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2007-01-12
|
Electron spin quantum beats in positively charged quantum dots: nuclear field effects
|
We have studied the electron spin coherence in an ensemble of positively
charged InAs/GaAs quantum dots. In a transverse magnetic field, we show that
two main contributions must be taken into account to explain the damping of the
circular polarization oscillations. The first one is due to the nuclear field
fluctuations from dot to dot experienced by the electron spin. The second one
is due to the dispersion of the transverse electron Lande g-factor, due to the
inherent inhomogeneity of the system, and leads to a field dependent
contribution to the damping. We have developed a model taking into account both
contributions, which is in good agreement with the experimental data. This
enables us to extract the pure contribution to dephasing due to the nuclei.
|
0701284v2
|
2007-02-05
|
Verification of stable operation of rapid single flux quantum devices with selective dissipation
|
It has been suggested that Rapid Single Flux Quantum (RSFQ) devices could be
used as the classical interface of superconducting qubit systems. One problem
is that the interface acts as a dissipative environment for a qubit. Recently
ways to modify the RSFQ damping to reduce the dissipation have been introduced.
One of the solutions is to damp the Josephson junctions by a
frequency-dependent linear circuit instead of the plain resistor. The approach
has previously been experimentally tested with a simple SFQ comparator. In this
paper we perform experiments with a full RSFQ circuit, and thus conclude that
in terms of stable operation the approach is applicable for scalable RSFQ
circuits. Realisation and optimisation issues are also discussed.
|
0702104v1
|
2007-02-21
|
RPAE versus RPA for the Tomonaga model with quadratic energy dispersion
|
Recently the damping of the collective charge (and spin) modes of interacting
fermions in one spatial dimension was studied. It results from the nonlinear
correction to the energy dispersion in the vicinity of the Fermi points. To
investigate the damping one has to replace the random phase approximation (RPA)
bare bubble by a sum of more complicated diagrams. It is shown here that a
better starting point than the bare RPA is to use the (conserving) linearized
time dependent Hartree-Fock equations, i.e. to perform a random phase
approximation (with) exchange
(RPAE) calculation. It is shown that the RPAE equation can be solved
analytically for the special form of the two-body interaction often used in the
Luttinger liquid framework. While (bare) RPA and RPAE agree for the case of a
strictly linear disperson there are qualitative differences for the case of the
usual nonrelativistic quadratic dispersion.
|
0702488v2
|
2007-03-01
|
Spin dynamics across the superfluid-insulator transition of spinful bosons
|
Bosons with non-zero spin exhibit a rich variety of superfluid and insulating
phases. Most phases support coherent spin oscillations, which have been the
focus of numerous recent experiments. These spin oscillations are Rabi
oscillations between discrete levels deep in the insulator, while deep in the
superfluid they can be oscillations in the orientation of a spinful condensate.
We describe the evolution of spin oscillations across the superfluid-insulator
quantum phase transition. For transitions with an order parameter carrying
spin, the damping of such oscillations is determined by the scaling dimension
of the composite spin operator. For transitions with a spinless order parameter
and gapped spin excitations, we demonstrate that the damping is determined by
an associated quantum impurity problem of a localized spin excitation
interacting with the bulk critical modes. We present a renormalization group
analysis of the quantum impurity problem, and discuss the relationship of our
results to experiments on ultracold atoms in optical lattices.
|
0703011v2
|
2007-03-21
|
Edge magnetoplasmons in a partially screened two-dimensional electron gas on a helium surface
|
We report a study of edge magnetoplasmons in a partially-screened system of
electrons on a helium surface. We compare experimental results with theories of
the frequency, damping, and penetration-depth dependence on magnetic field,
temperature-dependent damping, and the dependence of the frequency on
screening. We show explicitly the dependence of frequency on the edge density
profile. The frequency and screening are in qualitative agreement with the
theory of Fetter at small fields, and the frequencies agree with theory in the
limit of zero magnetic field. The frequency and linewidths in intermediate and
large fields exhibit the features of the qualitative predictions of Volkov and
Mikhailov, but differ numerically. Deviations from theory for a finite sample
occur at smaller fields. The dependence of frequency on the density profile is
stronger than predicted by these authors, and the penetration-depth variation
with field confirms their prediction for small fields.
|
0703558v1
|
1997-02-12
|
On the problem of semiinfinite beam oscillation with internal damping
|
We study the Cauchy problem for the equation of the form $$ \ddot{u}(t) +
(\aa A + B)\dot{u}(t) + (A+G)u(t) = 0,\tag* $$ where $A$, $B$, and $G$ are \o s
in a Hilbert space $\Cal H$ with $A$ selfadjoint, $\sigma(A)=[0,\infty)$,
$B\ge0$ bounded, and $G$ symmetric and $A$-subordinate in a certain sense.
Spectral properties of the correspondent operator pencil
$L(\lambda) := \lambda^2I + \lambda (\alpha A + B) + A + G$ are studied, and
existence and uniqueness of generalized and classical solutions of the Cauchy
problem are proved. Equations of the type (*) include, e.g., an abstract model
for the problem of semiinfinite beam oscillations with internal damping.
|
9702007v1
|
1994-04-14
|
Decoherence, Correlation, and Unstable Quantum States in Semiclassical Cosmology
|
It is demonstrated that almost any S-matrix of quantum field theory in curved
spaces posses an infinite set of complex poles (or branch cuts). These poles
can be transformed into complex eigenvalues, the corresponding eigenvectors
being Gamow vectors. All this formalism, which is heuristic in ordinary Hilbert
space, becomes a rigorous one within the framework of a properly chosen rigged
Hilbert space. Then complex eigenvalues produce damping or growing factors. It
is known that the growth of entropy, decoherence, and the appearance of
correlations, occur in the universe evolution, but only under a restricted set
of initial conditions. It is proved that the damping factors allow to enlarge
this set up to almost any initial conditions.
