坂本 昇一

This study analyzed the scar-like localization in the time-average of a time-evolving wavepacket on a desymmetrized stadium billiard. When a wavepacket is launched along the orbits, it emerges on classical unstable periodic orbits as a scar in stationary states. This localization along the periodic orbit is clarified through the semiclassical approximation. It essentially originates from the same mechanism of a scar in stationary states: piling up of the contribution from the classical actions of multiply repeated passes on a primitive periodic orbit. To achieve this, several states are required in the energy range determined by the initial wavepacket.

We present the first principle calculations of the electrical properties of graphene sheet/h-BN heterojunction (GS/h-BN) and 11 -armchair graphene nanoribbon/h-BN heterojunction (11 -AGNR/h-BN), which are carried out using the density functional theory (DFT) method and the non-equilibrium Green's function (NFGF) technique. Since 11 -AGNR belongs to the conductive (3n-l )-family of AGNR, both are metallic nanomaterials with two transverse arrays of li-BN, which is a wide-gap semi-conductor. The two h-BN arrays act as double barriers. The transmission functions (TF) and I-V characteristics of GS/h-BN and 11 -AGNR/h-BN are calculated by DFT and NFGF, and they show that quantum double barrier tunneling occurs. The TF becomes very spiky in both materials, and it leads to step-wise I-V characteristics rather than negative resistance, which is the typical behavior of double barriers in semiconductors. The results of our first principle calculations are also compared with ID Dirac equation model for the double barrier system. The model explains most of the peaks of the transmission functions nearby the Fermi energy quite well. They are due to quantum tunneling.

<p>グラフェンはシリコンに代わる次世代デバイスの材料として期待されている。本研究では、グラフェンを2次元電子デバイスに応用するために、グラフェン/h-BNヘテロ接合における電子特性を密度汎関数法および非平衡グリーン関数法に基づいて解析する。特にジグザグ型グラフェンナノリボンへの接合では、エッジ状態への影響や自発的スピン分極の発現の有無に注目し、h-BNがグラフェンに及ぼす効果を検証する。</p>

The scar-like enhancement is found in the accumulation of the time-evolving wavepacket in stadium billiard. It appears close to unstable periodic orbits, when the wavepackets are launched along the orbits. The enhancement is essentially due to the same mechanism of the well-known scar states in stationary eigenstates. The weighted spectral function reveals that the enhancement is the pileup of contributions from scar states on the same periodic orbit. The availavility of the weighted spectrum to the semiclassical approximation is also disscussed.

By using the ab initio density functional theory method and the non-equilibrium Green's function approach, electronic transfer properties in armchair shaped edges graphene nanoribbons (AGNRs) doped with one substitutional boron or nitrogen impurity are numerically investigated. We find that the quantization of transmission function is moderated after doping impurity on AGNRs due to a geometrical distortion by dopant atom. Also the current through AGNRs under bias voltage can be evaluated from transmission function. We finally demonstrate I-V characteristics of doped AGNRs, from which the mobility is estimated. Our results show that doped AGNR semiconductors have higher mobility than the intrinsic one.

We have numerically investigated electronic transport properties in single-walled carbon nanotubes (SWCNTs) doped with boron (B) and nitrogen (N) substitutional impurities. Our calculations are performed by the ab initio density functional theory (DFT) and the nonequilibrium Green's function (NEGF) approach. We show that the electronic transmissions are moderated after the doping on both metallic and semiconducting CNTs. In B and N codoping nanotubes, depending on the arrangements of B and N substitutions, electronic and transport properties have been also modified. Calculating from electronic transmissions under bias, I-V characteristics of doped CNTs are demonstrated. In our simulations, we find that the substituting impurities in the semiconducting CNT raise the conductivity regardless of p-or n-type doping, whereas the conductivity of metallic CNTs is reduced by doping.

Electronic transport properties in armchair shaped edges graphene nanoribbons (AGNRs) doped various impurities have been simulated by the non-equilibrium Green's function approach combined with the first principle calculation based on the density functional theory. We have observed that impurity levels appear in electronic structures, and that the quantization of transmission function is moderated for doped AGNRs. The I-V characteristic can be computed from the transmission function. Our simulation results show that AGNRs doped impurities have higher conductance than the non-doped one.

