Effective 1D Time-Dependent Schrödinger Equations for 3D Geometrically Correlated Systems

Area of Science:

• Computational Physics
• Quantum Mechanics
• Materials Science

Background:

• The Born-Huang ansatz is crucial for ab-initio molecular dynamics, separating fast and slow degrees of freedom.
• Simulating electron transport in nanostructures with geometrical constrictions is computationally demanding.

Purpose of the Study:

• To adapt the Born-Huang ansatz for electron transport problems with geometrical constrictions.
• To develop a computationally efficient method for solving the time-dependent Schrödinger equation in such systems.

Main Methods:

• A Born-Huang-like expansion of the 3D time-dependent Schrödinger equation was employed.
• Separated confinement (transverse) and transport (longitudinal) degrees of freedom.
• An eigenstate problem for confinement informed the propagation of coupled 1D equations for transport.

Main Results:

• Achieved quantitative accuracy in simulations.
• Reduced computational resources by one order for 2D constrictions.
• Reduced computational resources by up to three orders for 3D constrictions.

Conclusions:

• The proposed method offers a significant computational advantage for electron transport simulations.
• This approach provides an accurate and efficient way to study quantum transport in nanoconstrictions.