|
9404028v1
|
1994-09-27
|
Effects of weak self-interactions in a relativistic plasma on cosmological perturbations
|
The exact solutions for linear cosmological perturbations which have been
obtained for collisionless relativistic matter within thermal field theory are
extended to a self-interacting case. The two-loop contributions of scalar
$\lambda\phi^4$ theory to the thermal graviton self-energy are evaluated, which
give the $O(\lambda)$ corrections in the perturbation equations. The changes
are found to be perturbative on scales comparable to or larger than the Hubble
horizon, but the determination of the large-time damping behavior of subhorizon
perturbations requires a resummation of thermally induced masses.
|
9409055v2
|
1995-03-07
|
ON THE OSCILLATION SPECTRA OF ULTRA COMPACT STARS
|
Quasinormal modes of ultra compact stars with uniform energy density have
been calculated. For less compact stars, there is only one very slowly damped
polar mode (corresponding to the Kelvin f-mode) for each spherical harmonic
index $l$. Further long-lived modes become possible for a sufficiently compact
star (roughly when $M/R \ge 1/3$). We compare the characteristic frequencies of
these resonant polar modes to the axial modes first found by Chandrasekhar and
Ferrari [{\em Proc. Roy. Soc. London A} {\bf 434} 449 (1991)]. We find that the
two spectra approach each other as the star is made more compact. The
oscillation frequencies of the corresponding polar and axial modes agree to
within a percent for stars more compact than $M/R = 0.42$. At the same time,
the damping times are slightly different. The results illustrate that there is
no real difference between the origin of these axial and polar modes: They are
essentially spacetime modes.
|
9503012v1
|
1998-02-13
|
Radiation Damping in FRW Space-times with Different Topologies
|
We study the role played by the compactness and the degree of connectedness
in the time evolution of the energy of a radiating system in the
Friedmann-Robertson-Walker (FRW) space-times whose $t=const $ spacelike
sections are the Euclidean 3-manifold ${\cal R}^3$ and six topologically
non-equivalent flat orientable compact multiply connected Riemannian
3-manifolds. An exponential damping of the energy $E(t)$ is present in the
${\cal R}^3$ case, whereas for the six compact flat 3-spaces it is found
basically the same pattern for the evolution of the energy, namely relative
minima and maxima occurring at different times (depending on the degree of
connectedness) followed by a growth of $E(t)$. Likely reasons for this
divergent behavior of $E(t)$ in these compact flat 3-manifolds are discussed
and further developments are indicated. A misinterpretation of Wolf's results
regarding one of the six orientable compact flat 3-manifolds is also indicated
and rectified.
|
9802031v1
|
1998-05-06
|
Damping of Gravitational Waves and Density Perturbations in the Early Universe
|
Since the discovery of the large angular scale anisotropies in the microwave
background radiation, the behaviour of cosmological perturbations (especially,
density perturbations and gravitational waves) has been of great interest. In
this study, after a detailed and rigorous treatment of the behaviour of
gravitational waves in viscous cosmic media, we conclude that the damping of
cosmological gravitational waves of long wavelengths is negligible for most
cases of physical interest. A preliminary analysis suggests that similar
results hold for density perturbations in the long wavelength limit. Therefore,
long wavelength cosmological perturbations have not been practically affected
by viscous processes,and are good probes of the very early Universe.
|
9805016v1
|
1998-11-11
|
Late-Time Evolution of Realistic Rotating Collapse and The No-Hair Theorem
|
We study analytically the asymptotic late-time evolution of realistic
rotating collapse. This is done by considering the asymptotic late-time
solutions of Teukolsky's master equation, which governs the evolution of
gravitational, electromagnetic, neutrino and scalar perturbations fields on
Kerr spacetimes. In accordance with the no-hair conjecture for rotating
black-holes we show that the asymptotic solutions develop inverse power-law
tails at the asymptotic regions of timelike infinity, null infinity and along
the black-hole outer horizon (where the power-law behaviour is multiplied by an
oscillatory term caused by the dragging of reference frames). The damping
exponents characterizing the asymptotic solutions at timelike infinity and
along the black-hole outer horizon are independent of the spin parameter of the
fields. However, the damping exponents at future null infinity are spin
dependent. The late-time tails at all the three asymptotic regions are
spatially dependent on the spin parameter of the field. The rotational dragging
of reference frames, caused by the rotation of the black-hole (or star) leads
to an active coupling of different multipoles.
|
9811032v2
|
1999-09-22
|
Vorticity affects the stability of neutron stars
|
The spin rate \Omega of neutron stars at a given temperature T is constrained
by the interplay between gravitational-radiation instabilities and viscous
damping. Navier-Stokes theory has been used to calculate the viscous damping
timescales and produce a stability curve for r-modes in the (\Omega,T) plane.
