3,310 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
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.
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.
Pressure-induced phase transitions of halogen-bridged binuclear metal complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O
Recent contrasting observations for halogen (X)-bridged binuclear platinum
complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O, that is, pressure-induced Peierls and
reverse Peierls instabilities, are explained by finite-temperature Hartree-Fock
calculations. It is demonstrated that increasing pressure transforms the
initial charge-polarization state into a charge-density-wave state at high
temperatures, whereas the charge-density-wave state oppositely declines with
increasing pressure at low temperatures. We further predict that
higher-pressure experiments should reveal successive phase transitions around
room temperature.Comment: 5 pages, 4 figures embedded, to be published in Phys. Rev. B 64,
September 1 (2001) Rapid Commu
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
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
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
Gravitational Instability in Radiation Pressure Dominated Backgrounds
I consider the physics of gravitational instabilities in the presence of
dynamically important radiation pressure and gray radiative diffusion, governed
by a constant opacity, kappa. For any non-zero radiation diffusion rate on an
optically-thick scale, the medium is unstable unless the classical gas-only
isothermal Jeans criterion is satisfied. When diffusion is "slow," although the
dynamical Jeans instability is stabilized by radiation pressure on scales
smaller than the adiabatic Jeans length, on these same spatial scales the
medium is unstable to a diffusive mode. In this regime, neglecting gas
pressure, the characteristic timescale for growth is independent of spatial
scale and given by (3 kappa c_s^2)/(4 pi G c), where c_s is the adiabatic sound
speed. This timescale is that required for a fluid parcel to radiate away its
thermal energy content at the Eddington limit, the Kelvin-Helmholz timescale
for a radiation pressure supported self-gravitating object. In the limit of
"rapid" diffusion, radiation does nothing to suppress the Jeans instability and
the medium is dynamically unstable unless the gas-only Jeans criterion is
satisfied. I connect with treatments of Silk damping in the early universe. I
discuss several applications, including photons diffusing in regions of extreme
star formation (starburst galaxies & pc-scale AGN disks), and the diffusion of
cosmic rays in normal galaxies and galaxy clusters. The former (particularly,
starbursts) are "rapidly" diffusing and thus cannot be supported against
dynamical instability in the linear regime by radiation pressure alone. The
latter are more nearly "slowly" diffusing. I speculate that the turbulence in
starbursts may be driven by the dynamical coupling between the radiation field
and the self-gravitating gas, perhaps mediated by magnetic fields. (Abridged)Comment: 15 pages; accepted to Ap
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