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Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures.

Martin Veresko1, Ming-Cheng Cheng2

  • 1Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY, 13699-5720, USA.

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This study introduces a physics-based learning algorithm to efficiently simulate quantum nanostructures, significantly reducing computational demands for designing advanced materials and devices.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Materials science

Background:

  • Direct numerical simulation (DNS) of the Schrödinger equation is crucial for quantum nanostructure design but computationally intensive.
  • High degrees of freedom (DoF) in large nanostructures make DNS prohibitive for practical applications.

Purpose of the Study:

  • To develop a physics-based reduced-order learning algorithm for accurate and efficient Schrödinger equation simulation.
  • To investigate the performance of this algorithm on quantum-dot structures under external electric fields and internal potential variations.

Main Methods:

  • Employed a first-principles, physics-based reduced-order learning algorithm.
  • Applied the methodology to two distinct quantum-dot structures: one with an external electric field, another with periodic boundary conditions and internal potential variation.
  • Examined simulation cases both within and beyond the algorithm's training conditions.

Main Results:

  • Achieved a reduction in DoF by over 3 orders of magnitude and computational time by 2 orders compared to DNS.
  • Demonstrated accurate predictions even for untrained quantum states, including higher external fields and larger internal potentials.
  • Compared the physics-based learning approach with Fourier-based plane-wave methods for periodic cases.

Conclusions:

  • The proposed learning algorithm offers a highly accurate and efficient alternative to DNS for quantum nanostructure simulations.
  • This method enables the design and analysis of complex nanostructures with significantly reduced computational cost.
  • The algorithm shows potential for applications in nanoelectronics, materials design, and areas like density functional theory.