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<p>We consider a modified version of the well-known 2d vdP oscillator with a new non-Hermitian interaction. The usual perturbative approach fails to provide the classical dynamics of the system as the classical solutions become divergent in the long time limit. These kinds of divergences are similar to what occurs in quantum field theory and critical phenomena. The Renormalization Group (RG) technique for the dynamical system has been used to eliminate the divergences in the perturbative solution of the 2d vdP oscillator and to provide a physically acceptable solution which is shown to be consistent with numerical study. We further investigate the model in the framework of non-Hermitian quantum mechanics to show the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_5896_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{P}\mathcal{T}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">P</mi> <mi mathvariant="script">T</mi> </mrow> </math></EquationSource> </InlineEquation> phase transition in the system.</p>

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Renormalization Group Approach for Modified vdP Oscillator with \(\mathcal{P}\mathcal{T}\) Symmetric Non-Hermitian Interaction

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Biswajit Bhowmick,
  • Rohit Mahendra Shinde,
  • Bhabani Prasad Mandal

摘要

We consider a modified version of the well-known 2d vdP oscillator with a new non-Hermitian interaction. The usual perturbative approach fails to provide the classical dynamics of the system as the classical solutions become divergent in the long time limit. These kinds of divergences are similar to what occurs in quantum field theory and critical phenomena. The Renormalization Group (RG) technique for the dynamical system has been used to eliminate the divergences in the perturbative solution of the 2d vdP oscillator and to provide a physically acceptable solution which is shown to be consistent with numerical study. We further investigate the model in the framework of non-Hermitian quantum mechanics to show the \(\mathcal{P}\mathcal{T}\) P T phase transition in the system.