In Navier-Stokes theory, viscosity is independent of vorticity, but kinetic
theory predicts a coupling of vorticity to the shear viscosity. We calculate
this coupling and show that it can in principle significantly modify the
stability diagram at lower temperatures. As a result, colder stars can remain
stable at higher spin rates.
|
9909073v2
|
2000-02-02
|
Active controls in interferometric detectors of gravitational waves: inertial damping of the VIRGO superattenuator
|
The operation of an interferometer for gravitational waves detection requires
sophisticated feedback controls in many parts of the apparatus. The aim of this
lecture is to introduce the types of problems to be faced in this line of
research. The attention is focused on the "inertial damping" of the test mass
suspension of the VIRGO interferometer (the superattenuator): it is a
multidimensional local control aimed to reduce the residual motion of the
suspended mirror associated to the normal modes of the suspension. Its
performance is very important for the locking of the interferometer.
|
0002006v2
|
2000-08-09
|
Gravitational Wave Damping of Neutron Star Wobble
|
We calculate the effect of gravitational wave (gw) back-reaction on realistic
neutron stars (NS's) undergoing torque-free precession. By `realistic' we mean
that the NS is treated as a mostly-fluid body with an elastic crust, as opposed
to a rigid body. We find that gw's damp NS wobble on a timescale tau_{theta}
approx 2 x 10^5 yr [10^{-7}/(DId/I_0)]^2 (kHz/ nu_s)^4, where nu_s is the spin
frequency and DId is the piece of the NS's inertia tensor that "follows" the
crust's principal axis (as opposed to its spin axis). We give two different
derivations of this result: one based solely on energy and angular momentum
balance, and another obtained by adding the Burke-Thorne radiation reaction
force to the Newtonian equations of motion. This problem was treated long ago
by Bertotti and Anile (1973), but their claimed result is wrong. When we
convert from their notation to ours, we find that their tau_{theta} is too
short by a factor of order 10^5 for typical cases of interest, and even has the
wrong sign for DId negative. We show where their calculation went astray.
|
0008021v1
|
2000-11-30
|
Tests of strong-field gravity and gravitational radiation damping in binary-pulsar systems
|
This talk reviews the constraints imposed by binary-pulsar data on gravity
theories, and notably on "scalar-tensor" theories which are the most natural
alternatives to general relativity. Because neutron stars have a strong
gravitational binding energy, binary-pulsar tests are qualitatively different
from solar-system experiments: They have the capability of probing models which
are indistinguishable from general relativity in weak gravitational field
conditions. Besides the two most precise binary-pulsar experiments, in the
systems B1913+16 and B1534+12, we also present the results of the various
"null" tests of general relativity provided by several neutron star-white dwarf
binaries, notably those of gravitational radiation damping. [The main interest
of this very short paper is its figure, which also takes into account the
"strong equivalence principle" tests.]
|
0011114v1
|
2001-07-17
|
Properties of r modes in rotating magnetic neutron stars. I. Kinematic Secular Effects and Magnetic Evolution Equations
|
The instability of r-mode oscillations in rapidly rotating neutron stars has
attracted attention as a potential mechanism for producing high frequency,
almost periodic gravitational waves. The analyses carried so far have shown the
existence of these modes and have considered damping by shear and bulk
viscosity. However, the magnetohydrodynamic coupling of the modes with a
stellar magnetic field and its role in the damping of the instability has not
been fully investigated yet. Following our introductory paper (Rezzolla, Lamb
and Shapiro 2000), we here discuss in more detail the existence of secular
higher-order kinematical effects which will produce toroidal fluid drifts. We
also define the sets of equations that account for the time evolution of the
magnetic fields produced by these secular velocity fields and show that the
magnetic fields produced can reach equipartition in less than a year. The full
numerical calculations as well as the evaluation of the impact of strong
magnetic fields on the onset and evolution of the r-mode instability will be
presented in a companion paper.
|
0107061v1
|
2004-01-13
|
Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation
|
We compute for the first time very highly damped quasinormal modes of the
(rotating) Kerr black hole. Our numerical technique is based on a decoupling of
the radial and angular equations, performed using a large-frequency expansion
for the angular separation constant_{s}A_{l m}. This allows us to go much
further in overtone number than ever before. We find that the real part of the
quasinormal frequencies approaches a non-zero constant value which does not
depend on the spin s of the perturbing field and on the angular index l:
\omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order
corrections to the asymptotic frequency are likely to be of order 1/\omega_I.
The imaginary part grows without bound, the spacing between consecutive modes
being a monotonic function of a.
|
0401052v1
|
2006-12-07
|
Improved calculation of relic gravitational waves
|
In this paper, we improve the calculation of the relic gravitational waves
(RGW) in two aspects: First, we investigate the transfer function after
considering the redshift-suppression effect, the accelerating expansion effect,
the damping effect of free-streaming relativistic particles, and the damping
effect of cosmic phase transition, and give a simple approximate analytic
expression, which clearly illustrates the dependent relations on the
cosmological parameters. Second, we develop a numerical method to calculate the
primordial power spectrum of RGW at a very wide frequency range, where the
observed constraints on $n_s$ (the scalar spectral index) and $P_S(k_0)$ (the
amplitude of primordial scalar spectrum) and the Hamilton-Jacobi equation are
used. This method is applied to two kinds of inflationary models, which all
satisfy the current constraints on $n_s$, $\alpha$ (the running of $n_s$) and
$r$ (the tensor-scalar ratio). We plot them in the $r-\Omega_g$ diagram, where
$\Omega_g$ is the strength of RGW, and study their detection by the CMB
experiments and laser interferometers.
|
0612041v3
|
2007-01-16
|
Influence of Lorentz violation on Dirac quasinormal modes in the Schwarzschild black hole spacetime
|
Using the third-order WKB approximation and monodromy methods, we investigate
the influence of Lorentz violating coefficient $b$ (associated with a special
axial-vector $b_{\mu}$ field) on Dirac quasinormal modes in the Schwarzschild
black hole spacetime. At fundamental overtone, the real part decreases linearly
as the parameter $b$ increases. But the variation of the imaginary part with
$b$ becomes more complex. For the larger multiple moment $k$, the magnitude of
imaginary part increases with the increase of $b$, which means that presence of
Lorentz violation makes Dirac field damps more rapidly. At high overtones, it
is found that the real part of high-damped quasinormal frequency does not tend
to zero, which is quite a different from the symptotic Dirac quasinormal modes
without Lorentz violation.
