Quantum Tunneling and Complex Dynamics in the Suris's Integrable Map.

Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map and the associated Hamiltonian system is qualitatively the same, with only a slight difference in magnitude. However, the tunneling tails of the wave functions, obtained by superposing the eigenfunctions that form the doublet, exhibit significant differences. To explore the origin of the difference, we observe the classical dynamics in the complex plane and find that the existence of branch points appearing in the potential function of the integrable map could play the role of yielding non-trivial behavior in the tunneling tail. The result highlights the subtlety of quantum tunneling, which cannot be captured in nature only by the dynamics in the real plane.

Ergodicity of complex dynamics and quantum tunneling in nonintegrable systems.

The instanton approximation is a widely used approach to construct the semiclassical theory of tunneling. The instanton path bridges the regions that are not connected by classical dynamics, but the connection can be achieved only if the two regions have the same energy. This is a major obstacle when applying the instanton method to nonintegrable systems. Here we show that the ergodicity of complex orbits in the Julia set ensures the connection between arbitrary regions and thus provides an alternative to the instanton path in the nonintegrable system. This fact is verified using the ultra-near integrable system in which none of the visible structures inherent in nonintegrability exist in the classical phase space, yet nonmonotonic tunneling tails emerge in the corresponding wave functions. The simplicity of the complex phase space allows us to explore the origin of the nontrivial tunneling tails in terms of semiclassical analysis in the time domain. In particular, it is shown that not only the imaginary part but also the real part of the classical action plays a role in creating the characteristic step structure of the tunneling tail that appears as a result of the quantum resonance.

Dynamical tunneling across the separatrix.

The strong enhancement of tunneling couplings typically observed in tunneling splittings in the quantum map is investigated. We show that the transition from instanton to noninstanton tunneling, which is known to occur in tunneling splittings in the space of the inverse Planck constant, takes place in a parameter space as well. By applying the absorbing perturbation technique, we find that the enhancement invoked as a result of local avoided crossings and that originating from globally spread interactions over many states should be distinguished and that the latter is responsible for the strong and persistent enhancement. We also provide evidence showing that the coupling across the separatrix in phase space is crucial in explaining the behavior of tunneling splittings by performing the wave-function-based observation. In the light of these findings, we examine the validity of the resonance-assisted tunneling theory.

3D microfabrication by applying the laser-induced bubble method to the thermoset polymer PDMS using a conventional nanosecond laser.

We recently developed a microfabrication technique [microfabrication using laser-induced bubble (microFLIB)] and applied it to polydimethylsiloxane (PDMS), a thermoset polymer. The technique enabled the rapid fabrication of a microchannel on a PDMS substrate and selective metallization of the channel via subsequent plating; however, the technique was limited to surface microfabrication. Therefore, we explored the feasibility of three-dimensional (3D) microFLIB of PDMS using a nanosecond laser. In the experiment, a laser beam was focused inside pre-curing liquid PDMS and was scanned both perpendicular and parallel to the laser-beam axis to generate a 3D line of laser-induced bubbles. In the microFLIB processing, the shape of the created bubbles was retained in the pre-curing PDMS for more than 24 h; thus, the line of bubbles generated by the perpendicular laser scanning successfully produced a 3D hollow transverse microchannel inside the PDMS substrate after subsequent thermal curing. In addition, a through-hole with an aspect ratio greater than ∼200 was easily fabricated in the PDMS substrate by parallel laser scanning. The fabrication of a 3D microfluidic device comprising two open reservoirs in a PDMS substrate was also demonstrated for biochip applications.

Modeling Long-Range Dynamic Correlations of Words in Written Texts with Hawkes Processes.

It has been clarified that words in written texts are classified into two groups called Type-I and Type-II words. The Type-I words are words that exhibit long-range dynamic correlations in written texts while the Type-II words do not show any type of dynamic correlations. Although the stochastic process of yielding Type-II words has been clarified to be a superposition of Poisson point processes with various intensities, there is no definitive model for Type-I words. In this study, we introduce a Hawkes process, which is known as a kind of self-exciting point process, as a candidate for the stochastic process that governs yielding Type-I words; i.e., the purpose of this study is to establish that the Hawkes process is useful to model occurrence patterns of Type-I words in real written texts. The relation between the Hawkes process and an existing model for Type-I words, in which hierarchical structures of written texts are considered to play a central role in yielding dynamic correlations, will also be discussed.

