3,513 research outputs found
An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian
We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic
field in the n-dimensional torus. We obtained a complete set of solutions for a
broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a
quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice
{\Lambda}. The lattice is not necessary either cubic or rectangular. The
magnetic field is also arbitrary. However, we restrict ourselves within
potential-free problems; the Schr{\"o}dinger operator is assumed to be the
Laplace operator defined with the covariant derivative. We defined an algebra
that characterizes the symmetry of the Laplacian and named it the magnetic
algebra. We proved that the space of functions on which the Laplacian acts is
an irreducible representation space of the magnetic algebra. In this sense the
magnetic algebra completely characterizes the quantum mechanics in the magnetic
torus. We developed a new method for Fourier analysis for the magnetic torus
and used it to solve the eigenvalue problem of the Laplacian. All the
eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad
Nonlinear polarization evolution using time-dependent density functional theory
We propose a theoretical and computational approach to investigate temporal
behavior of a nonlinear polarization in perturbative regime induced by an
intense and ultrashort pulsed electric field. First-principles time-dependent
density functional theory is employed to describe the electron dynamics.
Temporal evolution of third-order nonlinear polarization is extracted from a
few calculations of electron dynamics induced by pulsed electric fields with
the same time profile but different amplitudes. We discuss characteristic
features of the nonlinear polarization evolution as well as an extraction of
nonlinear susceptibilities and time delays by fitting the polarization. We also
carry out a decomposition of temporal and spatial changes of the electron
density in power series with respect to the field amplitude. It helps to get
insight into the origin of the nonlinear polarization in atomic scale.Comment: 11 pages, 9 figure
Dynamics of an Acoustic Polaron in One-Dimensional Electron-Lattice System
The dynamical behavior of an acoustic polaron in typical non-degenerate
conjugated polymer, polydiacetylene, is numerically studied by using
Su-Schrieffer-Heeger's model for the one dimensional electron-lattice system.
It is confirmed that the velocity of a polaron accelerated by a constant
electric field shows a saturation to a velocity close to the sound velocity of
the system, and that the width of a moving polaron decreases as a monotonic
function of the velocity tending to zero at the saturation velocity. The
effective mass of a polaron is estimated to be about one hundred times as heavy
as the bare electron mass. Furthermore the linear mode analysis in the presence
of a polaron is carried out, leading to the conclusion that there is only one
localized mode, i.e. the translational mode. This is confirmed also from the
phase shift of extended modes. There is no localized mode corresponding to the
amplitude mode in the case of the soliton in polyacetylene. Nevertheless the
width of a moving polaron shows small oscillations in time. This is found to be
related to the lowest odd symmetry extended mode and to be due to the finite
size effect.Comment: 12 pages, latex, 9 figures (postscript figures abailble on request to
[email protected]) to be published in J. Phys. Soc. Jpn. vol.65
(1996) No.
Semi-Phenomenological Analysis of Dynamics of Nonlinear Excitations in One-Dimensional Electron-Phonon System
The structure of moving nonlinear excitations in one-dimensional
electron-phonon systems is studied semi-phenomenologically by using an
effective action in which the width of the nonlinear excitation is treated as a
dynamical variable. The effective action can be derived from Su, Schrieffer and
Heeger's model or its continuum version proposed by Takayama, Lin-Liu and Maki
with an assumption that the nonlinear excitation moves uniformly without any
deformation except the change of its width. The form of the action is
essentially the same as that discussed by Bishop and coworkers in studying the
dynamics of the soliton in polyacetylene, though some details are different.
For the moving excitation with a velocity , the width is determined by
minimizing the effective action. A requirement that there must be a minimum in
the action as a function of its width provides a maximum velocity. The velocity
dependence of the width and energy can be determined. The motions of a soliton
in p olyacetylene and an acoustic polaron in polydiacetylene are studied within
this formulation. The obtained results are in good agreement with those of
numerical simulations.Comment: 19 pages, LaTeX, 7 Postscript figures, to be published in J. Phys.
Soc. Jpn. vol.65 (1996) No.
Extra-large crystal emulsion detectors for future large-scale experiments
Photographic emulsion is a particle tracking device which features the best
spatial resolution among particle detectors. For certain applications, for
example muon radiography, large-scale detectors are required. Therefore, a huge
surface has to be analyzed by means of automated optical microscopes. An
improvement of the readout speed is then a crucial point to make these
applications possible and the availability of a new type of photographic
emulsions featuring crystals of larger size is a way to pursue this program.
