We measure the static friction F_c of agar gels on glass substrates immersed in water. F_c is independent of the nominal contact area, and increases with the normal load and the duration t_w of contact prior to sliding. Using a confocal laser-scanning microscope, many fine dark spots are clearly visible in the optical reflection distribution images on the glass interface in contact with the gel. The total area of the dark spots increases with t_w, corresponding qualitatively to that of F_c. These observations indicate that F_c originates from the formation of the contacting spots at the interface, which is not due to asperities of the gel surface alone but related to the drainage of water trapped by the gel polymer network at the frictional interface.

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By use of high-resolution soft X-rays, intrinsic temperature dependences of bulk Yb 4f photoelectron spectra were obtained for fractured surfaces of high-purity YbAl₃ single crystals. The spectra of not only bulk 4f¹³ but also 4f¹² final states are analyzed by noncrossing approximation (NCA) calculation for the f¹⁴, f¹³, and f¹² initial states based on the single impurity Anderson model (SIAM). In order to consistently interpret the temperature dependences of both 4f¹³ and 4f¹² final states, however, it is found that a constant set of parameters of the hybridization strength Δ, bare 4f energy ε_f and electron correlation energy U_ff is insufficient. The limitation of SIAM is confirmed for YbAl₃ and the importance of the Kondo lattice effects is suggested.

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Recently, Matsukawa et al. discovered a new superconductor, Pr₂Ba₄Cu₇O_15−δ, in which metallic CuO double chains are responsible for the superconductivity. To investigate its superconductivity, we employ the d–p double chain model where the tight-binding parameters are determined so as to fit a band structure in the local density approximation (LDA). On the basis of the Tomonaga–Luttinger liquid theory, we obtain a phase diagram that includes the superconducting phase in the weak coupling limit. We also calculate the Luttinger liquid parameter K_ρ as a function of the electron density n using the Hartree–Fock approximation. With increasing n from quarter filling, K_ρ increases and then exceeds 1/2 when the superconducting correlation becomes most dominant. K_ρ has a maximum at an optimal density between quarter- and half-filling. These results are consistent with the experimental observation.

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We observed de Haas–van Alphen (dHvA) oscillation in a paramagnetic plutonium compound, PuIn₃. In the present paper, we report the first observation of dHvA effect in plutonium compounds. One detected dHvA branch named γ corresponds to a closed band-27 electron Fermi surface, where three kinds of closed Fermi surfaces are calculated on the basis of the 5f-itinerant band model. The cyclotron mass of branch γ was determined as 4.8 m₀. The dHvA signals are found to be extremely reduced as a function of time due to point defects produced by α-decay of ²³⁹Pu.

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We have grown a single crystal of La_2−xSr_xCuO₄ in which the Sr concentration, x, continuously changes from 0.24 to 0.29 in the overdoped regime and obtained many pieces of single crystals with different x values by slicing the single crystal. From detailed measurements of the magnetic susceptibility, χ, of each piece, it has been found that the absolute value of χ at the measured lowest temperature 2 K, |χ_{2 K}|, on field cooling rapidly decreases with increasing x as well as the superconducting (SC) transition temperature. As the value of |χ_{2 K}| is regarded as corresponding to the SC volume fraction in a sample, it has been concluded that a phase separation into SC and normal-state regions occurs in a sample of La_2−xSr_xCuO₄ in the overdoped regime.

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The superconductivity that occurs below the charge ordering temperature in a quasi-two-dimensional (quasi-2D) organic conductor, the α-(ET)₂I₃ salt, has been examined by applying the mean field theory and the random phase approximation to the extended Hubbard model with four sites in the unit cell and anisotropic nearest-neighbor interactions. It is shown that, under uniaxial pressure, the insulating phase moves to the metal phase with small pockets of electrons and holes, while the charge ordering state with the horizontal stripe pattern is retained. The novel property of the metal phase gives rise to the superconducting (SC) state with the full gap. It is found that the pairing interaction for the superconductivity is given mainly by the spin fluctuation existing between hole-rich sites in the unit cell. The role of the anisotropic repulsive interaction is discussed for the mechanism of the present SC state.

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To investigate the possibility of charge order and superconductivity in a doped two-dimensional triangular lattice, we study an extended Hubbard model with the variational Monte Carlo method. At n=2⁄3, a commensurate filling for a triangular lattice, it is shown that the nearest-neighbor Coulomb interaction V induces honeycomb-type charge order and antiferromagnetic spin order at U\\gtrsim10t. We also discuss the possibility of superconductivity induced by charge fluctuation and the relation to the superconductivity in Na_0.35CoO₂·1.3H₂O and θ-type organic condoctors.