Quantum tunneling in ultra-near-integrable systems.

We study the tunneling tail of eigenfunctions of the quantum map using arbitrary precision arithmetic and find that nonmonotonic decaying tails accompanied by step structures appear even when the corresponding classical system is extremely close to the integrable limit. Using the integrable basis constructed with the Baker-Campbell-Hausdorff (BCH) formula, we clarify that the observed structure emerges due to the coupling with excited states via the quantum resonance mechanism. Further calculations reveal that the step structure gives stretched exponential decay as a function of the inverse Planck constant, which is not expected to appear in normal tunneling processes.

Sinking of Four Species of Living Diatom Cells Directly Observed by a "Tumbled" Optical Microscope.

The study of the sinking phenomenon of diatom cells, which have a slightly larger specific gravity (~1.3) compared to that of water, is an important research topic for understanding photosynthetic efficiency. In this study, we successfully demonstrated the observation of the sinking behaviors of four different species of diatom using a homemade "tumbled" optical microscope. A homemade 1 mm3 microchamber was employed to decrease the effects of convection currents. In the microchamber, diatom cells were basically settled in a linear manner without floating, although some of the cells were rotated during their sinking. Sinking speeds of the four species of diatom cells, Nitzschia sp., Pheodactylum tricornutum, Navicula sp., and Odontella aurita, were 0.81 ± 5.56, 3.03 ± 10.17, 3.29 ± 7.39, and 11.22 ± 21.42 µm/s, respectively, based on the automatic tracking analysis of the centroids of each cell. Manual analysis of a vector between two longitudinal ends of the cells (two-point analysis) was effective for quantitatively characterizing the rotation phenomenon; therefore, angles and angular velocities of rotating cells were well determined as a function of time. The effects of the cell shapes on sinking velocity could be explained by simulation analysis using the modified Stokes' law proposed by Miklasz et al.

Single cell analysis of sinking diatoms studied using a homemade 'tumbled' optical microscope system.

Diatoms are one of the major photosynthetic planktons. Here, we studied movements of aqueous suspensions of diatoms using a home-made 'tumbled' optical microscope system. The usual inverted optical microscope was reoriented using a homemade microscope stand so that the vertical sample stage contacted the surface. To observe the intrinsic sinking phenomenon of individual Navicula sp. cells, which have slender bodies, a homemade microchamber (1 mm3) was employed. Most of the cells uniformly sunk with a velocity of 2 to 14 µm/s. Automatic and manual two points trajectory analyses were carried out. The manual analysis was able to assess the rotation of cells. The novel methods provide new information about cell movements in aqueous systems that could not be obtained using conventional methods.

Renormalized perturbation approach to instanton-noninstanton transition in nearly integrable tunneling processes.

A renormalized perturbation method is developed for quantum maps of periodically kicked rotor models to study the tunneling effect in the nearly integrable regime. Integrable Hamiltonians closely approximating the nonintegrable quantum map are systematically generated by the Baker-Hausdorff-Campbell (BHC) expansion for symmetrized quantum maps. The procedure results in an effective integrable renormalization, and the unrenormalized residual part is treated as the perturbation. If a sufficiently high-order BHC expansion is used as the base of perturbation theory, the lowest order perturbation well reproduces tunneling characteristics of the quasibound eigenstates, including the transition from the instanton tunneling to a noninstanton one. This approach enables a comprehensive understanding of the purely quantum mechanisms of tunneling in the nearly integrable regime. In particular, the staircase structure of tunneling probability dependence on quantum number can be clearly explained as the successive transition among multiquanta excitation processes. The transition matrix elements of the residual interaction have resonantly enhanced invariant components that are not removed by the renormalization. Eigenmodes coupled via these invariant components form noninstanton (NI) tunneling channels of two types contributing to the two regions of each step of the staircase structure: one type of channel is inside the separatrix, and the other goes across the separatrix. The amplitude of NI tunneling across the separatrix is insensitive to the Planck constant but shows an essentially singular dependence upon the nonintegrablity parameter. Its relation to the Melnikov integral, which characterizes the scale of classical chaos emerging close to the saddle on the potential top, is discussed.

