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Quantum trajectory dynamics in imaginary time with the momentum-dependent quantum potential.

Sophya Garashchuk¹

¹Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA. sgarashc@mail.chem.sc.edu

The Journal of Chemical Physics

|January 19, 2010

Summary

Quantum trajectory dynamics now simulates wave function evolution in imaginary time. This method efficiently models quantum systems, including their decay to ground or excited states, using classical-like equations of motion.

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Area of Science:

Quantum Mechanics
Computational Chemistry
Theoretical Physics

Background:

Traditional quantum mechanics simulations can be computationally intensive.
Imaginary time evolution is crucial for finding ground states and thermal properties.
Quantum trajectory methods offer an alternative perspective on wave function dynamics.

Purpose of the Study:

To extend quantum trajectory dynamics to imaginary time evolution of wave functions.
To develop a computationally efficient method for simulating quantum systems.
To explore the application of this method for calculating energy levels and Boltzmann operator evolution.

Main Methods:

Formulating classical-like equations of motion for trajectories representing the wave function in imaginary time.
Incorporating a momentum-dependent quantum potential, which simplifies for Gaussian wave functions.
Utilizing a global least-squares fit for estimating the quantum potential in anharmonic potentials.
Employing a mixed coordinate space/trajectory representation for wave functions with nodes.

Main Results:

Nodeless wave functions represented by trajectory ensembles decay to the ground state.
Mixed representation wave functions decay to excited energy states by projecting out lower energy contributions.
Accurate computation of energy levels for anharmonic oscillators and energy level splitting for the double-well potential.
The quantum potential for Gaussian wave functions is a time-dependent constant, contributing to total energy without generating quantum force.

Conclusions:

The extended quantum trajectory dynamics provides an efficient method for imaginary time evolution.
This approach accurately models wave function decay and energy properties of quantum systems.
The method is applicable to Boltzmann operator evolution, offering a versatile computational tool.