In this paper we present a new approach to electron transports in nano-scale devices by using Nelson s quantum stochastic mechanical simulations Transferring electrons in pure and doped graphene ribbons (GRs) are numerically investigated as quantum Brownian motions with wavefunctions of isolated GRs The time evolution of the quantum stochastic process is given by Ito type stochastic differential equation From the analysis of the electron motion we directly obtain the electron mobilities in GRs under some electric fields We show the electron motion depends on the stochastic distribution of the eigenfunction or the molecular orbital and then the electron mobility is affected by the dopant atom (C) 2010 Elsevier BV All rights reserved

It is found that the decay rate of the quantum fidelity is suppressed when the periodic orbit scars in the accumulation of the time-evolving wavefunction become obvious in two-dimensional (2D) nanostructure The fidelity is numerically evaluated by the time-evolution of the wavepacket inside a 2D chaotic nanostructure the stadium which is the typical chaotic system The suppression is apparent in the Lyapunov regime where the decay rate does not depend on the strength of the perturbation (C) 2010 Elsevier BV All rights reserved

Recently, a brand-new phenomenon induced by microwave radiation was observed in AB ring systems. That is, a significantly wide dip appears in the magnetoresistance of AB ring structures in a weak magnetic field range. Its position (strength of a magnetic field) does not depend on the frequency of microwave. It is clearly considered that excitation of conducting electrons by microwave caused these phenomena. In the present study, we attempt to understand these features by means of a simple model. Here, numerical computation was performed as one-body problem by means of tight-binding model including electron-photon interaction. In addition to the above two experimental features, our model reproduced even the experimental fact that the excitation does not happen, namely, the dip does not appear, when the frequency of the microwave is too high. (C) 2010 Elsevier B.V. All rights reserved.

The time-evolution of the wavepacket inside chaotic and integrable two-dimensional (2D) nanostructures is numerically studied. We have found the enhancement around the classical periodic orbits during the time-evolution in the stadium billiard. It is similar to the scars in the standing wave of the chaotic billiards. The initial position and velocity, and the shape of the wavepacket are crucial for the enhancement, but we can observe that the remnant of the initial wavepacket travels along the unstable periodic orbit. Then the wavepacket gradually diffuses around the structure. This behavior has close relation to the dynamical properties of electrons in the structure, e.g., the conductivity, the magneto-resistance etc. The quantum fidelity, which can measure the robustness of dynamical states inside the nanostructures, is also discussed. © 2009 The Surface Science Society of Japan.

In this work, we numerically study electron transfer in two-dimensional quantum rings (QRs) by using a wavefunctional nodal pattern analysis. Recent progress in experimental techniques for nanostructures has enabled precise control of the electron number in a two-dimensional system such as a single-electron transistor. One interest in electron transport in nano-devices is to determine the characteristics of a resistance in an external magnetic field. In a microwave (MW) environment, especially, the resistance has unique behaviors under a weak magnetic field. From a nodal pattern analysis, we found that not all states could contribute to the electron transfer. We also found the wavefunctions that stick to the inner wall of the QR under a weak magnetic field, which implies that the transfer depends on the relation between the ring size of the inner hole and the cyclotron radius of an electron motion. Consequently, the resistance is affected by the MW drive and a possibility exists to excite the electron to higher eigenstates.

The time-evolution of the wave packet inside chaotic and integrable two-dimensional nanostructures is numerically studied. Recently the time-evolution of quantum states is seriously considered to treat the dynamical property of nanostructures. By computer simulation, we have found the enhancement around the classical periodic orbits, which has been theoretically predicted. It is similar to the scars in the standing wave of the chaotic billiards and is also beyond the naive prediction of the random nodal patterns from the chaotic nanostructure. The initial position and velocity and the shape of the wave packet are crucial for the enhancement, however, we can observe that the remnant of the initial wave packet travels along the unstable periodic orbit. Then the wave packet gradually diffuses around the structure. This behavior has close relation to the dynamical properties of electrons in the structure, e.g., the conductivity, the magneto-resistance etc. Copyright (C) 2008 John Wiley & Sons, Ltd.

Quantum dynamical properties of electron transfers through multiple quantum dots (QDs) are numerically investigated. The QDs are modeled as two-dimensional electron systems and the conductive properties are calculated from the time evolution of the electron wavefunctions. In addition, we propose a new technique dealing with the electron-electron correlation and demonstrate the dynamical simulations of the Coulomb blockade as well as the spin blockade. (C) 2008 Elsevier B.V. All rights reserved.

By using quantum dynamics, we investigate an electron transport in a two-dimensional (2D) quantum structure under applied external fields. The structure is defined as a double tunnel junction which consists of ferromagnetic regions and insulator regions. The one-electron wave function computed by numerical diagonalization determines the time evolution of the electron diffusion in the nanodevice. From the dynamical analysis of the electron motion, we find there exist some particular eigenstates in which the electron diffusion velocity has larger value under the weak magnetic field.

