<p>Parity and time-reversal (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> </InlineEquation>) symmetry is shown as the natural cause of quasi-integrability of deformed integrable models, crucial to represent real physical systems as they posses various irregularities. The condition for asymptotic conservation of quasi-conserved charges appear as a direct consequence of the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> </InlineEquation>-symmetric phase of the system, ensuring definite <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> </InlineEquation>-properties of the corresponding Lax pair as well as that of the anomalous contribution, consistent with the Wilson-loop criterion for integrability-like behavior. As a result, the quasi-deformed charge densities always acquire definite <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> </InlineEquation>-properties suitable for the asymptotic conservation, as the Abelianization approach to construct them also preserves the definite <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> </InlineEquation>-behavior of the Lax pair. This <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> </InlineEquation>-symmetry based origin of quasi-conservation is general and has been demonstrated for quasi-deformations of multiple systems such as KdV, NLSE and non-local NLSE.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Quasi-integrability from \(\mathcal{P}\mathcal{T}\)-symmetry

  • Kumar Abhinav,
  • Partha Guha,
  • Indranil Mukherjee

摘要

Parity and time-reversal ( \(\mathcal{P}\mathcal{T}\) ) symmetry is shown as the natural cause of quasi-integrability of deformed integrable models, crucial to represent real physical systems as they posses various irregularities. The condition for asymptotic conservation of quasi-conserved charges appear as a direct consequence of the \(\mathcal{P}\mathcal{T}\) -symmetric phase of the system, ensuring definite \(\mathcal{P}\mathcal{T}\) -properties of the corresponding Lax pair as well as that of the anomalous contribution, consistent with the Wilson-loop criterion for integrability-like behavior. As a result, the quasi-deformed charge densities always acquire definite \(\mathcal{P}\mathcal{T}\) -properties suitable for the asymptotic conservation, as the Abelianization approach to construct them also preserves the definite \(\mathcal{P}\mathcal{T}\) -behavior of the Lax pair. This \(\mathcal{P}\mathcal{T}\) -symmetry based origin of quasi-conservation is general and has been demonstrated for quasi-deformations of multiple systems such as KdV, NLSE and non-local NLSE.