Matriks Hamburan pada Graf Kuantum dengan Kondisi Simpul Robin

Moh. Januar Ismail Burhan, Adam Adam

Abstract


Artikel ini membahas formulasi matriks hamburan pada graf kuantum dengan
kondisi simpul tipe-δ (Robin), yang merupakan perluasan dari kondisi Neumann–
Kirchhoff. Analisis dilakukan melalui propagasi gelombang bidang pada setiap
ruas dan penerapan kondisi kontinuitas serta fluks di simpul-simpul graf. Dari
penyelesaian masalah nilai eigen operator Laplace, diperoleh ekspresi eksplisit untuk
amplitudo gelombang bidang dan entri matriks hamburan pada simpul batas
maupun simpul interior. Hasil penelitian menunjukkan bahwa parameter Robin
mengatur besarnya refleksi dan transmisi gelombang, serta mempengaruhi distribusi
energi di sekitar simpul. Temuan ini memberikan dasar matematis bagi studi lanjutan
mengenai transportasi kuantum dan fenomena resonansi pada jaringan berbasis
graf.

Keywords


Graf Kuantum; Operator Laplace; Matriks Hamburan; Kondisi simpul Robin; Gelombang Bidang

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DOI: https://doi.org/10.24198/jmi.v21.n2.68300.193-202

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