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 "title": "Sadao Nakajima",
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 "excerpt": "Sadao Nakajima (中嶋貞雄) was a Japanese theoretical physicist at Nagoya and Tokyo universities, known for the Nakajima–Zwanzig equation in statistical mechanics and for founding the ISQM symposium in 1983.",
 "snippet": "Sadao Nakajima (中嶋貞雄) was a Japanese theoretical physicist at Nagoya and Tokyo universities, known for the Nakajima–Zwanzig equation in statistical mechanics and for founding the ISQM symposium in 1983.",
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 "markdown": "# Sadao Nakajima\n\nBibliometric databases give 65 papers with about 3.4k citations and 2 hit papers; the Rankless profile reports an h-index of 16 with 2.5k indexed citations, while the Exa record reports h-index 18 and 3,401 citations, an unresolved disagreement between the two databases<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup><sup> • </sup><sup>[4](https://doi.org/10.1143/ptp.20.948)</sup>. The 1958 transport paper is his most-cited work, with 1,083 indexed citations on Rankless against 1,481 on Exa; the 1957 Kubo–Yokota–Nakajima paper follows with 508<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup><sup> • </sup><sup>[4](https://doi.org/10.1143/ptp.20.948)</sup>. Other cited works include *The Physics of Elementary Excitations* (Springer, 1980, with Yutaka Toyozawa and Ryuzo Abe), the 1973 paramagnon paper (76), and the 1963 electron-phonon papers with Watabe (57 and 17)<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup>. By research area, his most-cited clusters are superconductivity and magnetism (14 papers), laser-induced spectroscopy and plasma (9), and quantum and superfluid helium dynamics (8), and his work is most cited in atomic and molecular physics and statistical physics<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup>.\n\n| Key fact | Detail |\n|---|---|\n| Signature papers | \"On Quantum Theory of Transport Phenomena\" (PTP, 1958); \"On the Gauge-Invariant Meissner Effect\" (PTP, 1959); Kubo–Yokota–Nakajima response-theory paper (JPSJ, 1957)<sup>[1](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf)</sup><sup> • </sup><sup>[2](https://doi.org/10.1143/ptp.21.357)</sup><sup> • </sup><sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup> |\n\n## Scientific work\n\n**Steady diffusion.** His 1958 paper \"On Quantum Theory of Transport Phenomena\", received August 17, 1958 at Nagoya University's Physical Institute and published in *Progress of Theoretical Physics* Vol. 20, [No. 6](https://www.edgepedia.org/no-6), pp. 948–959, formulates the quantum statistical mechanics of steady diffusion as the most natural generalization of the Bloch kinetic equation<sup>[1](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf)</sup><sup> • </sup><sup>[4](https://doi.org/10.1143/ptp.20.948)</sup>. The method seeks a steady solution of Liouville's equation, with the boundary condition fixed by requiring the solution to lead to a given distribution of average density<sup>[5](https://inspirehep.net/literature/2736294)</sup>. The theory generalizes the Bloch equation to strongly interacting particles, reducing to it for weakly interacting particles, by extending a damping-theoretical expansion of Kohn and Luttinger<sup>[4](https://doi.org/10.1143/ptp.20.948)</sup>. Its key conclusion concerns the Einstein relation: the full text states it is valid only for the symmetric part of the diffusion- and electric-conductivity tensors, so for the [Hall effect](https://www.edgepedia.org/hall-effect) the gradient of chemical potential is not equivalent to the electric field, a difference first suggested by Kasuya and appreciable at low temperatures and strong magnetic fields<sup>[4](https://doi.org/10.1143/ptp.20.948)</sup>. The paper's own summary, however, reads \"antisymmetric part\" where the full text reads \"symmetric\", an unresolved discrepancy within the primary document<sup>[1](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf)</sup>.\n\n**Gauge invariance and superconductivity.