We numerically investigate electron transfers in nanowires which consist of deoxyribonucleic acid (DNA) molecules (up to five base pairs for double-strands and seven bases for single-strands) by quantum dynamical calculations. DNA molecules are applied to organic nanodevices and the performance depends on electronic transfer properties. Combining quantum chemical molecular-orbital calculations and stochastic mechanics, we provide an analyzing method of quantum dynamical electron motions. From one-electron wavefunctions or molecular orbitals, we calculate some dynamical properties, such as mean-square displacement and self-diffusion coefficients relating with electron mobility. Our calculation suggests that the electron transfers through the double-strands of GC base pairs while the electrons are localized in the double-strands of AT base pairs nor the single-strands of G bases.

A system of two quartic oscillators coupled by a quartic perturbation is numerically studied for quantum mechanical eigenvalues and classical periodic orbits. The coupling strength serves as a control parameter to simulate the transition from integrable to chaotic regimes. In order to obtain higher-energy eigenvalues of a huge dimensional matrix, the Lanczos method and the equi-energy method are investigated for a practical use. (c) 2005 Elsevier B.V. All rights reserved.

We numerically study quantum mechanics of one-dimensional (1D) time-independent system whose energy level statistics obeys the Gaussian orthogonal ensemble. 1D conservative systems are known to be integrable. However, at least numerically, it is also shown that we can construct the potential for the Schrodinger equation that reproduces a finite number of given energy levels of chaotic regime, e.g., the random matrix theory. In this work a potential is constructed numerically by the standard gradient method. The more energy levels of chaotic regime we take, the more complicated and finer the ripples of the potential become. Then the potential has fractal structure at high energy limit and its fractal dimension is determined to be d = 1.7.

By using stochastic mechanical simulations, we numerically investigate electron transfers in oligoacenes (anthracene, tetracene and pentacene). These pi-conjugated oligomers are applied to organic devices and the performance depends on the electronic transfer properties. From quantum mechanical or quantum chemical calculations, estimation of the transport properties have been so far discussed via transfer integrals. Stochastic mechanics provide the quantum motion of electrons from the wave functions. From the analysis of the quantum motion of electrons, we calculate some dynamical properties, such as mean-square displacement relating with the mobility and the electron transfer rate between two anthracenes. Our dynamical approach is efficient and practical and especially important for analysis of molecular or nanoscale devices. (C) 2004 Elsevier B.V. All rights reserved.

Quantum mechanics of one-dimensional time-independent system whose energy level statistics obeys the Gaussian ensemble is numerically studied. Recently the nano-size quantum dots and anti-dots made by the highly sophisticated fabrication process on the heterojunction structure of semiconductors often exhibit the anomalous physical behaviors. In order to understand them the study of the lower dimensional quantum electron transport from the viewpoint of quantum chaos is inevitably important. One-dimensional conserved systems are known to be integrable. However, at least numerically, it is also shown that we can construct the potential for the Schrödinger equation that reproduces a finite number of given energy levels of chaotic regime, e.g., the random matrix theory. In this work a potential is constructed numerically by the standard gradient method or by the inverse scattering method. The more energy levels of chaotic regime we take, the more complicated and finer the ripples of the potential become The potential has fractal structure at high energy limit. [DOI: 10.1380/ejssnt.2003.175]

I-V characteristics of high T-c superconductors, such as Bi2Sr2CaCu2O8, are well described by use of the multi-Josephson junction model. I-V characteristics are investigated, including both capacitive and inductive effects. It is shown that both effects are equally important to get systematic changes of I-V characteristics from short junctions to long ones, and their dependence on the applied magnetic field. (C) 2003 Elsevier Science B.V. All rights reserved.

We numerically investigate Bose-Einstein condensation (BEC) of finite number atoms in a mean field approximation. For the Bose gas interacting with a weak repulsive potential and trapped in an external parabolic potential, BEC occurs at finite temperature in one- and three-dimensional systems. Comparing free energies between the BEC state and the normal state, we define the transition temperature. The relation between the transition temperature and the repulsive coupling constant shows a simple power law for 1D and 3D systems. (C) 2003 Elsevier Science B.V. All rights reserved.

The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose-Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a hose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T, the total number of bosons N and the interaction V is also provided as a simple power law, T-c proportional to ((NV)-V-2)(2/3).

