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arXiv:quant-ph/0610091 · Physical Review A

Quantum-classical transition for an analog of the double-slit experiment in complex collisions: Dynamical decoherence in quantum many-body systems

Luis Benet, L.T. Chadderton, S. Yu. Kun, Qi Wang

Published Jun 20, 2007• 1 citation
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Abstract

We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the $\mathrm{H}+{\mathrm{D}}_{2}$ chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.

DOI
10.1103/physreva.75.062110

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We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D2\mathrm{H}+{\mathrm{D}}_{2}H+D2​ chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.
We demonstrate a breakdown in the macroscopic (classical-like) dynamics of wave-packets in complex microscopic and mesoscopic collisions. This breakdown manifests itself in coherent superpositions of the rotating clockwise and anticlockwise wave-packets in the regime of strongly overlapping many-body resonances of the highly-excited intermediate complex. These superpositions involve $\ensuremath{\sim}{10}^{4}$ many-body configurations so that their internal interactive complexity dramatically exceeds all of those previously discussed and experimentally realized. The interference fringes persist over a time-interval much longer than the energy relaxation-redistribution time due to the anomalously slow phase randomization (dephasing). Experimental verification of the effect is proposed.
We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anticlockwise wave packets in the regime of strongly overlapping resonances of the intermediate complex. Such highly excited deformed complexes may be created in binary collisions of heavy ions, molecules, and atomic clusters. It is shown that phase relaxation leads to a reduction of the interference fringes, thus mimicking the effect of decoherence. This reduction is crucial for the determination of the phase-relaxation width from the data on the excitation function oscillations in heavy-ion collisions and bimolecular chemical reactions. The difference between the effects of phase relaxation and decoherence is discussed.
We discuss the stability of quantum motion under system's perturbations in the light of the corresponding classical behavior. In particular we focus our attention on the so called "fidelity" or Loschmidt echo, its relation with the decay of correlations, and discuss the quantum-classical correspondence. We then report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.
We report on the numerical simulation of the double-slit experiment, where the initial wave packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.
Based on the Threshold Chain Reaction Hypothesis, we construct a complex field equation with a nonlinear threshold term and perform numerical simulations of electron double-slit interference. Results show: when the threshold parameter is extremely high (never triggered), the equation reduces to the linear Schrödinger equation, faithfully reproducing standard quantum interference fringes; as the threshold decreases, fringe visibility declines continuously; at very low thresholds, interference vanishes completely, leaving only the single-slit diffraction envelope. This model provides a quantitatively tunable quantum-classical transition mechanism without requiring environmental coupling, offering a new perspective on the quantum measurement problem.
We propose a novel method to study quantum-classical correspondence in complex, e.g., heavy-ion, atomic, molecular, and atomic cluster collisions. The many-body rotating wave packets are formed spontaneously and their stability is due to the slow decoherence between highly excited strongly overlapping states of the intermediate complex. The phenomenon is illustrated by analyzing the 12C+24Mg{}^{12}{\mathrm{C}+}^{24}\mathrm{Mg}12C+24Mg collision. The significant deviations from the random-matrix theory are reproduced in terms of the macroscopically rotating molecule formed in this collision.