論文 - 青木　健一郎

Fluctuation spectroscopy of surface melting of ice with and without impurities

Mitsui T., Aoki K.

Physical Review E （Physical Review E）  99 （ 1 ）  2019年01月

ISSN  24700045

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© 2019 American Physical Society. Water is ubiquitous, and the surface properties of ice have been studied for some time, due to their importance. A liquidlike layer (LLL) is known to exist on ice, below the melting point. We use surface thermal fluctuation spectroscopy to study the LLL, including its thickness, for pure ice, and for ice with impurities. We find that the properties of the LLL are experimentally those of liquid water, with thickness much smaller than previous results. We also find that impurities cause the LLL to be thicker, and quite inhomogeneous, with properties depending on the dopant.

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Dynamically enhanced low-coherence interferometry

Mitsui T., Aoki K.

Review of Scientific Instruments （Review of Scientific Instruments）  89 （ 9 ）  2018年09月

ISSN  00346748

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© 2018 Author(s). In the investigations of inhomogeneous media, availability of methods to study the interior of the material without affecting it is valuable. Optical coherence tomography provides such a functionality by providing depth resolved images of semi-transparent objects non-invasively. This is especially useful in medicine and is used not only in research but also in clinical practice. Optical coherence tomography characterizes each cross section by its reflectance. The basic physics principle underlying optical coherence tomography is low-coherence interferometry, which is combined with lateral scanning to produce cross sections. It is clearly desirable to obtain more detailed information regarding each cross section, if available. We have developed a system which measures the fluctuation spectra at all depths in low-coherence interferometry. By providing more information for each cross section, this can in principle be effective in tissue characterization and pathological diagnosis. The system uses the time dependence of the low-coherence interferometry data to obtain the fluctuation spectrum at each depth. Additionally, noise reduction is applied to obtain the spectra without unwanted noise, such as shot-noise, which can swamp the signal. The measurement system is applied to samples with no external stimuli, and depth resolved thermal fluctuation spectra of the samples are obtained. These spectra are compared with their corresponding theoretical expectations and are found to agree. The measurement system requires dualizing the detectors in the low-coherence interferometer but otherwise requires little additional equipment. The measurements were performed in ten to a hundred seconds.

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Thermal interface fluctuations of liquids and viscoelastic materials

Aoki K., Mitsui T.

Progress of Theoretical and Experimental Physics （Progress of Theoretical and Experimental Physics）  2018 （ 4 ）  2018年04月

ISSN  2050-3911

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© 2018 Physical Society of Japan. All rights reserved. Spectra of thermal fluctuations of a wide range of interfaces, from liquid/air, viscoelastic material/ air, liquid/liquid to liquid/viscoelastic material interfaces, were measured over a 100 Hz to 10MHz frequency range. The obtained spectra were compared with the fluctuation theory of interfaces, and found to be mostly in quite good agreement, when the theory was generalized to apply to thermal fluctuations of liquid/viscoelastic material interfaces. The loss modulus of viscoelastic materials has been incorporated into the theory, and its effects observed experimentally. The spectra were measured using a system that combines light reflection, statistical noise reduction through averaged correlations, and confocal microscopy. It requires only a small area of the interface (∼1μm2), relatively short times for measurements (≲ few min), and can also be applied to highly viscous materials.

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Order and chaos in the one-dimensional ϕ⁴ model: N-dependence and the Second Law of Thermodynamics

Hoover W., Aoki K.

Communications in Nonlinear Science and Numerical Simulation （Communications in Nonlinear Science and Numerical Simulation）  49   192 - 201 2017年08月

ISSN  10075704

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© 2017 Elsevier B.V. We revisit the equilibrium one-dimensional ϕ4 model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit positive Lyapunov exponents! The periodic orbits confine every particle in a periodic chain to trace out either the same or a mirror-image trajectory in its two-dimensional phase space. These “computationally stable” sets of pairs of single-particle orbits are either symmetric or antisymmetric to the very last computational bit. In such a periodic chain the odd-numbered and even-numbered particles’ coordinates and momenta are either identical or differ only in sign. “Positive Lyapunov exponents” can and do result if an infinitesimal perturbation breaking a perfect two-dimensional antisymmetry is introduced so that the motion expands into a four-dimensional phase space. In that extended space a positive exponent results. We formulate a standard initial condition for the investigation of the microcanonical chaotic number dependence of the model. We speculate on the uniqueness of the model's chaotic sea and on the connection of such collections of deterministic and time-reversible states to the Second Law of Thermodynamics.

