands and chaotic areas, the average non-Markovian behavior is enhanced to values even larger than those in the regular regime. This effect can be related to the non-Markovian behavior as a function of the initial state of the environment, where maxima are attained at the regions dividing separate areas in classical phase space, particularly at the borders between chaotic and regular regions. Moreover, we show that the fluctuations of the fidelity of the environment?which determine the non-Markovianity measure?give a precise image of the classical phase portrait.
Two fundamental quantum signatures of classically chaotic behaviour, large second derivatives and the logarithmic time barrier separating classical from quantum dynamics, have been observed near the separatrix of an integrable spin system. A systematic study in the neighbourhood of the separatrix reveals that the error in semiclassical eigenvalues (measured in units of the quantum level spacing) approaches a finite value at the classical limit. The generic factor which limits the validity of the correspondence principle is the presence of classical instabilities; chaotic behaviour is one such case; the separatrix of an integrable system is another.
The quantum-classical correspondence is studied for a periodically driven quartic oscillator exhibiting integrable and chaotic dynamics, by studying the Bohmian trajectory of the corresponding "classical" Schrödinger equation. Phase plots and the Kolmogorov-Sinai entropy are computed and compared with the classical trajectory as well as the Bohmian trajectory obtained from the time dependent Schrödinger equation. Bohmian mechanics at the classical limit appears to mimick the behavior of a dissipative dynamical system.