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We have studied the superconducting state of Sr₂RuO₄ under a magnetic field parallel to the superconducting plane. We show that due to a weak spin–orbit coupling, a nonunitary k_y(\\hatz−iα\\haty) state is formed right at H_c2, which then changes to a unitary k_y\\hatz state as the magnetic field is lowered. On the basis of this crossover, we address the origin of the observed double peaks of specific heat and the disappearance of the double peaks at low fields.

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We discovered that oxonium (H₃O⁺) ion content is a key parameter to the understanding of unique superconductivity in sodium cobalt oxyhydrate. As Na⁺ ions are substituted by H₃O⁺ ions, keeping the Co valence constant, the superconducting phase is transformed into a magnetically ordered phase, and then into a hitherto hidden superconducting phase. Furthermore, the superconducting phase previously discovered is suppressed by the magnetic phase under application of a magnetic field. These facts indicate that the superconductivity is induced by magnetic interactions which are substantially governed by the oxonium ion content.

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We have investigated the physical properties of Ce_0.7Pr_0.3B₆ in order to clarify the doping effect on the multipolar interactions in CeB₆ and PrB₆. As a result of the suppression of the antiferro-quadrupolar ordering temperature T_Q and the enhancement of T_N by Pr doping, six long-range ordered (LRO) phases appear. T_Q exhibits a smooth increase with increasing magnetic field as in CeB₆. At a high magnetic field, above ∼10 T, only phase II exists. As for the three LRO phases below ∼10 T and below T_Q, there exists a possibility of incommensurate quadrupolar and magnetic ordering. A new question of how the quadrupolar ordering is compatible with the magnetic ordering appears in the present study. The coexistence of the magnetic and quadrupolar orderings in Ce_0.7Pr_0.3B₆ indicates that the strong Ce–Pr interaction is different from the weak Ce–Nd interaction in Ce_xNd_1−xB₆.

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Specific heat measurements in a magnetic field up to 8 T have been performed on an S=1⁄2 weakly coupled alternating ferromagnetic (F) and antiferromagnetic (AF) dimer chain system, (CH₃)₂NH₂CuCl₃. We have observed a spontaneous AF ordering and a field-induced one below and above the 1/2 magnetization plateau field range from 2 to 3.5 T, respectively. The H–T phase boundaries for the orderings are completely different from the general reentrant ones of the other quantum spin systems investigated thus far. In the plateau field range, a double-peaked structure is observed in the temperature dependence of specific heat, reflecting the coexistence of F and AF excitations.

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We have investigated the optical response of a superradiant system composed of N two-level systems, which undergoes three different damping mechanisms: radiative dissipation (γ_r), dephasing (γ_d), and nonradiative dissipation (γ_n). Whereas the roles of γ_d and γ_n are equivalent in the linear susceptibility χ⁽¹⁾, the third-order nonlinear susceptibility χ⁽³⁾ drastically depends on the ratio of γ_d and γ_n: When γ_d\\lesssimγ_n, χ⁽³⁾ is essentially that of a single two-level system. In contrast, in the opposite case of γ_d>>Nγ_n, χ⁽³⁾ suffers the size enhancement effect and becomes proportional to the system size N after an incubation period.

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A pressure-induced neutral-to-ionic (N–I) transition in tetrathiafulvalene-p-chroranil was studied by infrared vibration spectra. With increasing pressure, two CO stretching bands probing coexisting N and I states merge due to rapid valence fluctuations. From the spectral analyses with the exchange-narrowing model, we derive the pressure dependence of the N–I exchange rate related to the N–I domain-wall motions, which explains the anomalous increase in conductivity under pressure. We also demonstrate a para- to ferro-electric transition at 1.5 GPa as well as the N–I transition at 0.95 GPa.

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We determine the optimal conditions for achieving strong nonlinearity in semiconductor cavities as a function of the Q factor, coupling constant g, and longitudinal (γ₁) and pure transverse (γ₂) damping constants. The intensity of the third-order nonlinear field becomes maximum in the strong-coupling regime near the condition γ₁+2γ₂=ω_c⁄2Q, where ω_c is the cavity-quasimode frequency. However, the most effective optical Kerr effect can be realized in the intermediate-coupling regime. Both of the nonlinearities are enhanced significantly also in the weak-coupling regime satisfying ω_c⁄Q=(g²⁄γ₁)[\\sqrt1+8γ₁⁄(γ₁+2γ₂)−1], and their intensities depend only on the damping constants.

