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関連する概念動画

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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Graphing the Wave Function01:13

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The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
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The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,
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Transfer Function to State Space01:23

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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時間発展するニューラルネットワークベース波動関数の確率論的表現

Bizi Huang1, Weizhong Fu1, Ji Chen1,2,3

  • 1School of Physics, Peking University, Beijing 100871, People's Republic of China.

The Journal of chemical physics
|December 24, 2025
PubMed
まとめ
この要約は機械生成です。

本研究は、電子ダイナミクスのための時間依存シュレーディンガー方程式（TDSE）を解くための、確率論的表現とニューラルネットワークを組み合わせた新しい計算手法を導入する。このアプローチは、強レーザー場におけるイオン化プロセスを正確にモデル化する。

キーワード:
確率論的表現ニューラルネットワーク時間依存シュレーディンガー方程式電子ダイナミクスイオン化強レーザー場

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科学分野:

  • 量子力学
  • 計算物理学
  • アト秒物理学

背景:

  • 時間依存シュレーディンガー方程式（TDSE）の解明は、超高速分光法およびレーザー・物質相互作用における電子ダイナミクスの理解に不可欠である。
  • 正確なTDSE解は、系の次元によるヒルベルト空間の指数関数的な増大により、計算コストが高い。

研究 の 目的:

  • TDSEを解くための計算効率の高い手法を開発・検証すること。
  • 非断熱電子ダイナミクス、特に強レーザー場下でのイオン化プロセスをモデル化すること。

主な方法:

  • 確率論的表現フレームワークとニューラルネットワーク波動関数アンザッツの統合。
  • イオン化ダイナミクスをシミュレートする1次元、単一電子系での検証。
  • 3次元系への拡張の検討。

主要な成果:

  • イオン化中のエネルギーおよび双極子進化を含む、量子進化の正確な再現。
  • 手法を3次元系に適用する実現可能性を実証。
  • 高次元シミュレーションのための高度な安定化戦略の必要性を特定した。

結論:

  • 提案されたハイブリッドアプローチは、複雑な量子ダイナミクスのシミュレーションのための有望な道を提供する。
  • この手法は、現実的な系における超高速電子ダイナミクスの正確なモデリングの可能性を示す。
  • 高次元問題への堅牢な適用には、さらなる開発が必要である。