In the Bose-Einstein condensation of a dilute alkaline atomic gas trapped in a magnetic potential, one has to deal with a strongly space- (and time-) dependent order parameter, which violates the phase symmetry. In this case, certain relations are required among propagators and vertices, known as Ward-Takahashi identities. In this paper, we show that a systematic self-consistent perturbation scheme can be developed even with a space-time order parameter in such a way as to satisfy the requirement of phase symmetry. The key procedure is that the information concerning the full order parameter, which is self-consistently determined, is included in the unperturbed Hamiltonian.

In Bose-Einstein condensation of dilute alkaline atomic gases, a magnetic trapped potential forces particle-excitation levels to have a discrete spectrum. This indicates that there must arise a discrete zero-mode associated with the phase symmetry to be consistent with the Goldstone theorem. It is shown that the zero-mode can be identified as a quantum phase coordinate and that its presence is required from the canonical relation of field operators. Thermal fluctuations of the quantum phase coordinate induce a T log (NeT)-T-3/5 term in the free energy and a k(B)TN(c)(-2/5) term in the particle number, where N-c is the number of condensed particles.

In recent experiments of Bose-Einstein condensation of a magnetically trapped dilute alkaline atomic gas, the nonequilibrium process of thermalization into the condensed state has been observed in a reasonably long time scale. This presents a new challenge to develop a theory to treat strongly space-time dependent nonequilibrium processes. In this paper, we present a nonequilibrium formulation of Bose-Einstein condensed states in the field theoretical framework of thermo-field dynamics. By use of an effective Hamiltonian method, a quasi-particle field equation is derived. This equation contains information regarding the renormalized energy, decay width and time-variation of particle distributions. It is shown that, in the present formulation, the strong space-time dependence call be treated, even including quantum corrections, as the use of the quasi-particle field equation enables us to factorize double-time functions of the self-energy.

By the use of multi-Josephson junction model, we investigate the voltage-biased I-V characteristics by numerical simulation. There appear three voltage regions where the current shows either (i) periodic behavior with trigonometric functional increase and rapid drop, or (ii) chaotic behavior or (iii) periodic behavior on hysteresis branches. (C) 2000 Elsevier Science B.V. All rights reserved.

We numerically analyze the multiple Josephson junction (MJJ) model of high T-C superconductors. MJJ applied a constant current has many hysteresis branches in I-V characteristics and generates oscillating voltage. We find that the hysteresis branches are originated from various modes of votating phase differences between superconducting layers, and that the frequency characteristics depend on rotational velocity of each phase. In MJJ applied an alternating current we also:show harmonizations of spontaneous and external oscillations. (C) 2000 Elsevier Science B.V. All rights reserved.

By use of the multiple Josephson junction model, we investigate voltage-biased I-V characteristics by numerical simulation. We show that there exist three characteristic regions in the I-V curve. In the low voltage region, the total current is periodic with trigonometric functional increases and rapid drops. Then a kind of chaotic region follows. Above a certain voltage, the total current behaves with a simple harmonic oscillation and the I-V characteristics form a multiple branch structure as in the current-biased case.

We numerically investigated frequency characteristics of the multiple Josephson junctions (MJJ) model. MJJ with a constant current generates oscillating voltage. We find that the frequency characteristics depend on various patterns of rotating phase differences between superconducting layers. In MJJ with an alternating current; we show harmonization of spontaneous and external oscillations. Our calculation also shows electromagnetic waves radiated from MJJ are coherent.

I-V characteristics of the high-T-c, superconductor Bi2Sr2Ca1C2O8 shows a strong hysteresis, producing many branches. The origin of hysteresis jumps is studied by use of the model of multilayered Josephson junctions proposed by one of the authors (T.K.). The charging effect at superconducting layers produces a coupling between the next-nearest-neighbor phase differences, which determines the structure of hysteresis branches. It will be shown that a solution of phase motions is understood as a combination of rotating and oscillating phase differences, and that, at points of hysteresis jumps, there occurs a change in the number of rotating phase differences. Effects of dissipation are analyzed. The dissipation in insulating layers works to damp the phase motion itself, while the dissipation in superconducting layers works to damp relative motions of phase differences. Their effects to hysteresis jumps are discussed. [S0163-1829(99)04529-4].

In order to investigate segregation of granular binary-mixtures in a horizontally rotating cylinder, three-dimensional molecular dynamics simulations are carried out. Two kinds of particles, which have different diameters and/or different roughness of surfaces, are segregated into three bands. It is found that particles receive averaged force cohesively at the boundaries of segregated bands. The present analysis shows that segregated narrow bands are formed by diffusion process and that the cohesive forces operating at the boundaries stabilize them.