|
0701089v1
|
2007-03-29
|
Constraint Damping in First-Order Evolution Systems for Numerical Relativity
|
A new constraint suppressing formulation of the Einstein evolution equations
is presented, generalizing the five-parameter first-order system due to Kidder,
Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST
system first-order, are given modified evolution equations designed to drive
constraint violations toward zero. The algebraic structure of the new system is
investigated, showing that the modifications preserve the hyperbolicity of the
fundamental and constraint evolution equations. The evolution of the
constraints for pertubations of flat spacetime is completely analyzed, and all
finite-wavelength constraint modes are shown to decay exponentially when
certain adjustable parameters satisfy appropriate inequalities. Numerical
simulations of a single Schwarzschild black hole are presented, demonstrating
the effectiveness of the new constraint-damping modifications.
|
0703145v1
|
1992-06-21
|
Gauge Dependence of the Resummed Thermal Gluon Self Energy
|
The gauge dependence of the hot gluon self energy is examined in the context
of Pisarski's method for resumming hard thermal loops. Braaten and Pisarski
have used the Ward identities satisfied by the hard corrections to the n-point
functions to argue the gauge fixing independence of the leading order resummed
QCD plasma damping rate in covariant and strict Coulomb gauges. We extend their
analysis to include all linear gauges that preserve rotational invariance and
display explicitly the conditions required for gauge fixing independence. It is
shown that in covariant gauges the resummed damping constant is gauge fixing
independent only if an infrared regulator is explicitly maintained throughout
the calculation.
|
9206239v1
|
1993-05-07
|
Thermal quark production in pure glue and quark gluon plasmas
|
We calculate production rates for massless $(u,d)$ and massive $(s,c,b)$
quarks in pure glue and quark gluon plasmas to leading order in the strong
coupling constant $g$. The leading contribution comes from gluon decay into
$q\bar q$ pairs, using a thermal gluon propagator with finite thermal mass and
damping rate. The rate behaves as $\alpha_S^2(\ln 1/\alpha_S)^2 T^4$ when $m,
\alpha_S \rightarrow 0$ and depends linearly on the transverse gluon damping
rate for all values of the quark mass $m$. The light quark ($u$, $d$, $s$)
chemical equilibration time is approximately 10-100 $T^{-1}$ for $g=$2-3, so
that quarks are likely to remain far from chemical equilibrium in
ultrarelativistic nuclear collisions.
|
9305227v1
|
1994-01-21
|
Transport Properties of Quark and Gluon Plasmas
|
The kinetic properties of relativistic quark-gluon and electron-photon
plasmas are described in the weak coupling limit. The troublesome Rutherford
divergence at small scattering angles is screened by Debye screening for the
longitudinal or electric part of the interactions. The transverse or magnetic
part of the interactions is effectively screened by Landau damping of the
virtual photons and gluons transferred in the QED and QCD interactions
respectively. Including screening a number of transport coefficients for QCD
and QED plasmas can be calculated to leading order in the interaction strength,
including rates of momentum and thermal relaxation, electrical conductivity,
viscosities, flavor and spin diffusion of both high temperature and degenerate
plasmas. Damping of quarks and gluons as well as color diffusion in quark-gluon
plasmas is, however, shown not to be sufficiently screened and the rates
depends on an infrared cut-off of order the ``magnetic mass", $m_{\rm mag}\sim
g^2 T$.
|
9401300v1
|
1994-04-20
|
Electroweak Baryogenesis and Standard Model CP Violation
|
We analyze the mechanism of electroweak baryogenesis proposed by Farrar and
Shaposhnikov in which the phase of the CKM mixing matrix is the only source of
$CP$ violation. This mechanism is based on a phase separation of baryons via
the scattering of quasiparticles by the wall of an expanding bubble produced at
the electroweak phase transition. In agreement with the recent work of Gavela,
Hern\'andez, Orloff and P\`ene, we conclude that QCD damping effects reduce the
asymmetry produced to a negligible amount. We interpret the damping as quantum
decoherence. We compute the asymmetry analytically. Our analysis reflects the
observation that only a thin, outer layer of the bubble contributes to the
coherent scattering of the quasiparticles. The generality of our arguments
rules out any mechanism of electroweak baryogenesis that does not make use of a
new source of $CP$ violation.
|
9404302v1
|
1994-06-11
|
Standard Model CP-violation and Baryon asymmetry Part II: Finite Temperature
|
We consider the scattering of quasi-particles off the boundary created during
a first order electroweak phase transition. Spatial coherence is lost due to
the quasi-quark damping rate, and we show that reflection on the boundary is
suppressed, even at tree-level. Simply on CP considerations, we argue against
electroweak baryogenesis in the Standard Model via the charge transport
mechanism. A CP asymmetry is produced in the reflection properties of quarks
and antiquarks hitting the phase boundary. An effect is present at order
$\alpha_W^2$ in rate and a regular GIM behaviour is found, which can be
expressed in terms of two unitarity triangles. A crucial role is played by the
damping rate of quasi-particles in a hot plasma, which is a relevant scale
together with $M_W$ and the temperature. The effect is many orders of magnitude
below what observation requires.