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Observation of reflectance fluctuations in metals

Mitsui T., Aoki K.

Physical Review A （Physical Review A）  95 （ 4 ）  2017年04月

ISSN  24699926

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© 2017 American Physical Society. Through the study of the power spectra of a monochromatic light beam reflected by metallic mirrors, fluctuations in their reflectance are observed. The power spectra were obtained down to a factor 10-6 below the standard quantum limit, with a dynamic range of 105 in frequency and power, using methods we developed. The properties of the spectra are investigated, and their dependence on the material is analyzed. The physics underlying the phenomenon is also discussed. These fluctuations provide a window into the degrees of freedom responsible for the reflection process in metals.

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Stable and unstable periodic orbits in the one-dimensional lattice φ4 theory

Aoki K.

Physical Review E （Physical Review E）  94 （ 4 ）  2016年10月

ISSN  24700045

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© 2016 American Physical Society. Periodic orbits for the classical φ4 theory on the one-dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, free and fixed boundary conditions. Through the process, we investigate which normal modes of the linear theory can or cannot be extended to the full nonlinear theory and why. We then analyze the stability of these orbits, clarifying the link between the stability, parametric resonance, and Lyapunov spectra for these orbits. The construction of the periodic orbits and the stability analysis is applicable to theories governed by Hamiltonians with quadratic intersite potentials and a general on-site potential. We also apply the analysis to theories with on-site potentials that have qualitatively different behavior from the φ4 theory, with some concrete examples.

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Observing random walks of atoms in buffer gas through resonant light absorption

Aoki K., Mitsui T.

Physical Review A （Physical Review A）  94 （ 1 ）  2016年07月

ISSN  24699926

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© 2016 American Physical Society. Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has 1/f2 (f is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.

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Noise reduction and hyperfine level coherence in spontaneous noise spectroscopy of atomic vapor

Mitsui T., Aoki K.

Journal of the Optical Society of America B: Optical Physics （Journal of the Optical Society of America B: Optical Physics）  31 （ 2 ） 195 - 200 2014年02月

ISSN  07403224

　概要を見る

We developed a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light, and derive its power spectrum. We use this to observe the spontaneous noise spectra of photon atom interactions. Applying light with frequency modulation, we can also observe the spontaneous noise reflecting the coherence between the hyperfine levels in the excited state. There are two main novel components in the measurement system, the noise reduction scheme and the stabilization of the laser system. The noise reduction mechanism can be used to reduce the shot noise contribution to arbitrarily low levels through averaging, in principle. This is combined with differential detection to keep unwanted noise at low levels. The laser system is stabilized to obtain spectral width below 1 kHz without high frequency (≳10 MHz) noise. These methods are described systematically and the performance of the measurement system is examined through experimental results. © 2014 Optical Society of America.

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Observation of spontaneous quantum fluctuations in photon absorption by atoms

Mitsui T., Aoki K.

European Physical Journal D （European Physical Journal D）  67 （ 10 ）  2013年12月

ISSN  14346060

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Fluctuations in light absorption by atoms are observed by applying laser light on rubidium atoms and measuring the transmitted light intensity fluctuations. These fluctuations are spontaneous noise, generic to photon atom interactions. By making use of the sub-shot noise random signal detection technology, we have measured the spectra at sub-shot noise levels to reveal their rich nature, whose whole structure had previously been unobserved. The effects of atoms transiting the laser beam, Rabi flopping in the optical transitions and Larmor precession of the magnetic moment are observed in the spectra. The properties of the fluctuations reflect not only the quantum behavior of atoms but also that of light. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2013.

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Measurements of liquid surface fluctuations at sub-shot-noise levels with Michelson interferometry

Mitsui T., Aoki K.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics （Physical Review E - Statistical, Nonlinear, and Soft Matter Physics）  87 （ 4 ）  2013年04月

ISSN  15393755

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Surface fluctuation spectra of liquids are measured to unprecedented precision, down to 3 orders of magnitude below the shot-noise level using averaged correlations of interferometry measurements. This allows us to investigate the limits in our current theoretical understanding of these phenomena. The spectrum derived from hydrodynamical considerations agrees well with the observed results for water. However, for oil, deviations are seen at high frequencies (1 MHz), perhaps indicating its more complex underlying physics. The measurements are made possible by dualizing the Michelson interferometry measurements and employing the averaged correlation of signals, in which the shot noise is statistically reduced. The method works in the presence of the quantum noise of a coherent state of light. The optical part of the experimental setup is essentially the same as that of Michelson interferometry so that the method can be applied when Michelson interferometry can be used. Furthermore, the measurement method requires a relatively low light power and a short time so that it has a wide range of applicability. © 2013 American Physical Society.

