9,191 research outputs found
Localized induction equation and pseudospherical surfaces
We describe a close connection between the localized induction equation
hierarchy of integrable evolution equations on space curves, and surfaces of
constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A:
Mathematical and Genera
Theory for Superconducting Properties of the Cuprates: Doping Dependence of the Electronic Excitations and Shadow States
The superconducting phase of the 2D one-band Hubbard model is studied within
the FLEX approximation and by using an Eliashberg theory. We investigate the
doping dependence of , of the gap function and
of the effective pairing interaction. Thus we find that becomes maximal
for doping. In {\it overdoped} systems decreases due to the
weakening of the antiferromagnetic correlations, while in the {\it underdoped}
systems due to the decreasing quasi particle lifetimes. Furthermore, we find
{\it shadow states} below which affect the electronic excitation spectrum
and lead to fine structure in photoemission experiments.Comment: 10 pages (REVTeX) with 5 figures (Postscript
Evolution of Rotating Accreting White Dwarfs and the Diversity of Type Ia Supernovae
Type Ia supernovae (SNe Ia) have relatively uniform light curves and spectral
evolution, which make SNe Ia useful standard candles to determine cosmological
parameters. However, the peak brightness is not completely uniform, and the
origin of the diversity has not been clear. We examine whether the rotation of
progenitor white dwarfs (WDs) can be the important source of the diversity of
the brightness of SNe Ia. We calculate the structure of rotating WDs with an
axisymmetric hydrostatic code. The diversity of the mass induced by the
rotation is ~0.08 Msun and is not enough to explain the diversity of
luminosity. However, we found the following relation between the initial mass
of the WDs and their final state; i.e., a WD of smaller initial mass will
rotate more rapidly before the supernova explosion than that of larger initial
mass. This result might explain the dependence of SNe Ia on their host
galaxies.Comment: 7 pages, 6 figure
Microstructural Shear Localization in Plastic Deformation of Amorphous Solids
The shear-transformation-zone (STZ) theory of plastic deformation predicts
that sufficiently soft, non-crystalline solids are linearly unstable against
forming periodic arrays of microstructural shear bands. A limited nonlinear
analysis indicates that this instability may be the mechanism responsible for
strain softening in both constant-stress and constant-strain-rate experiments.
The analysis presented here pertains only to one-dimensional banding patterns
in two-dimensional systems, and only to very low temperatures. It uses the
rudimentary form of the STZ theory in which there is only a single kind of zone
rather than a distribution of them with a range of transformation rates.
Nevertheless, the results are in qualitative agreement with essential features
of the available experimental data. The nonlinear theory also implies that
harder materials, which do not undergo a microstructural instability, may form
isolated shear bands in weak regions or, perhaps, at points of concentrated
stress.Comment: 32 pages, 6 figure
A high-reflectivity high-Q micromechanical Bragg-mirror
We report on the fabrication and characterization of a micromechanical
oscillator consisting only of a free-standing dielectric Bragg mirror with high
optical reflectivity and high mechanical quality. The fabrication technique is
a hybrid approach involving laser ablation and dry etching. The mirror has a
reflectivity of 99.6%, a mass of 400ng, and a mechanical quality factor Q of
approximately 10^4. Using this micromirror in a Fabry Perot cavity, a finesse
of 500 has been achieved. This is an important step towards designing tunable
high-Q high-finesse cavities on chip.Comment: 3 pages, 2 figure
Scattering theory for Klein-Gordon equations with non-positive energy
We study the scattering theory for charged Klein-Gordon equations:
\{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x,
D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)=
f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq
n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x),
describing a Klein-Gordon field minimally coupled to an external
electromagnetic field described by the electric potential and magnetic
potential . The flow of the Klein-Gordon equation preserves the
energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+
\bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x)
\d x. We consider the situation when the energy is not positive. In this
case the flow cannot be written as a unitary group on a Hilbert space, and the
Klein-Gordon equation may have complex eigenfrequencies. Using the theory of
definitizable operators on Krein spaces and time-dependent methods, we prove
the existence and completeness of wave operators, both in the short- and
long-range cases. The range of the wave operators are characterized in terms of
the spectral theory of the generator, as in the usual Hilbert space case
Self-cooling of a micro-mirror by radiation pressure
We demonstrate passive feedback cooling of a mechanical resonator based on
radiation pressure forces and assisted by photothermal forces in a high-finesse
optical cavity. The resonator is a free-standing high-reflectance micro-mirror
(of mass m=400ng and mechanical quality factor Q=10^4) that is used as
back-mirror in a detuned Fabry-Perot cavity of optical finesse F=500. We
observe an increased damping in the dynamics of the mechanical oscillator by a
factor of 30 and a corresponding cooling of the oscillator modes below 10 K
starting from room temperature. This effect is an important ingredient for
recently proposed schemes to prepare quantum entanglement of macroscopic
mechanical oscillators.Comment: 11 pages, 9 figures, minor correction
Theory of Quasi-Universal Ratio of Seebeck Coefficient to Specific Heat in Zero-Temperature Limit in Correlated Metals
It is shown that the quasi-universal ratio of
the Seebeck coefficient to the specific heat in the limit of T=0 observed in a
series of strongly correlated metals can be understood on the basis of the
Fermi liquid theory description. In deriving this result, it is crucial that a
relevant scattering arises from impurities, but not from the mutual scattering
of quasiparticles. The systematics of the sign of is shown to reflect the
sign of the logarithmic derivative of the density of states and the inverse
mass tensor of the quasiparticles, explaining the systematics of experiments.
In particular, the positive sign of for Ce-based and -based heavy
fermions, and the negative sign for Yb-based and -based heavy fermions,
are explained. The case of non-Fermi liquid near the quantum critical point
(QCP) is briefly mentioned, showing that the ratio decreases considerably
toward antiferromagnetic QCP while it remains essentially unchanged for the
ferromagnetic QCP or QCP due to a local criticality.Comment: 12 pages, 1 figur
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