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## Full-Text Articles in Physics

Efficient Quantum Trajectory Representation Of Wavefunctions Evolving In Imaginary Time, Sophya V. Garashchuk, J. Mazzuca, T. Vazhappilly

#### Efficient Quantum Trajectory Representation Of Wavefunctions Evolving In Imaginary Time, Sophya V. Garashchuk, J. Mazzuca, T. Vazhappilly

*Faculty Publications*

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 is more accurate while the latter is more practical because the Lagrangian ...

Quantum Trajectory Dynamics In Imaginary Time With The Momentum-Dependent Quantum Potential, Sophya V. Garashchuk

#### Quantum Trajectory Dynamics In Imaginary Time With The Momentum-Dependent Quantum Potential, Sophya V. Garashchuk

*Faculty Publications*

The quantum trajectory dynamics is extended to the wave function evolution in imaginary time. For a nodelesswave function a simple exponential form leads to the classical-like equations of motion of trajectories, representing the wave function, in the presence of the momentum-dependent quantum potential in addition to the external potential. For a Gaussian wave function this quantum potential is a time-dependent constant, generating zero quantum force yet contributing to the total energy. For anharmonic potentials the momentum-dependent quantum potential is cheaply estimated from the global Least-squares Fit to the trajectory momenta in the Taylor basis. Wave functions with nodes are described ...

Modified Quantum Trajectory Dynamics Using A Mixed Wave Function Representation, Sophya V. Garashchuk, V. A. Rassolov

#### Modified Quantum Trajectory Dynamics Using A Mixed Wave Function Representation, Sophya V. Garashchuk, V. A. Rassolov

*Faculty Publications*

Dynamics of quantum trajectories provides an efficient framework for description of various quantum effects in large systems, but it is unstable near the wave function density nodes where the quantum potential becomes singular. A mixed coordinate space/polar representation of the wave function is used to circumvent this problem. The resulting modified trajectory dynamics associated with the polar representation is nonsingular and smooth. The interference structure and the nodes of the wave function density are described, in principle, exactly in the coordinate representation. The approximate version of this approach is consistent with the semiclassical linearized quantum force method [S. Garashchuk ...