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関連する概念動画

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

314
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
314
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

329
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
329
Classification of Systems-I01:26

Classification of Systems-I

533
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
533
Linear time-invariant Systems01:23

Linear time-invariant Systems

839
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
839
Feedback control systems01:26

Feedback control systems

657
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
657
State Space Representation01:27

State Space Representation

496
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...
496

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関連する実験動画

Updated: Jan 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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非線形非ハミルトン系の量子化

Andy Chia1, Wai-Keong Mok2, Leong-Chuan Kwek1,3

  • 1Centre for Quantum Technologies, National University of Singapore, Singapore.

Physical review. E
|December 23, 2025
PubMed
まとめ

我々は、古典力学系の量子化のための新しい方法であるカスケード量子化を紹介します。このアプローチは、任意の多項式系の物理的な量子化を可能にし、以前の方法の限界を克服します。

キーワード:
カスケード量子化非ハミルトン系量子化非線形力学開端系理論

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科学分野:

  • 量子力学
  • 力学系理論
  • 開端系理論

背景:

  • 古典的なハミルトン系は、正準量子化を用いて量子化でき、物理的な量子力学的な発展をもたらす。
  • 物理的な要件（例えば、完全な正値性、トレース保存）を維持しながら非ハミルトン系を量子化することは、長年の課題であった。

研究 の 目的:

  • 多項式微分方程式によって定義される非ハミルトン古典系の量子化のための系統的な方法を開発すること。
  • そのような系が開端系理論を用いて物理的な量子発展に量子化され得ることを証明すること。

主な方法:

  • 開端系理論を活用して、多項式系の時間発展（リンドブラディアン）の物理的生成子を構築すること。
  • 「カスケード量子化」法を導入し、適用すること。

主要な成果:

  • 全ての多項式系が時間発展の物理的生成子を許容することを示した。
  • 分岐、ノイズ活性化スパイク、リェナール系などの非線形力学へのカスケード量子化の適用に成功した。
  • カスケード量子化は正確であり、弱い非線形性や回転対称性のような制限的な仮定を必要としないことを示した。

結論:

  • カスケード量子化は、非ハミルトン系を含む広範な古典系の量子化のための一般的かつ正確な方法を提供する。
  • この方法は、以前の量子化アプローチの限界を克服し、複雑な非線形力学の解析に大きな利点を提供する。