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Ampere-Maxwell's Law: Problem-Solving01:17

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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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Ampere's law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the current enclosed in the loop. If the fingers of the right hand curl along the direction of the integration path, the current in the direction of the thumb is considered positive. The current opposite to the thumb direction is considered negative.
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Matrix eigenvalue solver based on reconfigurable photonic neural network.

Kun Liao1, Chentong Li1, Tianxiang Dai1

  • 1State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China.

Nanophotonics (Berlin, Germany)
|December 5, 2024
PubMed
Summary
This summary is machine-generated.

Researchers developed a photonic neural network for solving matrix eigenvalues, achieving 78.8% accuracy for 4x4 matrices. This breakthrough enables faster, more efficient eigenvalue calculations on a chip.

Keywords:
graphene/Si thermo-optical modulationmatrix eigenvalue solverreconfigurable photonic neural networksaturated absorption effect

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Area of Science:

  • Numerical analysis
  • Photonic computing
  • Artificial intelligence

Background:

  • Eigenvalue problem is crucial in engineering and science.
  • Existing algorithms lack photonic implementation.
  • Photonic neural networks offer speed and low energy consumption.

Purpose of the Study:

  • Propose a photonic neural network for real-value symmetric matrix eigenvalue solving.
  • Demonstrate feasibility on a photonic platform.
  • Enable on-chip integrated all-optical computing.

Main Methods:

  • Utilized reconfigurable photonic neural networks.
  • Employed graphene/Si thermo-optical modulation.
  • Incorporated a saturated absorption nonlinear activation layer.
  • Tested on 2x2, 3x3, and 4x4 matrices.

Main Results:

  • Demonstrated eigenvalue solving for real-value symmetric matrices.
  • Achieved 78.8% experimental accuracy for 4x4 matrices.
  • Theoretically predicted 93.6% accuracy for 2x2 matrices.

Conclusions:

  • The proposed strategy is feasible for on-chip photonic eigenvalue solvers.
  • This work lays the foundation for next-generation all-optical computing.
  • Enables efficient and high-speed matrix computations.