|
9406289v2
|
1995-01-03
|
High temperature QCD and QED with unstable excitations
|
We consider the partition functions of QCD and QED at high temperature
assuming small coupling constants, and present arguments in favor of an
improved perturbative expansion in terms of unstable excitations. Our effective
propagators are derived from spectral functions with a constant width. These
spectral functions describe screening and damping of gluons (photons) as well
as ``Brownian'' motion of quarks (electrons). BRST-invariance allows us to
reduce the number of independent width parameters to three. These are
determined in a self-consistent way from the one-loop self energy and
polarization tensor in the infrared limit thus rendering this limit finite. All
spectral width parameters are found to be proportional to $g T$. We reproduce
the well known expression for the electric ``Debye''-screening mass. The
transverse (magnetic) gluons (photons) are found to interact only at nonzero
momentum or energy, at least to leading order. As a consequence their spectral
function acquires a width only away from the infrared limit. Finally, plasmon
modes are determined and found to be strongly damped.
|
9501203v1
|
1995-12-12
|
Bubble Collisions and Defect Formation in a Damping Environment
|
Within the context of a first-order phase transition in the early Universe,
we study the collision process for vacuum bubbles expanding in a plasma. The
effects of the plasma are simulated by introducing a damping term in the
equations of motion for a $U(1)$ global field. We find that Lorentz-contracted
spherically symmetric domain walls adequately describe the overdamped motion of
the bubbles in the thin wall approximation, and study the process of collision
and phase equilibration both numerically and analytically. With an analytical
model for the phase propagation in 1+1 dimensions, we prove that the phase
waves generated in the bubble merging are reflected by the walls of the true
vacuum cavity, giving rise to a long-lived oscillating state that delays the
phase equilibration. The existence of such a state in the 3+1 dimensional model
is then confirmed by numerical simulations, and the consequences for the
formation of vortices in three-bubble collisions are considered.
|
9512290v1
|
1996-09-02
|
The quasiparticle structure of hot gauge theories
|
The study of the ultrarelativistic plasmas in perturbation theory is plagued
with infrared divergences which are not eliminated by the screening
corrections. They affect, in particular, the computation of the lifetime of the
elementary excitations, thus casting doubt on the validity of the quasiparticle
picture. We show that, for Abelian plasmas at least, the infrared problem of
the damping rate can be solved by a non-perturbative treatment based on the
Bloch-Nordsieck approximation. The resulting expression of the fermion
propagator is free of divergences, and exhibits a {\it non-exponential} damping
at large times: $S_R(t)\sim \exp\{-\alpha T t \ln\omega_pt\}$, where
$\omega_p=gT/3$ is the plasma frequency and $\alpha=g^2/4\pi$.
|
9609225v1
|
1996-10-18
|
Finiteness of Hot Classical Scalar Field Theory and the Plasmon Damping Rate
|
We investigate the renormalizability of the classical $\phi^4$ theory at
finite temperature. We calculate the time-dependent two point function to two
loop order and show that it can be rendered finite by the counterterms of the
classical static theory. As an application the classical plasmon damping rate
is found to be $\gamma = \lambda^2 T^2/1536 \pi m$. When we use the high
temperature expression for $m$ given by dimensional reduction, the rate is
found to agree with the quantum mechanical result.
|
9610415v2
|
1996-12-30
|
Defect Formation in First Order Phase Transitions with Damping
|
Within the context of first order phase transitions in the early universe, we
study the influence of a coupling between the (global U(1)) scalar driving the
transition and the rest of the matter content of the theory. The effect of the
coupling on the scalar is simulated by introducing a damping term in its
equations of motion, as suggested by recent results in the electroweak phase
transition. After a preceeding paper, in which we studied the influence that
this coupling has in the dynamics of bubble collisions and topological defect
formation, we proceed in this paper to quantify the impact of this new effects
on the probability of defect creation per nucleating bubble.
|
9612487v1
|
1997-07-28
|
Plasmon properties in classical lattice gauge theory
|
In order to investigate the features of the classical approximation at high
temperatures for real time correlation functions, the plasmon frequencies and
damping rates were recently computed numerically in the SU(2)+Higgs model and
in the pure SU(2) theory. We compare the lattice results with leading order
hard thermal loop resummed perturbation theory. In the broken phase of the
SU(2)+Higgs model, we show that the lattice results can be reproduced and that
the lattices used are too coarse to observe some important plasmon effects. In
the symmetric phase, the main qualitative features of the lattice results can
also be understood. In the pure SU(2) theory, on the other hand, there are
discrepancies which might point to larger Landau and plasmon damping effects
than indicated by perturbation theory.
|
9707489v2
|
1998-09-11
|
Dynamical renormalization group resummation of finite temperature infrared divergences
|
We introduce the method of dynamical renormalization group to study
relaxation and damping out of equilibrium directly in real time and applied it
to the study of infrared divergences in scalar QED. This method allows a
consistent resummation of infrared effects associated with the exchange of
quasistatic transverse photons and leads to anomalous logarithmic relaxation of
the form $e^{-\alpha T t \ln[t/t_0]}$ which prevents a quasiparticle
interpretation of charged collective excitations at finite temperature. The
hard thermal loop resummation program is incorporated consistently into the
dynamical renormalization group yielding a picture of relaxation and damping
phenomena in a plasma in real time that trascends the conceptual limitations of
the quasiparticle picture and other type of resummation schemes. We derive a
simple criterion for establishing the validity of the quasiparticle picture to
lowest order.