Rapid, high-quality microfabrication of thermoset polymer PDMS using laser-induced bubbles.

Bubbles can be formed by focusing a high-power laser in a liquid. Based on this phenomenon, the present study demonstrated a novel technique, referred to as microFabrication using Laser-Induced Bubbles (microFLIB), for the microfabrication of the thermoset polymer polydimethylsiloxane (PDMS). A conventional nanosecond green laser was focused at the interface between uncured PDMS and a metal target and scanned to generate a line of bubbles at the boundary. The hemispherical shapes of these bubbles produced a groove on the rear side of the PDMS substrate following subsequent thermal curing. After the fabrication of such specimens, metal films could be selectively deposited along the grooves by electroless plating. This process allows rapid, high-quality microfluidic fabrication with potential applications to biochips.

Etching-Assisted Ablation of the UV-Transparent Fluoropolymer CYTOP Using Various Laser Pulse Widths and Subsequent Microfluidic Applications.

This work demonstrated the surface microfabrication of the UV-transparent fluoropolymer CYTOP (perfluoro 1-butenyl vinyl ether), by etching-assisted ablation using lasers with different pulse widths. In previous studies, we developed a technique for CYTOP microfluidic fabrication using laser ablation followed by etching and annealing. However, this technique was not suitable for some industrial applications due to the requirement for prolonged etching of the irradiated areas. The present work developed a faster etching-assisted ablation method in which the laser ablation of CYTOP took place in fluorinated etching solvent and investigated into the fabrication mechanism of ablated craters obtained from various pulse width lasers. The mechanism study revealed that the efficient CYTOP microfabrication can be achieved with a longer pulse width laser using this technique. Therefore, the rapid, high-quality surface microfabrication of CYTOP was demonstrated using a conventional nanosecond laser. Additionally, Microfluidic systems were produced on a CYTOP substrate via the new etching-assisted laser ablation process followed by annealing within 1 h, which is faster than the prior work of the microfluidic chip fabrication. Subsequently, CYTOP and polydimethylsiloxane substrates were bonded to create a 3D microfluidic chip that allowed for a clear microscopic image of the fluid boundary.

Controllable alignment of elongated microorganisms in 3D microspace using electrofluidic devices manufactured by hybrid femtosecond laser microfabrication.

This paper presents a simple technique to fabricate new electrofluidic devices for the three-dimensional (3D) manipulation of microorganisms by hybrid subtractive and additive femtosecond (fs) laser microfabrication (fs laser-assisted wet etching of glass followed by water-assisted fs laser modification combined with electroless metal plating). The technique enables the formation of patterned metal electrodes in arbitrary regions in closed glass microfluidic channels, which can spatially and temporally control the direction of electric fields in 3D microfluidic environments. The fabricated electrofluidic devices were applied to nanoaquariums to demonstrate the 3D electro-orientation of Euglena gracilis (an elongated unicellular microorganism) in microfluidics with high controllability and reliability. In particular, swimming Euglena cells can be oriented along the z-direction (perpendicular to the device surface) using electrodes with square outlines formed at the top and bottom of the channel, which is quite useful for observing the motions of cells parallel to their swimming directions. Specifically, z-directional electric field control ensured efficient observation of manipulated cells on the front side (45 cells were captured in a minute in an imaging area of ~160×120 µm), resulting in a reduction of the average time required to capture the images of five Euglena cells swimming continuously along the z-direction by a factor of ~43 compared with the case of no electric field. In addition, the combination of the electrofluidic devices and dynamic imaging enabled observation of the flagella of Euglena cells, revealing that the swimming direction of each Euglena cell under the electric field application was determined by the initial body angle.

Making the invisible visible: a microfluidic chip using a low refractive index polymer.

