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Efficient Quantum Trajectory Representation Of Wavefunctions Evolving In Imaginary Time, Sophya V. Garashchuk, James Mazzuca, Tijo Vazhappilly
Efficient Quantum Trajectory Representation Of Wavefunctions Evolving In Imaginary Time, Sophya V. Garashchuk, James Mazzuca, Tijo Vazhappilly
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The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential – computed approximately to be practical in high-dimensional systems – influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys.132, 014112 (2010)]. For a nodelesswavefunction represented as ψ(x, t) = exp ( − S(x, t)/ℏ) with the trajectory momenta defined by ∇S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former …