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A highly sensitive heterodyne-detected photon echo enabled us to observe the signal from one layer of neutral self-assembled InP quantum dots under an electric field. The photon echo signal dramatically increased when charged InP quantum dots were neutralized with the application of negative electric bias. This fact suggests the hypothesis that charged quantum dots do not produce the photon echo. With the further increase of negative electric bias, photoluminescence was quenched and the photon echo decayed faster. The photon echo showed tunneling-induced dephasing and decayed nonexponentially, reflecting the non-Markovian nature of the tunneling process.

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A dual-phase Y–W metallic glass is observed in nanoscaled Y–W multilayered films upon 200 keV xenon ion irradiation. Diffraction analysis and bright field images reveal that the metallic glass consists of separated glass phases evolved from the Y and W lattices, respectively, through spinodal decomposition, and that the glass features a two-dimensional fractal morphology consisting of the W-based glass phase branches sitting on the Y-based glass substrate. The fractal dimension is determined to be 1.75±0.05, suggesting that the fractal is grown through a cluster-diffusion-limited-aggregation model. Moreover, based on a newly derived n-body Y–W potential, atomistic simulations confirm the possibility of metallic glass formation in the equilibrium immiscible Y–W system.

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It is shown that the WKI model of type II which is solved in terms of the WKI scheme arises from the motion of curves in E³. Its symmetry groups and an one-dimensional optimal system are presented, and the corresponding group-invariant solutions are obtained.

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In this work, an analog analogue of Grover’s quantum search algorithm was studied. A generalized Hamiltonian driving the evolution of a quantum state in the analog search system was derived. Equations relating all parameters considered in the present problem were given according to the required maximal probability for finding the marked state. Using these equations, both the measuring time and the system energy gap suitable for a quantum search with or without certainty can thus be evaluated. Moreover, the reduction of the searching probability caused by a random and uncontrollable phase error for an initial state has been investigated. It was shown that in an efficient quantum search computation, the measuring time should be proportional to the square root of the size of the database.

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To simultaneously detect random and burst quantum errors which may be generalized as quantum event errors, a quantum error detection code, called the quantum event-error detection code, is first investigated in analogy to the classical event-error detection code. The proposed code can be used to detect the length, number and location of errors occurring in every error event. Two special quantum event-error detection codes are constructed by exploiting different approaches according to the derived syndrome, and their number-bound of generators of the stabilizer is also derived. Finally, the proposed theory on the quantum event-error detection code for quantum single-event error is extended to a more general case, i.e., the quantum composite-event error, so that the general quantum event-error detection code can be constructed.

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We consider the Blume–Capel model with quantum tunneling between the excited states. We find a magnetically ordered phase transition induced by quantum fluctuation in the model. The model has no phase transition in the corresponding classical case. Usually, quantum fluctuation breaks the ordered phase, as in the case of the transverse field Ising model. However, in the present case, an ordered phase is enhanced by a quantum fluctuation. Moreover, we find a phase transition between a quantum paramagnetic phase and a classical diamagnetic phase at a zero temperature. We study the properties of the phase transition using mean-field approximation (MFA) and a quantum Monte Carlo method to confirm the result of the MFA.

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We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample dependence. Networks of this type do not have well-defined thermodynamic limits, and self-averaging breaks down. We therefore need to develop a suitable theory without relying on these common properties. While the effects of the common synaptic inputs have been analyzed in layered neural networks, it was apparently difficult to analyze these effects in recurrent neural networks due to feedback connections. We investigated a sequential associative memory model as an example of recurrent networks and succeeded in deriving a macroscopic dynamical description as a recurrence relation form of a probability density function.

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We analyze ensemble learning including the noisy case where teacher or student noise is present. Linear perceptrons are used as teacher and student. First, we analyze the homogeneous correlation of initial weight vectors. The generalization error consists of two parts: the first term depends on the number of perceptrons K and is proportional to 1⁄K, the second does not depend on K in the first case. In the inhomogeneous correlation of initial weight vectors case, the weighted average could be optimized to minimize the generalization error. We found that the optimal weights do not depend on time without student noise, while the optimal weights depend on time and become 1⁄K with student noise.

