Edge states of a diffusion equation in one dimension : Rapid heat conduction to the heat bath
We propose a one-dimensional diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period a. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalizing the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short-time regime, which is estimated to be t<10^{-2}s for the a∼10^{-3}m system and t<1s for the a∼10^{-2}m system composed of two kinds of familiar metals such as titanium, zirconium, and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high-energy edge states also contribute to very rapid heat conduction in a very short-time regime.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2022 |
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| Erschienen: |
2022 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:105 |
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| Enthalten in: |
Physical review. E - 105(2022), 2-1 vom: 15. Feb., Seite 024137 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Makino, Shusei [VerfasserIn] |
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| Links: |
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| Anmerkungen: |
Date Revised 16.03.2022 published: Print Citation Status PubMed-not-MEDLINE |
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| doi: |
10.1103/PhysRevE.105.024137 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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NLM338218769 |
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| 100 | 1 | |a Makino, Shusei |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Edge states of a diffusion equation in one dimension |b Rapid heat conduction to the heat bath |
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| 500 | |a Date Revised 16.03.2022 | ||
| 500 | |a published: Print | ||
| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a We propose a one-dimensional diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period a. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalizing the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short-time regime, which is estimated to be t<10^{-2}s for the a∼10^{-3}m system and t<1s for the a∼10^{-2}m system composed of two kinds of familiar metals such as titanium, zirconium, and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high-energy edge states also contribute to very rapid heat conduction in a very short-time regime | ||
| 650 | 4 | |a Journal Article | |
| 700 | 1 | |a Fukui, Takahiro |e verfasserin |4 aut | |
| 700 | 1 | |a Yoshida, Tsuneya |e verfasserin |4 aut | |
| 700 | 1 | |a Hatsugai, Yasuhiro |e verfasserin |4 aut | |
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| 773 | 1 | 8 | |g volume:105 |g year:2022 |g number:2-1 |g day:15 |g month:02 |g pages:024137 |
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