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Generalized multi-symplectic PINN method and its application in quantum tunneling simulations.

Xinying Yan1, Weipeng Hu1,2, Zhengqi Han1

  • 1Xi'an University of Technology, School of Civil Engineering and Architecture, Xi'an, 710048 Shaanxi, China.

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The generalized multi-symplectic physics-informed neural network (GMPINN) accurately models dissipative quantum tunneling by preserving system geometry. This method reveals inverse relationships between dissipation, barrier thickness, and probability distribution, aiding device design.

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Area of Science:

  • Computational Physics
  • Quantum Mechanics
  • Machine Learning

Background:

  • Physics-informed neural networks (PINNs) struggle to accurately reproduce dissipative effects in complex systems.
  • Infinite-dimensional dissipative systems require advanced numerical methods to capture their physical information.

Purpose of the Study:

  • To introduce the generalized multi-symplectic physics-informed neural network (GMPINN) for improved modeling of dissipative systems.
  • To enhance the ability of physics-informed neural networks (PINNs) to reproduce dissipative effects by embedding geometric structures.

Main Methods:

  • The generalized multi-symplectic physics-informed neural network (GMPINN) method embeds geometric structures of dissipative systems into the loss function.
  • Simulations were conducted on a dissipative quantum tunneling problem governed by the dissipative Schrödinger equation.

Main Results:

  • GMPINN successfully reproduced dissipative effects, preserving geometric structures and conservation laws.
  • Inverse proportion laws were found between dissipation coefficient/barrier thickness and probability distribution density.
  • Dissipation coefficient significantly impacts quantum coherence more than barrier thickness.

Conclusions:

  • GMPINN demonstrates excellent capability in modeling nonconservative systems and their dissipative effects.
  • The findings provide guidance for designing devices based on quantum tunneling principles.