The Shift of the Constant Energy Level After the Interaction of Particles with the Polarizing Phonons

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dc.citation.epage54
dc.citation.issue1
dc.citation.spage48
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorТовстюк, Корнелія
dc.contributor.authorTovstyuk, Cornelija
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-04-26T09:41:17Z
dc.date.available2023-04-26T09:41:17Z
dc.date.created2022-04-04
dc.date.issued2022-04-04
dc.description.abstractДосліджено зсув енергетичного рівня частинки, що взаємодіє із поляризаційними фононами. Енергія частинки і частота фонона постійні – вони не залежать від хвильового вектора (квазіімпульсу) частинок. Показано, як зменшується енергетичний рівень залежно від електрон-фононної константи зв’язку та енергії фонона. У роботі використано метод діаграм Фейнмана та метод подвійної перестановки, що дало змогу ідентифікувати подвійні перестановки, що відповідають діаграмам Фейнмана, без перетину фононних ліній. Виконано перестановки, що відповідають виразам, які утворюють масовий оператор, та виявлено спільні риси для DPs, що утворюють ряди для одного, двох і трьох фононних наближень.
dc.description.abstractThe shift of the electron energy level due to its interaction with the polarizing phonons is investigated here for the particles whose energy does not depend on the wave vector. We also analyze the influence of the value of the constant of electron – phonon interaction and other parameters of the problem on the electron energy change. The methods of Green’s functions, presented by the the Feynman diagrams and using the double permutations, are present here. The paper contains the analysis of the columns of the corresponding double permutations, the analytical expressions of which form the mass operator presented by the chain fractions. We received the expressions for admissibles and inadmissibles columns for phonon components of double permutations. The numerical calculations allow to conclude about the energy shift and how it depends on the parameters.
dc.format.extent48-54
dc.format.pages7
dc.identifier.citationTovstyuk C. The Shift of the Constant Energy Level After the Interaction of Particles with the Polarizing Phonons / Cornelija Tovstyuk // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 12. — No 1. — P. 48–54.
dc.identifier.citationenTovstyuk C. (2022) The Shift of the Constant Energy Level After the Interaction of Particles with the Polarizing Phonons. Computational Problems of Electrical Engineering (Lviv), vol. 12, no 1, pp. 48-54.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/58478
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofComputational Problems of Electrical Engineering, 1 (12), 2022
dc.relation.references[1] M. Tkach, Quasiparticles in geterosystems/ Quantum dots and wires, Yuriy Fedkovych Chernivtsi University, p. 312, 2003 (in Ukrainian).
dc.relation.references[2] C. Tovstyuk, “Electron energy in quantum dots with different configurations”, Molecular Crystals and Liquid Crystals, vol. 700, no. 1, pp. 30–33, 2020.
dc.relation.references[3] C. Tovstyuk, “Topologically distinct Feynman diagrams for mass operator in electron – phonon interaction”, Condensed Matter Physics, vol. 12, no. 2, pp. 225–239, 2009.
dc.relation.references[4] C. Tovstyuk, “The Polarizing Phonons Influence on the Energy Shift of Electrons in the quantum dots”, Proc. in 10th International Conference Nanomaterials: Applications & Properties (NAP-2020), 2020, pp. 02TM08-1 – 02TM08-5, Nov. 9 – 132020.
dc.relation.references[5] Ye. M. Lifshits and L.P. Pitayevskiy, Statistical Physics. Part 2, Moscow: Nauka, p. 448, 1978.
dc.relation.references[6] A. A. Abrikosov, L. P. Gorkov, and I. E. Dzialoshinski, Methods of quantum field theory in statistical physics. Dover Publ., New York, (1975).
dc.relation.references[7] C. Тovstyuk, “Mass operator of the interacting electrons in formalism of permutation group theory”, Int. J. of Modern Phys. B, vol. 24, no. 19, pp. 3735–3748, 2010.
dc.relation.references[8] C. С. Tovstyuk, “Double permutation method of designing Feynman diagrams for mass operator of interacting electrons,” AIP Conference Proceedings, Proc. of the 3rd conference “Statistical Physics: Modern trends and applications”, vol. 1198, pp. 185–195, 2009.
dc.relation.referencesen[1] M. Tkach, Quasiparticles in geterosystems/ Quantum dots and wires, Yuriy Fedkovych Chernivtsi University, p. 312, 2003 (in Ukrainian).
dc.relation.referencesen[2] C. Tovstyuk, "Electron energy in quantum dots with different configurations", Molecular Crystals and Liquid Crystals, vol. 700, no. 1, pp. 30–33, 2020.
dc.relation.referencesen[3] C. Tovstyuk, "Topologically distinct Feynman diagrams for mass operator in electron – phonon interaction", Condensed Matter Physics, vol. 12, no. 2, pp. 225–239, 2009.
dc.relation.referencesen[4] C. Tovstyuk, "The Polarizing Phonons Influence on the Energy Shift of Electrons in the quantum dots", Proc. in 10th International Conference Nanomaterials: Applications & Properties (NAP-2020), 2020, pp. 02TM08-1 – 02TM08-5, Nov. 9 – 132020.
dc.relation.referencesen[5] Ye. M. Lifshits and L.P. Pitayevskiy, Statistical Physics. Part 2, Moscow: Nauka, p. 448, 1978.
dc.relation.referencesen[6] A. A. Abrikosov, L. P. Gorkov, and I. E. Dzialoshinski, Methods of quantum field theory in statistical physics. Dover Publ., New York, (1975).
dc.relation.referencesen[7] C. Tovstyuk, "Mass operator of the interacting electrons in formalism of permutation group theory", Int. J. of Modern Phys. B, vol. 24, no. 19, pp. 3735–3748, 2010.
dc.relation.referencesen[8] C. S. Tovstyuk, "Double permutation method of designing Feynman diagrams for mass operator of interacting electrons," AIP Conference Proceedings, Proc. of the 3rd conference "Statistical Physics: Modern trends and applications", vol. 1198, pp. 185–195, 2009.
dc.rights.holder© Національний університет „Львівська політехніка“, 2022
dc.subjectenergy shift in multiparticle interaction
dc.subjectdouble permutation method for determining Green’s function for multiparticle interaction
dc.titleThe Shift of the Constant Energy Level After the Interaction of Particles with the Polarizing Phonons
dc.title.alternativeЗміст постійного рівня енергії після взаємодії частинок з поляризуючими фононами
dc.typeArticle

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