Microfluidic frameworks known as micro-total-analysis-systems or lab-on-a-chip have become versatile tools in cell biology research, since functional biochips are able to streamline dynamic observations of various cells. Glass or polymers are generally used as the substrate due to their high transparency, chemical stability and cost-effectiveness. However, these materials are not well suited for the microscopic observation of cell migration at the fluid boundary due to the refractive index mismatch between the medium and the biochip material. For this reason, we have developed a new method of fabricating three-dimensional (3D) microfluidic chips made of the low refractive index fluoric polymer CYTOP. This novel fabrication procedure involves the use of a femtosecond laser for direct writing, followed by wet etching with a dilute fluorinated solvent and annealing, to create high-quality 3D microfluidic chips inside a polymer substrate. A microfluidic chip made in this manner enabled us to more clearly observe the flagellum motion of a Dinoflagellate moving in circles near the fluid surface compared to the observations possible using conventional microfluidic chips. We believe that CYTOP microfluidic chips made using this new method may allow more detailed analysis of various cell migrations near solid boundaries.

Single cell analysis using a glass microchamber for studying movement fluctuations of Navicula pavillardii and Seminavis robusta diatom cells.

We propose a new technique for quantitative trajectory analysis of gliding phenomenon of Navicula pavillardii (NP) and Seminavis robusta (SR) diatom cells by single cell observation using a glass microchamber in this short technical note. Two-dimensional trajectory analysis of cell movements was used to determine the angular velocity, velocity, and migration distances of the diatom movement. Based on the trajectory analysis, we found that asymmetrically shaped SR had a larger angular velocity with large fluctuations compared to symmetrically shaped NP, although the velocity of SR was less than that of NP. It suggests that lateral frictional force in a culture medium is an important factor for diatom movements. Our results revealed that the single cell observation using a glass microchamber is effective on quantitative analysis of angular velocity of diatom gliding.

Origin of the enhancement of tunneling probability in the nearly integrable system.

The enhancement of tunneling probability in the nearly integrable system is closely examined, focusing on tunneling splittings plotted as a function of the inverse of the Planck's constant. On the basis of the analysis using the absorber which efficiently suppresses the coupling, creating spikes in the plot, we found that the splitting curve should be viewed as the staircase-shaped skeleton accompanied by spikes. We further introduce renormalized integrable Hamiltonians and explore the origin of such a staircase structure by investigating the nature of eigenfunctions closely. It is found that the origin of the staircase structure could trace back to the anomalous structure in tunneling tail which manifests itself in the representation using renormalized action bases. This also explains the reason why the staircase does not appear in the completely integrable system.

Femtosecond laser 3D micromachining: a powerful tool for the fabrication of microfluidic, optofluidic, and electrofluidic devices based on glass.

Femtosecond lasers have unique characteristics of ultrashort pulse width and extremely high peak intensity; however, one of the most important features of femtosecond laser processing is that strong absorption can be induced only at the focus position inside transparent materials due to nonlinear multiphoton absorption. This exclusive feature makes it possible to directly fabricate three-dimensional (3D) microfluidic devices in glass microchips by two methods: 3D internal modification using direct femtosecond laser writing followed by chemical wet etching (femtosecond laser-assisted etching, FLAE) and direct ablation of glass in water (water-assisted femtosecond laser drilling, WAFLD). Direct femtosecond laser writing also enables the integration of micromechanical, microelectronic, and microoptical components into the 3D microfluidic devices without stacking or bonding substrates. This paper gives a comprehensive review on the state-of-the-art femtosecond laser 3D micromachining for the fabrication of microfluidic, optofluidic, and electrofluidic devices. A new strategy (hybrid femtosecond laser processing) is also presented, in which FLAE is combined with femtosecond laser two-photon polymerization to realize a new type of biochip termed the ship-in-a-bottle biochip.

Electrofluidics fabricated by space-selective metallization in glass microfluidic structures using femtosecond laser direct writing.