|
9809346v2
|
1999-02-12
|
Beyond HTL: The Classical Kinetic Theory of Landau Damping for Selfinteracting Scalar Fields in the Broken Phase
|
The effective theory of low frequency fluctuations of selfinteracting scalar
fields is constructed in the broken symmetry phase. The theory resulting from
integrating fluctuations with frequencies much above the spontanously generated
mass scale $(p_0>>M)$ is found to be local. Non-local dynamics, especially
Landau damping emerges under the effect of fluctuations in the $p_0 \sim M$
region. A kinetic theory of relativistic scalar gas particles interacting via
their locally variable mass with the low frequency scalar field is shown to be
equivalent to this effective field theory for scales below the characteristic
mass, that is beyond the accuracy of the Hard Thermal Loop (HTL) approximation.
|
9902331v1
|
2000-04-05
|
A consistent nonperturbative approach to thermal damping-rates
|
We propose a nonperturbative scheme for the calculation of thermal
damping-rates using exact renormalization group (RG)-equations. Special
emphasis is put on the thermal RG where first results for the rate were given
in M. Pietroni, Phys. Rev. Lett. 81 (1998), 2424. We point out that in order to
obtain a complete result that also reproduces the known perturbative behaviour
one has to take into account effects that were neglected in the work cited
above. We propose a well-defined way of doing the calculations that reproduces
perturbation theory in lowest order but goes considerably beyond perturbative
results and should be applicable also at second order phase-transitions.
|
0004039v2
|
2000-06-09
|
Random values of the cosmological constant
|
One way that an anthropic selection mechanism may be manifest in a physical
theory involves multiple domains in the universe with different values of the
physical parameters. If this mechanism is to be relevant for understanding the
small observed value of the cosmological constant, it may involve a mechanism
by which some contributions to the cosmological constant can be fixed at a
continuous range of values in the different domains. I study the properties of
four possible mechanisms, including the possibility of the Hubble damping of a
scalar field with an extremely flat potential. Another interesting possibility
involves fixed random values of non-dynamical form fields, and a cosmological
mechanism is suggested. This case raises the possibility of anthropic selection
of other parameters in addition. Further requirements needed for a consistent
cosmology are discussed.
|
0006088v2
|
2000-07-07
|
Finite pion width effects on the rho--meson
|
We study the influence of the finite damping width of pions on the in-medium
properties of the rho-meson in an interacting meson gas model at finite
temperature. Using vector dominance also implications on the resulting dilepton
spectra from the decay of the rho-meson are presented. A set of coupled Dyson
equations with self energies up to the sunset diagram level is solved self
consistently. Following a Phi-derivable scheme the self energies are
dynamically determined by the self consistent propagators. Some problems
concerning the self consistent treatment of vector or gauge bosons on the
propagator level, in particular, if coupled to currents arising from particles
with a sizable damping width, are discussed.
|
0007070v3
|
2000-08-31
|
New Regime for Dense String Networks
|
We uncover a new transient regime that reconciles the apparent inconsistency
of the Martins Shellard one scale damped string evolution model with the
initial conditions predicted by the Kibble mechanism for string formation in a
second order phase transition. This regime carries (in a short cosmic time
$\sim .1 t_c$) the dense string network created by the Kibble {\it{mechanism}}
to the (dilute) Kibble {\it{regime}} in which friction dominated strings remain
till times $t_* \sim (M_P/T_c)^2 t_c$. This is possible beacause the cosmic
time at the phase transition ($t_c$) is much larger than the damping time scale
$l_f\sim T_c^2/T^3$. Our result has drastic implications for various non-GUT
scale string mediated mechanisms.}
|
0008330v1
|
2001-01-25
|
The Fermion Boson Interaction Within the Linear Sigma Model at Finite Temperature
|
We reinvestigate the interaction of massless fermions with massless bosons at
finite temperature. Specifically, we calculate the self-energy of massless
fermions due the interaction with massless bosons at high temperature, which is
the region where thermal effects are maximal. The calculations are concentrated
in the limit of vanishing fermion three momentum and after considering the
effective fermion and boson dressed masses, we obtain the damping rate of the
fermion up to order $g^3$. It is shown that in the limit $k_0 \ll T$ the
fermion acquire a thermal mass of order $gT$ and the leading term of the
fermion damping rate is of order $g^2T+g^3T$.
|
0101283v3
|
2001-11-02
|
Quark Number Susceptibility in Hard Thermal Loop Approximation
|
We calculate the quark number susceptibility in the deconfined phase of QCD
using the hard thermal loop (HTL) approximation for the quark propagator. This
improved perturbation theory takes into account important medium effects such
as thermal quark masses and Landau damping in the quark-gluon plasma. We
explicitly show that the Landau damping part in the quark propagator for
spacelike quark momenta does not contribute to the quark number susceptibility
due to the quark number conservation. We find that the quark number
susceptibility only due to the collective quark modes deviates from that of
free one around the critical temperature but approaches free results at
infinite temperature limit. The results are in conformity with recent lattice
calculations.
|
0111022v4
|
2001-12-29
|
Damped $\sin(β-α)$ of Higgs couplings and the lightest Higgs production at $γγ$ colliders in MSSM
|
In the decoupling limit, $M^2_{A^0} \gg M^2_Z$, the heavy CP-even, CP-odd and
charged Higgs boson masses are nearly degenerate, $\sin(\beta-\alpha)$
approaches 1, and the lightest CP-even Higgs boson almost displays the same
properties as the Standard Model Higgs boson. But the stop and sbottom sector
can change this pattern through radiative corrections. We find that there are
parameter regions at small, moderate and large $\tan\beta$ in MSSM under
experimental constraints of $(g-2)_{\mu}$ and $b\to s\gamma$, where
$\sin^2(\beta-\alpha)$ is damped (say below 0.8), which has a significant
effect on Higgs couplings $g_{h^0VV} (V=W^\pm,Z^0)$ and $g_{h^0\gamma\gamma}$.