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We propose a simple theoretical model for a molecular chemical engine that catalyzes a chemical reaction and converts the free energy released by the reaction into mechanical work. Binding and unbinding processes of reactant and product molecules to and from the engine are explicitly taken into account. The work delivered by the engine is calculated analytically for infinitely slow (“pseudo-static”) processes, which can be reversible (quasi-static) or irreversible, controlled by an external agent. It is shown that the work larger than the maximum value limited by the second law of thermodynamics can be obtained in a single cycle of operation by chance, although the statistical average of the work never exceeds this limit and the maximum work is delivered if the process is reversible. The mechanism of the energy transduction is also discussed.

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We have for the first time determined with high precision the energy spectrum of low-energy neutrons (E_n<10 keV) which are produced in the ⁷Li(p,n)⁷Be reaction, by detecting γ-rays of the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction whose cross section is known. An anti-Compton NaI(Tl) spectrometer played an essential role in detecting the γ-rays with a good signal to noise ratio by discriminating large background due to thermalized neutrons in the measurement room. The low energy neutrons thus derived were successfully used to measure the ⁶²Ni(n,γ)⁶³Ni reaction cross section. The present low energy neutrons could be extensively used for cross section measurements for neutron capture reactions and elastic scatterings from nuclei of nuclear astrophysical interests.

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A set of model transport equations is analyzed which induces the radial transition of the electric field by use of the theoretical model for the anomalous transport diffusivities as a candidate. Condition for the onset of the transition as well as a scaling relation between the reduced thermal diffusivity and the normalized temperature gradient is obtained. The test of the adopted theoretical model for the anomalous transport diffusivities is done compared with the experimental result in Large Helical Device (LHD).

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The structure of bundles of single-walled carbon nanotubes (SWNT) has been refined by Rietveld analysis using neutron and X-ray powder diffraction data. Based on previous simulation studies of powder diffraction data of SWNT and standard Rietveld analyses, we have developed a pattern fit technique for SWNT which provides precise structure parameters. We also show that the present technique can be used with the maximum entropy method (MEM), which is complementary to the Rietveld analysis. Using the neutron diffraction data of pristine SWNT, we have successfully reconstructed the density of carbon nuclei and zero density in the inner cavity of SWNT by MEM.

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The change of Ga smoke particles to GaN particles in a plasma field of a mixture of nitrogen and helium gasses has been studied by transmission electron microscopy. The size of Ga drop and amounts of exited nitrogen clearly influenced the single-crystalline nanoparticle growth. Most of the particles had a wurtzite structure. Small crystallites with a zincblende structure were frequently included in a wurtzite particle. When the nitrogen partial pressure became 10 Torr, perfect single-crystal particles less than 30 nm in size were formed.

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The temperature and zone dependence of the lattice dynamics in Pb(Mg_1⁄3Nb_2⁄3)O₃ is characterized using neutron inelastic scattering. Through a detailed study of the phonon lineshape and a comparison of the structure factors to SrTiO₃, we conclude that the coupling between the acoustic and optic modes is weak. However, based on a direct comparison between the (110) Brillouin zone where the diffuse scattering is strong to the (220) zone where the diffuse scattering is weak, a strong coupling between the diffuse component and low-energy acoustic phonon mode is observed. We conclude that the coupling to the diffuse component is the reason for several recent conflicting interpretations of the lattice dynamics based on data from zones with a strong diffuse component.

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The ground state energy and the wavefunction of proton in the cubic perovskite-type oxides ABO₃ are studied by using the double-well potential constructed from the one-dimensional O–H–O bond. We have found that when the O–O separation between the nearest neighbor oxygens becomes lower than 2.9 A the proton wavefunction spreads over the double-well potential and the proton transfers between the minimum sites in the double-well potential. We have calculated the activation energy E_a for the proton transfer by using the small polaron model coupled with the lattice vibration of the O–B–O bond-bending mode. The calculated activation energy is found to be E_a=0.56 eV for the cubic ABO₃. We have also found the B-atom mass dependence that E_a decreases with the B-atom mass in the O–B–O bond-bending mode. This B-atom mass dependence of E_a is similar to that shown in the deformed perovskite-type oxides ABO₃.