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Direct observations of thermal fluctuations below shot noise levels

青木 健一郎，三井 隆久

素粒子論研究 13 （ 4 ）  2013年

研究論文（学術雑誌）, 共著

Michelson interferometry with quantum noise reduction

三井 隆久，青木 健一郎

Physical Review E87   042403 2013年

研究論文（学術雑誌）, 単著, 査読有り

Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels

青木 健一郎，三井 隆久

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics （Physical Review E - Statistical, Nonlinear, and Soft Matter Physics）  E86 （ 1 ） 011602 2012年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  15393755

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We study the spectral properties of thermal fluctuations on simple liquid surfaces, sometimes called ripplons. Analytical properties of the spectral function are investigated and are shown to be composed of regions with simple analytic behavior with respect to the frequency or the wave number. The derived expressions are compared to spectral measurements performed orders of magnitude below shot-noise levels, which is achieved using a novel noise reduction method. The agreement between the theory of thermal surface fluctuations and the experiment is found to be excellent, elucidating the spectral properties of the surface fluctuations. The measurement method requires relatively only a small sample both spatially (few μm) and temporally (∼20s). The method also requires relatively weak light power (∼0.5mW) so that it has a broad range of applicability, including local measurements, investigations of time-dependent phenomena, and noninvasive measurements. © 2012 American Physical Society.

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Direct optical observations of surface of thermal motions at sub-shot noise levels

青木 健一郎,三井隆久

Physical Review E80   020602(R)-1-4 2009年

研究論文（学術雑誌）, 共著, 査読有り

A tabletop experiment for the direct measurement of the speed of light

Aoki K., Mitsui T.

American Journal of Physics （American Journal of Physics）  76 （ 9 ） 812 - 815 2008年09月

ISSN  00029505

　概要を見る

We describe a tabletop experiment for the direct measurement of the speed of light to an accuracy of a few percent. The experiment is accessible to students not majoring in science or engineering. The experiment can include a measurement of the index of refraction of a sample. We discuss the experimental apparatus and safety considerations. The results and limitations of the experiment are analyzed, based partly on our experience in employing the experiment in student laboratories. © 2008 American Association of Physics Teachers.

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Some thermal transport properties of the FPU model with quadratic pinning

青木 健一郎

Progress of Theoretical Physics （Progress of Theoretical Physics）  119 （ 119 ） 717-724 - 724 2008年

研究論文（学術雑誌）, 単著, 査読有り,  ISSN  0033068X

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Thermal transport properties of the FPU β model with a quadratic pinning term are investigated for various couplings and temperatures. In particular, the size dependence of the thermal conductivity, κ α Lα, is studied. α agrees with that of the FPU β model (with no pinning) at high temperatures but decreases at low temperatures. This crossover behavior occurs at a temperature depending on the strength of the quadratic pinning.

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A small tabletop experiment for a direct measurement of the speed of light

青木 健一郎

American Journal of Physics  （ 76 ） 812-815 2008年

研究論文（学術雑誌）, 共著, 査読有り

Momentum cumulants, local equilibrium and stochastic thermostats

青木 健一郎

Physics Letters, Section A: General, Atomic and Solid State Physics （Physics Letters, Section A: General, Atomic and Solid State Physics）  368 （ A368 ） 77 - 81 2007年

研究論文（学術雑誌）, 単著, 査読有り,  ISSN  03759601

　概要を見る

We quantitatively investigate the behavior of momentum cumulants in the φ{symbol}4 theory under thermal gradients, using stochastic thermostats. We relate this to the violations of local equilibrium. The non-equilibrium behavior is found to be quite well described by a dependence ∼ (∇ T)2, on the temperature gradient. Dependence of the quantities on the thermostat type is analyzed and its physical implications are discussed. © 2007 Elsevier B.V. All rights reserved.

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ブラウン運動観測の学生実験について

青木健一郎， 柴崎彬

慶應義塾大学日吉紀要 31   21-52 2006年

研究論文（学術雑誌）, 単著

Energy transport in weakly anharmonic chains

Aoki K., Lukkarinen J., Spohn H.

Journal of Statistical Physics （Journal of Statistical Physics）  124 （ 124 ） 1105-1129 - 1129 2006年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  00224715

　概要を見る

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed. © Springer Science+Business Media, LLC 2006.

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