# Sadao Nakajima
Bibliometric 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[3](https://www.rankless.org/authors/sadao-nakajima) • [4](https://doi.org/10.1143/ptp.20.948). 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[3](https://www.rankless.org/authors/sadao-nakajima) • [4](https://doi.org/10.1143/ptp.20.948). 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)[3](https://www.rankless.org/authors/sadao-nakajima). 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[3](https://www.rankless.org/authors/sadao-nakajima).
| Key fact | Detail |
|---|---|
| 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)[1](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf) • [2](https://doi.org/10.1143/ptp.21.357) • [3](https://www.rankless.org/authors/sadao-nakajima) |
## Scientific work
**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[1](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf) • [4](https://doi.org/10.1143/ptp.20.948). 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[5](https://inspirehep.net/literature/2736294). 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[4](https://doi.org/10.1143/ptp.20.948). 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[4](https://doi.org/10.1143/ptp.20.948). The paper's own summary, however, reads "antisymmetric part" where the full text reads "symmetric", an unresolved discrepancy within the primary document[1](https://academic.oup.com/ptp/article-pdf/20/6/948/5440766/20-6-948.pdf).
**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[2](https://doi.org/10.1143/ptp.21.357). 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[2](https://doi.org/10.1143/ptp.21.357).
**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[3](https://www.rankless.org/authors/sadao-nakajima). 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[3](https://www.rankless.org/authors/sadao-nakajima).
## Place among his contemporaries
Co-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[3](https://www.rankless.org/authors/sadao-nakajima). 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[2](https://doi.org/10.1143/ptp.21.357).
## Legacy and influence
**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[6](https://www.reuffel.de/detail/ISBN-9784431701989/Herausgegeben-von-Nakajima-Sadao/Advances-in-Superconductivity-IX-Vol.2).
## References
1. [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)
2. [Sadao Nakajima, On the Gauge-Invariant Meissner Effect, Progress of Theoretical Physics (1959), full-text record](https://doi.org/10.1143/ptp.21.357)
3. [Rankless author profile: Sadao Nakajima](https://www.rankless.org/authors/sadao-nakajima)
4. [On Quantum Theory of Transport Phenomena, PTP 20(6), 948–959 (1958), Exa record](https://doi.org/10.1143/ptp.20.948)
5. [On Quantum Theory of Transport Phenomena: Steady Diffusion, INSPIRE-HEP record](https://inspirehep.net/literature/2736294)
6. [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)
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*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Physicists and astronomers › Researchers in condensed matter physics and quantum materials*
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