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We have studied a change of the Fermi surface in an antiferromagnet CeIn₃ via the de Haas–van Alphen experiment under pressure up to 3 GPa. With increasing pressure P, the Néel temperature T_N=10 K decreases and becomes zero at a critical pressure P_c\\simeq2.6 GPa. In the pressure region P>P_c, we have observed a large main Fermi surface named a, which indicates that the electronic state of 4f electron in CeIn₃ changes from localized to itinerant at P_c, as observed in the similar antiferromagnets CeRh₂Si₂ and CeRhIn₅. The cyclotron effective mass m_c^∗ of this main Fermi surface is extremely enhanced around P_c: m_c^∗\\simeq60m₀ at 2.7 GPa for the magnetic field along the ⟨100⟩ direction.

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The Boltzmann conductivity is calculated for carbon nanotubes in the presence of an Aharonov–Bohm magnetic flux. Effects of impurity scattering are considered at low temperatures and those of electron–phonon scattering are considered at room temperature. Effects of strains and curvature manifest themselves as a prominent conductivity peak as a function of the flux. The appearance of the peak corresponds to the absence of backscattering in metallic linear bands.

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Transport properties of quantum-wire arrays with disorder in the period are studied theoretically within a self-consistent Born approximation. Although no band gap opens to the lowest order because of the flat average potential, a pseudo-band-structure is recovered in higher order due to effects of strong diffuse Bragg scattering as long as the disorder remains small. A pseudo-band-gap manifests itself in the density of states, the spectral function, and the anisotropic conductivities, and modifies the conductivity in the quantum-wire direction qualitatively in the vicinity of the zone boundary.

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Josephson critical current I_c between a single crystal CePt₃Si and Al has been measured for the junctions on the CePt₃Si surface perpendicular to the a and c axes. In the magnetic-field dependence of I_c, a dominant maximum peak at zero field has been observed only for the junction on the a-axis face thus far, indicating that the Josephson effect is allowed at least for current flow parallel to the a axis. This result places a restriction on the representations of the order parameter in the noncentrosymmetric superconductor CePt₃Si.

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Data taken by various methods including NMR/NQR and neutron scattering are presented for Na_xCoO₂, particularly Na_0.5CoO₂. Attention has also been paid to the x dependence of the electronic nature of this system. The pseudo-gap-like behavior observed in the region of x<x_c∼0.6 is emphasized. For samples with x≤0.6, signals from two kinds of Co sites with different quadrupole frequencies ν_Q of ∼4.1 and ∼2.8 MHz were observed, and the former ν_Q, which is nearly equal to that of the superconducting system Na_0.3CoO₂·yH₂O, becomes dominant with decreasing x to 0.3. For Na_0.5CoO₂, the Co sites with the larger ν_Q have larger magnetic moments. They align antiferromagnetically at T_c1∼87 K with their direction within the plane, while the Co sites with the smaller ν_Q have smaller moments. They align in the direction parallel to the c axis. The ordered moments at the two distinct sites exhibit the same T-dependence, indicating that the existence of these sites is not due to macroscopic phase separation. Although we have observed the splitting of the zero-field NMR signals from Co sites with smaller ν_Q at the second transition temperature T_c2∼53 K, any other anomaly of the ordered magnetization has not been observed at T_c2 in the T-dependences of neutron and NMR data. As x decreases, the two-dimensional nature of the electrons is enhanced and the antiferromagnetic correlation increases. On the basis of these results, the superconducting pair state in Na_0.3CoO₂·yH₂O is discussed.

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We investigate magnetic properties of Fe nanoislands on Cu(111) in the relaxed structure within the density functional theory. We observe that the nanoislands exhibit the ferromagnetic properties with large magnetic moment. We find that the change in the magnetic moment of each Fe atom is induced by deposition on Cu(111) and structure relaxation of Fe nanoislands. Moreover, we examine the stability of ferromagnetic states of Fe nanoislands by performing the total energy calculations.

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Depth-resolved induced magnetic polarization in the Cu layer of the [Gd (57.4 Å)/Cu (16.5 Å)] multilayer is determined by resonant X-ray magnetic diffraction technique. The X-ray energy was tuned near the Cu K absorption edge (8981 eV). The resonant magnetic diffraction peaks from second to fourth order were measured at 10 and 75 K by helicity switching combined with field reversal. The analysis indicates that the induced magnetic polarization extends to the center of the Cu layer and that the magnetization polarization distribution scaled to the Gd magnetization is unchanged against temperature. The shape of the magnetic polarization distribution in the Gd/Cu multilayer is different from that predicted theoretically in the Co/Cu multilayer, where the induced magnetic polarization is concentrated mainly at the interface. A possible reason for the different distribution of the magnetic polarization in the Gd/Cu and Co/Cu systems is discussed.