This would allow a lower magnification for the microscopes, a consequent larger
field of view resulting in a faster data analysis. In this framework, we
developed new kinds of emulsion detectors with a crystal size of 600-1000 nm,
namely 3-5 times larger than conventional ones, allowing a 25 times faster data
readout. The new photographic emulsions have shown a sufficient sensitivity and
a good signal to noise ratio. The proposed development opens the way to future
large-scale applications of the technology, e.g. 3D imaging of glacier bedrocks
or future neutrino experiments.Comment: Version accepted for publication in JINS
Photogeneration Dynamics of a Soliton Pair in Polyacetylene
Dynamical process of the formation of a soliton pair from a photogenerated
electron-hole pair in polyacetylene is studied numerically by adopting the SSH
Hamiltonian. A weak local disorder is introduced in order to trigger the
formation. Starting from an initial configuration with an electron at the
bottom of the conduction band and a hole at the top of the valence band,
separated by the Peierls gap, the time dependent Schrndinger
equation for the electron wave functions and the equation of motion for the
lattice displacements are solved numerically. After several uniform
oscillations of the lattice system at the early stage, a large distortion
corresponding to a pair of a soliton and an anti-soliton develops from a point
which is determined by the location and type of the disorder. In some cases,
two solitons run in opposite directions, leaving breather like oscillations
behind, and in other cases they form a bound state emitting acoustic lattice
vibrational modes.Comment: 16 pages 7 figure
Magnetic translation groups in an n-dimensional torus
A charged particle in a uniform magnetic field in a two-dimensional torus has
a discrete noncommutative translation symmetry instead of a continuous
commutative translation symmetry. We study topology and symmetry of a particle
in a magnetic field in a torus of arbitrary dimensions. The magnetic
translation group (MTG) is defined as a group of translations that leave the
gauge field invariant. We show that the MTG on an n-dimensional torus is
isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x
Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible
unitary representations of the MTG on a three-torus and apply the
representation theory to three examples. We shortly describe a representation
theory for a general n-torus. The MTG on an n-torus can be regarded as a
generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in
Journal of Mathematical Physic
Development of Nuclear Emulsion Detector for Muon Radiography
AbstractMuon radiography is the non-destructive testing technique of large-scale constructions with cosmic ray muon. Cosmic ray muon has high penetrating power and it always comes from the whole sky. In the same way of taking a X-ray photograph, we can obtain integrated density of constructions which thickness are several tens to several hundreds. We had ever applied this technique to nuclear reactors, volcanos, and so on. Nuclear emulsion is three dimensional track detector with micrometric position accuracy. Thanks to high position resolution, Nuclear emulsion has mrad angular resolution. In addition, the features which require no power supply and can observe in a large area suitable for muon radiography. In Nagoya University, we launched emulsion manufacturing equipment at 2010. It has become possible to flexible development of our detector and succeeded to development of high sensitive nuclear emulsion film (Nagoya emulsion). An important factor is the temperature characteristic to withstand the outdoor observation as a detector to be used in the muon radiography. There is a phenomenon of a latent image fading, whichit is well known in the photographic industry, and this phenomenon is known that temperature and water are involved. So we examined temperature and humidity characteristic of latent image fading about Nagoya emulsion. As a result, we found latent image fading is strongly depends on both temperature and humidity. By dehydrating emulsion film in RH8%, over 95% (Grain Density>40) detection efficiency of muon track keeps over 3months in 25degree, for 2months in 35degree. Additionally it was showed in this test that increasing back ground noise “fog”, which may have occurred by sealing emulsion film in a narrow space, is reduced by buffer space in the bag
The anomalous behavior of coefficient of normal restitution in the oblique impact
The coefficient of normal restitution in an oblique impact is theoretically
studied. Using a two-dimensional lattice models for an elastic disk and an
elastic wall, we demonstrate that the coefficient of normal restitution can
exceed one and has a peak against the incident angle in our simulation.
Finally, we explain these phenomena based upon the phenomenological theory of
elasticity.Comment: 4 pages, 4 figures, to be appeared in PR
Paramagnetic GaN:Fe and ferromagnetic (Ga,Fe)N - relation between structural, electronic, and magnetic properties
We report on the metalorganic chemical vapor deposition (MOCVD) of GaN:Fe and
(Ga,Fe)N layers on c-sapphire substrates and their thorough characterization
via high-resolution x-ray diffraction (HRXRD), transmission electron microscopy
(TEM), spatially-resolved energy dispersive X-ray spectroscopy (EDS),
secondary-ion mass spectroscopy (SIMS), photoluminescence (PL), Hall-effect,
electron-paramagnetic resonance (EPR), and magnetometry employing a
superconducting quantum interference device (SQUID). A combination of TEM and
EDS reveals the presence of coherent nanocrystals presumably FexN with the
composition and lattice parameter imposed by the host. From both TEM and SIMS
studies, it is stated that the density of nanocrystals and, thus the Fe
concentration increases towards the surface. In layers with iron content x<0.4%
the presence of ferromagnetic signatures, such as magnetization hysteresis and
spontaneous magnetization, have been detected. We link the presence of
ferromagnetic signatures to the formation of Fe-rich nanocrystals, as evidenced
by TEM and EDS studies. This interpretation is supported by magnetization
measurements after cooling in- and without an external magnetic field, pointing
to superparamagnetic properties of the system. It is argued that the high
temperature ferromagnetic response due to spinodal decomposition into regions
with small and large concentration of the magnetic component is a generic
property of diluted magnetic semiconductors and diluted magnetic oxides showing
high apparent Curie temperature.Comment: 21 pages, 30 figures, submitted to Phys. Rev.
- …