We discuss its impact on the lightest CP-even Higgs production at
$\gamma\gamma$ colliders.
|
0112356v1
|
2004-05-31
|
Gauge dependence of the fermion quasiparticle poles in hot gauge theories
|
The gauge dependence of the complex fermion quasiparticle poles corresponding
to soft collective excitations is studied in hot gauge theories at one-loop
order and next-to-leading order in the high-temperature expansion, with a view
towards going beyond the leading order hard thermal loops and resummations
thereof. We find that for collective excitations of momenta k ~ eT the
dispersion relations are gauge independent, but the corresponding damping rates
are gauge dependent. For k<<eT and in k \to 0 limit, both the dispersion
relations and the damping rates are found to be gauge dependent. The gauge
dependence of the position of the complex quasiparticle poles signals the need
for resummation. Possible cancellation of the leading gauge dependence at
two-loop order in the case of QED is briefly discussed.
|
0406002v2
|
2004-11-09
|
Numerical investigation of friction in inflaton equations of motion
|
The equation of motion for the expectation value of a scalar quantum field
does not have the local form that is commonly assumed in studies of
inflationary cosmology. We have recently argued that the true, temporally
non-local equation of motion does not possess a time-derivative expansion and
that the conversion of inflaton energy into particles is not, in principle,
described by the friction term estimated from linear response theory. Here, we
use numerical methods to investigate whether this obstacle to deriving a local
equation of motion is purely formal, or of some quantitative importance. Using
a simple scalar-field model, we find that, although the non-equilibrium
evolution can exhibit significant damping, this damping is not well described
by the local equation of motion obtained from linear response theory. It is
possible that linear response theory does not apply to the situation we study
only because thermalization turns out to be slow, but we argue that that the
large discrepancies we observe indicate a failure of the local approximation at
a more fundamental level.
|
0411130v1
|
2006-03-03
|
Damping of supernova neutrino transitions in stochastic shock-wave density profiles
|
Supernova neutrino flavor transitions during the shock wave propagation are
known to encode relevant information not only about the matter density profile
but also about unknown neutrino properties, such as the mass hierarchy (normal
or inverted) and the mixing angle theta_13. While previous studies have
focussed on "deterministic" density profiles, we investigate the effect of
possible stochastic matter density fluctuations in the wake of supernova shock
waves. In particular, we study the impact of small-scale fluctuations on the
electron (anti)neutrino survival probability, and on the observable spectra of
inverse-beta-decay events in future water-Cherenkov detectors. We find that
such fluctuations, even with relatively small amplitudes, can have significant
damping effects on the flavor transition pattern, and can partly erase the
shock-wave imprint on the observable time spectra, especially for
sin^2(theta_13) > O(10^-3).
|
0603033v2
|
2006-08-11
|
Constraining SuperWIMPy and Warm Subhalos with Future Submillilensing
|
We propose to observe QSO-galaxy strong lens systems to give a new constraint
on the damping scale of the initial fluctuations. We find that the future
observation of submilliarc scale astrometric shifts of the multiple lensed
images of QSOs would find \sim 10^{(3-9)} M_{\odot} subhalos inside the
macrolens halo. The superweakly interacting massive particles (superWIMPs)
produced from a WIMP decay and the warm dark matter (WDM) particles that
predict a comoving damping scale larger than \sim 2 kpc can be constrained if
\sim 10^3 M_{\odot} subhalos are detected.
|
0608126v2
|
2006-11-15
|
Time-to-Space Conversion in Neutrino Oscillations
|
We study the neutrino oscillation problem in the framework of the wave packet
formalism. The neutrino state is described by a packet located initially in a
region S (source) and detected in another region D at a distance R from S. We
examine how the oscillation probability as a function of variable R can be
derived from he oscillation probability as a function of time t, the latter
being found by using the Schrodinger equation. We justify the known
prescription "t --> R/c" without referring to a specific form of the neutrino
wave packet and only assuming the finiteness of its support. The effect of the
oscillation damping at large R is revealed. For an illustration, an explicit
expression for the damping factor is obtained using Gaussian packet.
|
0611202v1
|
1991-09-26
|
The Damping of Energetic Gluons and Quarks in High-Temperature QCD
|
When a gluon or a quark is sent through the hot QCD plasma it can be absorbed
into the ambient heat bath and so can acquire an effective lifetime. At high
temperatures and for weak couplings the inverse lifetime, or damping rate, for
energetic quarks and transverse gluons, (those whose momenta satisfy $|\p| \gg
gT$) is given by $\gamma(\p) = c\; g^2 \log\left({1\over g}\right)\; T +
O(g^2T)$. We show that very simple arguments suffice both to fix the numerical
coefficient, $c$, in this expression and to show that the $O(g^2T)$
contribution is incalculable in perturbation theory without further
assumptions. For QCD with $N_c$ colours we find (expressed in terms of the
casimir invariants $C_a=N_c$ and $C_f=(N_c^2-1)/(2N_c)$): $c_g=+{C_a\over
4\pi}$ for gluons and $c_q=+{C_f\over 4\pi}$ for quarks. These numbers agree
with the more detailed calculations of Pisarski \etal\ but disagree with those
of Lebedev and Smilga. The simplicity of the calculation also permits a direct
verification of the gauge-invariance and physical sign of the result.