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We report electron spin resonance (ESR) studies on field-induced charge carriers in regioregular poly(3-hexylthiophene) (RR-P3HT) and regioregular poly(3-octylthiophene) (RR-P3OT) for metal–insulator–semiconductor (MIS) diode structures with Al₂O₃ as an insulating layer. The field-induced ESR signals (g∼2.002) were clearly observed; their intensities monotonically increased as the absolute value of the gate bias increased in the accumulation mode with a saturation behavior at higher voltages. The ESR signals were consistent with those of the photogenerated positive polarons in RR-P3HT and RR-P3OT, demonstrating that the carriers are polarons. The transient responses of the field-induced ESR intensity show fast and slow components. The self-organized lamellar molecular orientation was confirmed by the anisotropic ESR signals due to π-electrons, which is semiquantitatively reproduced by an ESR simulation.

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We have vapor-deposited CuCl films on rutile TiO₂, Al₂O₃ and synthesized quartz surfaces. The photoluminescence spectra of the films with the thickness from 50 to 1500 nm were observed and compared with that of bulk CuCl. The energy position of the free Z₃ exciton luminescence was found to shift to lower energy side with the increase in the film thickness. This phenomenon suggested that the Z₃ exciton polaritons could not relax to the bottleneck region during their lifetime in the thin films. The observed substrate dependence of the spectra suggested that the relaxation was determined by the film thickness rather than the substrates we used in the experiment.

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Confined acoustic phonons in CuBr quantum dots (QDs) are studied for the first time using coherent phonon measurements and persistent spectral hole burning (PSHB) spectroscopy. A size-dependent damped oscillation with sub-THz frequency is observed in femtosecond pump-probe measurements of CuBr QDs in glass. Similarly, a size-dependent acoustic phonon hole with an energy shift of 1–2 meV is observed in PSHB spectra of CuBr QDs in glass and NaBr crystals. The energies of the confined acoustic phonons obtained by the two methods are in good agreement with each other. In addition, there is no difference in size-dependence between the glass matrix and NaBr matrix. The size dependence of acoustic phonons can be explained well as low frequency vibrational modes of CuBr QDs based on an elastic sphere model. The dominant mode is assigned to the l=2 spheroidal mode, while the l=0 mode is also observed.

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We give a general method to calculate photonic band structure in the form of wave number k as a function of frequency ω, which is required whenever we want to calculate signal intensity related with photonic band structure. This method is based on the fact that the elements of the coefficient matrix for the plane wave expansion of the Maxwell equations contain wave number up to the second order, which allows us to rewrite the original eigenvalue equation for ω² into that for wave number. This method is much better, especially for complex wave numbers, than the transfer matrix method of Pendry, which gives the eigenvalues in the form of exp[ikd]. The present method leads to a good improvement in the calculation of reflectivity spectrum by eliminating unphysical part due to insufficient precision of numerical results, showing the cross-section dependence of a surface of given Miller index more precisely.

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The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately 6⁄|η_r|, where η_r is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime τ_r=4.3 ms and of the enhancement factor M=7.8×10⁷ is found at the resonant frequency ω_r=367 GHz for the Cantor set of the fourth generation of length L=10 cm made of a medium of the dielectric constant ε=10.

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We analyzed isotope effects on the geometrical and electronic relaxations of hydrogen/deuterium-absorbing Pt_nH(D)⁻ (n=1–4, 6) clusters using the first principles multi-component molecular orbital (MC_MO) method, which can take into account the quantum effect of the proton/deuteron. The average of Pt–Pt bond distances of the Pt_nH⁻ clusters was calculated to be no more than 0.004 Å longer than the bond distances of corresponding Pt_nD⁻ clusters. Calculations on Pt_nH(D)₂ (n=2–4, 6) clusters clearly demonstrated that significant geometrical differences between Pt–Pt bond distances caused by the isotope effect depend on the number of hydrogen/deuterium atoms. Slight relaxation of the electronic charge densities was observed by the replacement from H to D. The exponent values indicate that the distribution of the wavefunction of proton and deuteron reflected the geometrical changes and electronic charge densities around the proton and deuteron.

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The highly sensitive method to search for WIMPs dark matter particles is proposed. An array of thin NaI(Tl) plate has the great selectivity for distinguishing the WIMPs events and background ones. The principle of signal selection for WIMPs is described. The high sensitivity for SD (spin-dependent) type WIMPs is expected by applying multi-layer system of NaI(Tl) detector.

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