** In a paper dated November 26, 1958 at Nagoya and published in February 1959, Nakajima addressed the gauge-invariant [Meissner effect](https://www.edgepedia.org/meissner-effect). Following Bardeen's suggestion and Anderson's emphasis that plasma excitations must be included, he showed that taking account of collective excitations yields the gauge-invariant result, and that the non-gauge-invariant term in [BCS theory](https://www.edgepedia.org/bcs-theory) introduces only a minor error in the normal part of the diamagnetic current<sup>[2](https://doi.org/10.1143/ptp.21.357)</sup>. The paper applies Tomonaga's method to split the Hamiltonian and the electron momentum density into collective and individual modes, and acknowledges Professor Matsubara and Dr. Yosida for discussions<sup>[2](https://doi.org/10.1143/ptp.21.357)</sup>.\n\n**Linear response and later topics.** The 1957 paper \"Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance\", written with [Ryogo Kubo](https://www.edgepedia.org/ryogo-kubo) and Mario Yokota in the *Journal of the Physical Society of Japan*, is his second most-cited work<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup>. Later work included the electron-phonon interaction in normal metals (two 1963 papers with Mitsuo Watabe) and the paramagnon effect on the BCS transition in He3 (*PTP*, 1973); the wiki-mirror source credits him with introducing paramagnons into the theory of superfluid He3 and with work on electron-phonon interaction as a basis of superconductivity theory<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup>.\n\n## Place among his contemporaries\n\nCo-authorship with Kubo and Yokota places Nakajima in the Japanese statistical-mechanics circle around Ryogo Kubo; his frequent co-authors also include Ryuzo Abe, Yutaka Toyozawa, Mitsuo Watabe, Kiichiro Kagawa, Daijiro Yoshioka, Yoshimasa Murayama, Hiromichi Suzuki, and Takao Saruta<sup>[3](https://www.rankless.org/authors/sadao-nakajima)</sup>. His use of Tomonaga's method in the Meissner-effect paper, and his acknowledgments to Matsubara and Yosida, tie him to the wider postwar Japanese theoretical-physics community<sup>[2](https://doi.org/10.1143/ptp.21.357)</sup>.\n\n## Legacy and influence\n\n**Conference leadership.** He also co-edited, with Masato Murakami, the proceedings of the 9th International Symposium on [Superconductivity](https://www.edgepedia.org/superconductivity) (ISS 96), held October 21–24, 1996 in Sapporo<sup>[6](https://www.reuffel.de/detail/ISBN-9784431701989/Herausgegeben-von-Nakajima-Sadao/Advances-in-Superconductivity-IX-Vol.2)</sup>.\n\n\n## References\n\n1. [Sadao Nakajima, On Quantum Theory of Transport Phenomena, Progress of Theoretical Physics 20(6):948 (1958), full-text PDF](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf)\n2. [Sadao Nakajima, On the Gauge-Invariant Meissner Effect, Progress of Theoretical Physics (1959), full-text record](https://doi.org/10.1143/ptp.21.357)\n3. [Rankless author profile: Sadao Nakajima](https://www.rankless.org/authors/sadao-nakajima)\n4. [On Quantum Theory of Transport Phenomena, PTP 20(6), 948–959 (1958), Exa record](https://doi.org/10.1143/ptp.20.948)\n5. [On Quantum Theory of Transport Phenomena: Steady Diffusion, INSPIRE-HEP record](https://inspirehep.net/literature/2736294)\n6. [Advances in Superconductivity IX Vol. 2 (ISS 96 proceedings), ed. Nakajima and Murakami, publisher record](https://www.reuffel.de/detail/ISBN-9784431701989/Herausgegeben-von-Nakajima-Sadao/Advances-in-Superconductivity-IX-Vol.2)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Physicists and astronomers › Researchers in condensed matter physics and quantum materials*\n\n*Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026; Oct 25, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n",
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 "credit": "\"Sadao Nakajima\", Edgepedia (EdgeChat), https://www.edgepedia.org/sadao-nakajima. Edgepedia Community License 1.0.",
 "credit_md": "\"[Sadao Nakajima](https://www.edgepedia.org/sadao-nakajima)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/sadao-nakajima](https://www.edgepedia.org/sadao-nakajima). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).",
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 "speakable": "Sadao Nakajima was a Japanese theoretical physicist at Nagoya and Tokyo universities, known for the Nakajima–Zwanzig equation in statistical mechanics and for founding the ISQM symposium in 1983."
}