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Volume 12
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10.3390/universe12010015
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Momentum Transport in Ferromagnetic–Plasmon Heterostructures Within the Keldysh Formalism

by
Feiyi Liu
1,
Min Guo
1,
Mingyang Liu
1,* and
Yang Wang
2
1
School of Physics, Electrical and Energy Engineering, Chuxiong Normal University, Chuxiong 675000, China
2
School of Big Data and Basic Science, Shandong Institute of Petroleum and Chemical Technology, Dongying 257061, China
*
Author to whom correspondence should be addressed.
Universe 2026, 12(1), 15; https://doi.org/10.3390/universe12010015
Submission received: 25 November 2025 / Revised: 30 December 2025 / Accepted: 1 January 2026 / Published: 3 January 2026
(This article belongs to the Section Field Theory)
Versions Notes

Abstract

We investigate momentum transport in ferromagnetic–plasmon heterostructures using Keldysh field theory and energy–momentum tensor formalism. A three-layer model reveals that plasmon frequency shifts generate a non-zero expectation value for the xz-component of the energy–momentum tensor ⟨Txz⟩ through magnon–plasmon coupling. The momentum transport exhibits linear velocity dependence, with temperature behavior transitioning from exponential suppression at low temperatures to linear growth at high temperatures, governed by the magnon energy gap. Spatial oscillations follow sin(2nπz/h) patterns within the ferromagnetic layer. This framework provides fundamental insights into quantum momentum transport mechanisms in magnetic systems.
Keywords: Keldysh field theory; energy–momentum tensor; Galilean boost; momentum transport; path integral; magnon–plasmon coupling Keldysh field theory; energy–momentum tensor; Galilean boost; momentum transport; path integral; magnon–plasmon coupling

Share and Cite

MDPI and ACS Style

Liu, F.; Guo, M.; Liu, M.; Wang, Y. Momentum Transport in Ferromagnetic–Plasmon Heterostructures Within the Keldysh Formalism. Universe 2026, 12, 15. https://doi.org/10.3390/universe12010015

AMA Style

Liu F, Guo M, Liu M, Wang Y. Momentum Transport in Ferromagnetic–Plasmon Heterostructures Within the Keldysh Formalism. Universe. 2026; 12(1):15. https://doi.org/10.3390/universe12010015

Chicago/Turabian Style

Liu, Feiyi, Min Guo, Mingyang Liu, and Yang Wang. 2026. "Momentum Transport in Ferromagnetic–Plasmon Heterostructures Within the Keldysh Formalism" Universe 12, no. 1: 15. https://doi.org/10.3390/universe12010015

APA Style

Liu, F., Guo, M., Liu, M., & Wang, Y. (2026). Momentum Transport in Ferromagnetic–Plasmon Heterostructures Within the Keldysh Formalism. Universe, 12(1), 15. https://doi.org/10.3390/universe12010015

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