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Decoherence Effects in Reactive Scattering

Han, H, Brumer, P

Published Feb 9, 2005• 12 citations
OpenAlex

Abstract

Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of dynamics of the collinear H+H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reaction and transmission probabilities, primarily by increasing the energy dispersion in a well defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.

Related papers

Decoherence effects in reactive scattering

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Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of the dynamics of the collinear H + H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reactions and transmission probabilities, primarily by increasing the energy dispersion in a well-defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.

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Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.

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We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances, and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. In that frequency region, the classical and quantum transmission coefficients are in optimal agreement. Moreover, the transmission threshold (i.e., the energy above which the transmission coefficient becomes larger than a specific small threshold value) is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well-separated coherent pulses, a phenomenon that admits purely classical kinematic interpretation.

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Decoherence is traditionally viewed as a purely destructive process in quantum mechanics, primarily responsible for the loss of quantum information. However, this paper proposes and investigates a novel perspective: that decoherence can exhibit non-linear effects, significantly impacting the dynamical evolution of quantum systems. We construct a comprehensive quantum decoherence model, analyzing the intricate interactions between the decoherence process and the system's dynamics. Our analysis reveals the emergence of non-linear behavior during decoherence, providing a deeper understanding of the mechanism. Furthermore, we propose strategies for controlling these non-linear effects. The core claim of this paper is that decoherence is not merely a destructive mechanism, but a dynamic one capable of producing non-linear phenomena. This research offers a fundamental shift in the comprehension of decoherence's role and consequences within quantum systems.

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Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of dynamics of the collinear H+H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reaction and transmission probabilities, primarily by increasing the energy dispersion in a well defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.
Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of the dynamics of the collinear H + H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reactions and transmission probabilities, primarily by increasing the energy dispersion in a well-defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.
Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.
Abstract This thesis has two parts, in the first, the Caldeira-Leggett model is introduced; its derivation and general consequences are explored following a paper by Caldeira and Leggett[1]. An operator-formalism shortcut through some of the more mathematically cumbersome parts of the derivation of the model is also developed. The correlation of the force resulting from reservoir-interaction is examined in the high- and low-temperature limits, and the Langevin equation is shown to emerge in the classical limit.Abstract The second part introduces decoherence through a thought experiment that demonstrates the destructive effect of random phase shifts on interference terms, and then follows another paper by Caldeira and Leggett[2] in applying their model further to study the phenomenon of dissipative decoherence. The time-evolution of the interference terms in a superposition of Gaussian wave packets in a harmonic oscillator potential is studied when interacting with a heat bath, and they are shown to vanish at a rate much faster than the relaxation of the system.
We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling phenomena, resonances, and kinematic effects emanating from the time dependence of the potential. We show that when kinematic effects dominate (mainly in intermediate frequencies), classical mechanics provides very good approximation of quantum results. In that frequency region, the classical and quantum transmission coefficients are in optimal agreement. Moreover, the transmission threshold (i.e., the energy above which the transmission coefficient becomes larger than a specific small threshold value) is found to exhibit a minimum. We also consider the form of the transmitted wave packet and we find that for low values of the frequency the incoming classical and quantum wave packet can be split into a train of well-separated coherent pulses, a phenomenon that admits purely classical kinematic interpretation.
Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared to the corresponding unperturbed cases. In the literature this effect is known as superarrival in transmission probability. We present a trajectory-based explanation for this effect by using the concept of quantum potential energy and computing a selection of Bohmian trajectories. Relevant parameters in superarrivals are determined for the case that the barrier width increases linearly during the dispersion of the wavepacket. Nonlinearity in time perturbation is also considered.
Decoherence is traditionally viewed as a purely destructive process in quantum mechanics, primarily responsible for the loss of quantum information. However, this paper proposes and investigates a novel perspective: that decoherence can exhibit non-linear effects, significantly impacting the dynamical evolution of quantum systems. We construct a comprehensive quantum decoherence model, analyzing the intricate interactions between the decoherence process and the system's dynamics. Our analysis reveals the emergence of non-linear behavior during decoherence, providing a deeper understanding of the mechanism. Furthermore, we propose strategies for controlling these non-linear effects. The core claim of this paper is that decoherence is not merely a destructive mechanism, but a dynamic one capable of producing non-linear phenomena. This research offers a fundamental shift in the comprehension of decoherence's role and consequences within quantum systems.