Space-selective metallization of the inside of glass microfluidic structures using femtosecond laser direct-write ablation followed by electroless plating is demonstrated. Femtosecond laser direct writing followed by thermal treatment and successive chemical etching allows us to fabricate three-dimensional microfluidic structures inside photosensitive glass. Then, femtosecond laser ablation followed by electroless metal plating enables flexible deposition of patterned metal films on desired locations of not only the top and bottom walls but also the sidewalls of fabricated microfluidic structures. A volume writing scheme for femtosecond laser irradiation inducing homogeneous ablation on the sidewalls of microfluidic structures is proposed for sidewall metallization. The developed technique is used to fabricate electrofluidics in which microelectric components are integrated into glass microchannels. The fabricated electrofluidics are applied to control the temperature of liquid samples in the microchannels for the enhancement of chemical reactions and to manipulate the movement of biological samples in the microscale space.

Characterization and mechanism of glass microwelding by double-pulse ultrafast laser irradiation.

We investigated the physical mechanism of high-efficiency glass microwelding by double-pulse ultrafast laser irradiation by measuring the dependences of the size of the heat-affected zone and the bonding strength on the delay time between the two pulses for delay time up to 80 ns. The size of the heat-affected zone increases rapidly when the delay time is increased from 0 to 12.5 ps. It then decreases dramatically when the delay time is further increased to 30 ps. It has a small peak around 100 ps. For delay time up to 40 ns, the size of the heat-affected zone exceeds that for a delay time of 0 ps, whereas for delay time over 60 ps, it becomes smaller than that for a delay time of 0 ps. The bonding strength exhibits the same tendency. The underlying physical mechanism is discussed in terms of initial electron excitation by the first pulse and subsequent excitation by the second pulse: specifically, the first pulse induces multiphoton ionization or tunneling ionization, while the second pulse induces electron heating or avalanche ionization or the second pulse is absorbed by the localized state. Transient absorption of glass induced by the ultrafast laser pulse was analyzed by an ultrafast pump-probe technique. We found that the optimum pulse energy ratio is unity. These results provide new insights into high-efficiency ultrafast laser microwelding of glass and suggest new possibilities for further development of other ultrafast laser processing techniques.

Highly sensitive optofluidic chips for biochemical liquid assay fabricated by 3D femtosecond laser micromachining followed by polymer coating.

The demand for increased sensitivity in the concentration analysis of biochemical liquids is a crucial issue in the development of lab on a chip and optofluidic devices. We propose a new design for optofluidic devices for performing highly sensitive biochemical liquid assays. This design consists of a microfluidic channel whose internal walls are coated with a polymer and an optical waveguide embedded in photostructurable glass. The microfluidic channel is first formed by three-dimensional femtosecond laser micromachining. The internal walls of the channel are then coated by the dipping method with a polymer that has a lower refractive index than water. Subsequently, the optical waveguide is integrated with the microfluidic channel. The polymer coating on the internal walls permits the probe light, which is introduced by the optical waveguide, to propagate along the inside of the microfluidic channel. This results in a sufficiently long interaction length between the probe light and a liquid sample in the channel and thus significantly improves the sensitivity of absorption measurements. Using the fabricated optofluidic chips, we analyzed protein in bovine serum albumin to concentrations down to 7.5 mM as well as 200 nM glucose-D.

3D microfluidic chips with integrated functional microelements fabricated by a femtosecond laser for studying the gliding mechanism of cyanobacteria.

Phormidium, a genus of filamentous cyanobacteria, forms endosymbiotic associations with seedling roots that accelerate the growth of the vegetable seedlings. Understanding the gliding mechanism of Phormidium will facilitate improved formation of this association and increased vegetable production. To observe the gliding movements, we fabricated various microfluidic chips termed nanoaquariums using a femtosecond (fs) laser. Direct fs laser writing, followed by annealing and successive wet etching in dilute hydrofluoric acid solution, can easily produce three-dimensional (3D) microfluidics with different structures embedded in a photostructurable glass. Using the fs laser, optical waveguides and filters were integrated with the microfluidic structures in the microchips, allowing the gliding mechanism to be more easily clarified. Using this apparatus, we found that CO(2) secreted from the seedling root attracts Phormidium in the presence of light, and determined the light intensity and specific wavelength necessary for gliding.