We describe an approach to subsystem decoherence without the usual tracing out of the environment. The subsystem of focus is described entirely by a pure state evolving nonunitarily along a single classical trajectory of its environment. The approach is deduced from the exact factorization framework for arbitrary systems of electrons and nuclei. The nonunitarity of the electronic dynamics arises exclusively from nonadiabatic correlations between electrons and nuclei. We demonstrate that the approach correctly describes the coherence gain and the subsequent decoherence for the example of a nuclear trajectory passing through an avoided crossing, the prototypical case where single-trajectory Ehrenfest dynamics fails to produce decoherence.
We describe an approach to subsystem decoherence without the usual tracing out of the environment. The subsystem of focus is described entirely by a pure state evolving nonunitarily along a single classical trajectory of its environment. The approach is deduced from the exact factorization framework for arbitrary systems of electrons and nuclei. The nonunitarity of the electronic dynamics arises exclusively from nonadiabatic correlations between electrons and nuclei. We demonstrate that the approach correctly describes the coherence gain and the subsequent decoherence for the example of a nuclear trajectory passing through an avoided crossing, the prototypical case where single-trajectory Ehrenfest dynamics fails to produce decoherence.
We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasiclassical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the nuclear wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.
Decoherence is the tendency of a time-evolved reduced density matrix for a subsystem to assume a form corresponding to a statistical ensemble of states rather than a coherent combination of pure-state wave functions. When a molecular process involves changes in the electronic state and the coordinates of the nuclei, as in ultraviolet or visible light photochemistry or electronically inelastic collisions, the reduced density matrix of the electronic subsystem suffers decoherence, due to its interaction with the nuclear subsystem. We present the background necessary to conceptualize this decoherence; in particular, we discuss the density matrix description of pure states and mixed states, and we discuss pointer states and decoherence time. We then discuss how decoherence is treated in the coherent switching with decay of mixing algorithm and the trajectory surface hopping method for semiclassical calculations of electronically nonadiabatic processes.
We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.
Quantum trajectory calculations for electrons are a useful tool in the field of molecular dynamics, e.g. to understand processes in ultrafast spectroscopy. They have, however, two limitation: On the one hand, such calculations are typically based on the Born-Oppenheimer approximation (BOA) and the electron dynamics for stationary nuclei is considered, thus neglecting quantum effects of the nuclei. On the other hand, even if the quantum nuclear motion would be taken into account, a BOA dynamics on a single potential energy surface would not provide any electron trajectories because the electronic part is treated as a stationary problem. By using the exact factorization method, we overcome these limitations and generalize the theory of electronic quantum trajectories to a fully quantum-mechanical treatment of the nuclei. After reviewing the time-dependent theory of quantum hydrodynamics and quantum trajectories, we show that the nuclei can be viewed as a quantum clock for the electronic motion and we develop a fully quantum-mechanical clock-dependent version of quantum hydrodynamics. This theory is used to obtain electronic trajectories for quantum nuclei, as is exemplified for a model system of a proton-coupled electron transfer dynamics. Our work generalizes the concept of quantum trajectories and lays the foundations for the development of trajectory-based simulation methods of electron dynamics beyond the BOA.
We analyze a mixed quantum-classical algorithm recently derived from the exact factorization equations [Min, Agostini, Gross, PRL 115, 073001 (2015)] to show the role of the different terms in the algorithm in bringing about decoherence and wavepacket branching. The algorithm has the structure of Ehrenfest equations plus a "coupled-trajectory" term for both the electronic and nuclear equations, and we analyze the relative roles played by the different nonadiabatic terms in these equations, including how they are computed in practice. In particular, we show that while the coupled-trajectory term in the electronic equation is essential in yielding accurate dynamics, that in the nuclear equation has a much smaller effect. A decoherence time is extracted from the electronic equations and compared with that of augmented fewest-switches surface-hopping. We revisit a series of nonadiabatic Tully model systems to illustrate our analysis.
We analyze a mixed quantum-classical algorithm recently derived from the exact factorization equations [Min, Agostini, Gross, PRL 115, 073001 (2015)] to show the role of the different terms in the algorithm in bringing about decoherence and wavepacket branching. The algorithm has the structure of Ehrenfest equations plus a "coupled-trajectory" term for both the electronic and nuclear equations, and we analyze the relative roles played by the different nonadiabatic terms in these equations, including how they are computed in practice. In particular, we show that while the coupled-trajectory term in the electronic equation is essential in yielding accurate dynamics, that in the nuclear equation has a much smaller effect. A decoherence time is extracted from the electronic equations and compared with that of augmented fewest-switches surface-hopping. We revisit a series of nonadiabatic Tully model systems to illustrate our analysis.