本研究の目的は原子，分子レベルでの有限温度における自発的な原子，分子スケールでの揺らぎの高精度測定を行い，その性質を理論解析することでした．2022年度は三井隆久氏（医学部）と共同研究を行い，アルコール，水，メタノール等の液体，またさらにその液体に塩，砂糖等を加えた水溶液の自発的な揺らぎを透過光強度の変動を通じて測定し，解析しました．塩水の例でわかるように，これら液体は透明で，自発的揺らぎの信号は非常に微弱です．特に散射雑音とよばれる量子統計的な光の揺らぎが必然的に生じ，多くの場合に対象の揺らぎより桁違いに大きいです．我々は独自に開発した雑音除去法を用いて，散射雑音を含めた雑音を3桁以上減少させることにより，揺らぎスペクトルの高密度測定を達成しました．
測定された揺らぎスペクトルを理論解析し，混合液内の分子の運動と温度揺らぎから構成されていることを明らかにしました．液体中では異なる分子やイオンが運動する場合には，非一様性が生じて光の散乱を生じさせ，透過光強度に微弱な揺らぎをもたらします．第一原理からの理論解析を行い，スペクトルの性質は1粒子のランダムな運動のダイナミックスで説明できることを明らかにしました．スペクトルの形が一致するだけでなく，そこから求まる拡散係数が既知の拡散係数と一致することを示しました．また，液体内の温度にはわずかな非一様性が存在し，これは時間とともに変化します．このスペクトルを理論的に求め，測定されたスペクトルと一致し，そこから求まる拡散係数は熱拡散係数と一致することを水，アルコール，そしてその混合物で示しました．
我々が今回測定した拡散の揺らぎと温度揺らぎは初めて測定されたものであり，さらに，その理論も今回第一原理より導いたものです．さらなる発展につながる重要な成果だと考えています．成果の一部は論文として発表しており，さらに数編の論文を近日中に発表する準備をしています．
The aim of this project was to make high precision optical measurements of spontaneous fluctuations that arise for finite temperatures, at the atomic and molecular scales. In the academic year 2022, in collaboration with Takahisa Mitsui (School of Medicine), we observed and analyzed the spontaneous fluctuations that arise in water, ethanol and methanol, and their mixtures, as well as water solutions of salt, sugar and other substances, through the intensity fluctuations they cause. As can be surmised from the properties of salt water, these liquids are transparent, and the signals due to spontaneous fluctuations are quite weak. In particular, shot-noise that inevitably arises from the quantum statistical nature of light is larger than the signals we aim to observe in many cases, by orders of magnitude. By using noise reduction methods we developed, the shot-noise, as well as other types of noise, were reduced by three orders of magnitudes or more to achieve measurements of the spontaneous fluctuation spectra in liquids.
We analyzed the observed spectra and established that they are composed of fluctuations due to molecular and ionic motions that lead to diffusion, and temperature fluctuations. When multiple types of molecules or ions exist in the liquid, the inhomogeneities they induce leads to scattering, causing intensity fluctuations in the transmitted light. Using the theory of single particle motions, we derived the corresponding theoretical spectrum from first principles, that describes the observed spectra. Not only the shapes of the spectra agree with the theory, but the diffusion constants obtained from the spectra agree with those from previous literature. Also, temperature in liquids is not completely uniform, and dynamic temperature fluctuations arise in liquids. We derived the corresponding spectrum theoretically, and the diffusion constants obtained from the observed spectra using this theory were shown to agree with the thermal diffusivities of water, ethanol and their mixtures.
These fluctuations we measured were previously unobserved, and their underlying theory was derived from first principles in our work. We believe that the work constitutes an important foundation, leading to future developments. The part of the work described here has been published, and a number of further papers on this work are in preparation.
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