|
9109051v1
|
1998-09-11
|
Damping and reaction rates and wave function renormalization of fermions in hot gauge theories
|
We examine the relation between the damping rate of a chiral fermion mode
propagating in a hot plasma and the rate at which the mode approaches
equilibrium. We show how these two quantities, obtained from the imaginary part
of the fermion self-energy, are equal when the reaction rate is defined using
the appropriate wave function of the mode in the medium. As an application, we
compute the production rate of hard axions by Compton-like scattering processes
in a hot QED plasma starting from both, the axion self-energy and the electron
self-energy. We show that the latter rate coincides with the former only when
this is computed using the corresponding medium spinor modes.
|
9809083v2
|
2003-12-28
|
A mechanism of the large-scale damping in the CMB anisotropy
|
We present a mechanism through which a certain class of short-distance cutoff
affects the CMB anisotropies at large angular scales. Our analysis is performed
in two steps. The first is given in an intuitive way, using the property of the
inflationary universe that quantum fluctuations of an inflaton field become
classical after crossing the Hubble horizon. We give a condition for a cutoff
to yield a damping on large scales, and show that the holographic cutoff
introduced in the preceding paper (hep-th/0307029) does satisfy the condition.
The second analysis is carried out by setting an initial condition such that
each mode of inflaton starts as the vacuum fluctuation of the Hamiltonian when
being released from the constraint of cutoff. The first intuitive discussion is
then shown to be correct qualitatively.
|
0312298v7
|
2005-03-03
|
Scalar field perturbations of the Schwarzschild black hole in the Gödel Universe
|
We investigate the scalar field perturbations of the 4+1-dimensional
Schwarzschild black hole immersed in a G\"{o}del Universe, described by the
Gimon-Hashimoto solution.This may model the influence of the possible rotation
of the Universe upon the radiative processes near a black hole. In the regime
when the scale parameter $j$ of the G\"{o}del background is small, the
oscillation frequency is linearly decreasing with $j$, while the damping time
is increasing. The quasinormal modes are damping, implying stability of the
Schwarzschild-G\"{o}del space-time against scalar field perturbations. The
approximate analytical formula for large multipole numbers is found.
|
0503029v2
|
2005-06-28
|
Liouville Decoherence in a Model of Flavour Oscillations in the presence of Dark Energy
|
We study in some detail the master equation, and its solution in a simplified
case modelling flavour oscillations of a two-level system, stemming from the
Liouville-string approach to quantum space time foam. In this framework we
discuss the appearance of diffusion terms and decoherence due to the
interaction of low-energy string matter with space-time defects, such as
D-particles in the specific model of ``D-particle foam'', as well as dark
energy contributions. We pay particular attention to contrasting the decoherent
role of a cosmological constant in inducing exponential quantum damping in the
evolution of low-energy observables, such as the probability of flavour
oscillations, with the situation where the dark energy relaxes to zero for
asymptotically large times, in which case such a damping is absent. Our
findings may be of interest to (astrophysical) tests of quantum space-time foam
models in the not-so-distant future.
|
0506242v1
|
2005-08-25
|
The Dynamics of Small Instanton Phase Transitions
|
The small instanton transition of a five-brane colliding with one end of the
S1/Z2 interval in heterotic M-theory is discussed, with emphasis on the
transition moduli, their potential function and the associated non-perturbative
superpotential. Using numerical methods, the equations of motion of these
moduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solved
including non-perturbative interactions. It is shown that the five-brane
collides with the end of the interval at a small instanton. However, the moduli
then continue to evolve to an isolated minimum of the potential, where they are
trapped by gravitational damping. The torsion free sheaf at the small instanton
is ``smoothed out'' into a vector bundle at the isolated minimum, thus
dynamically completing the small instanton phase transition. Radiative damping
at the origin of moduli space is discussed and shown to be insufficient to trap
the moduli at the small instanton point.
|
0508190v2
|
2006-11-21
|
Renormalization group study of damping in nonequilibrium field theory
|
In this paper we shall study whether dissipation in a $\lambda\phi^{4}$ may
be described, in the long wavelength, low frequency limit, with a simple Ohmic
term $\kappa\dot{\phi}$, as it is usually done, for example, in studies of
defect formation in nonequilibrium phase transitions. We shall obtain an
effective theory for the long wavelength modes through the coarse graining of
shorter wavelengths. We shall implement this coarse graining by iterating a
Wilsonian renormalization group transformation, where infinitesimal momentum
shells are coarse-grained one at a time, on the influence action describing the
dissipative dynamics of the long wavelength modes. To the best of our
knowledge, this is the first application of the nonequilibrium renormalization
group to the calculation of a damping coefficient in quantum field theory.
|
0611222v1
|
2006-02-16
|
Exit from a basin of attraction for stochastic weakly damped nonlinear Schrödinger equations
|
We consider weakly damped nonlinear Schr\"odinger equations perturbed by a
noise of small amplitude. The small noise is either complex and of additive
type or real and of multiplicative type. It is white in time and colored in
space. Zero is an asymptotically stable equilibrium point of the deterministic
equations. We study the exit from a neighborhood of zero, invariant by the flow
of the deterministic equation, in $\xLtwo$ or in $\xHone$. Due to noise, large
fluctuations off zero occur. Thus, on a sufficiently large time scale, exit
from these domains of attraction occur. A formal characterization of the small
noise asymptotic of both the first exit times and the exit points is given.
|
0602350v1
|
2006-04-07
|
Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
|
We consider a class of ordinary differential equations describing
one-dimensional analytic systems with a quasi-periodic forcing term and in the
presence of damping. In the limit of large damping, under some generic
non-degeneracy condition on the force, there are quasi-periodic solutions which
have the same frequency vector as the forcing term. We prove that such
solutions are Borel summable at the origin when the frequency vector is either
any one-dimensional number or a two-dimensional vector such that the ratio of
its components is an irrational number of constant type. In the first case the
proof given simplifies that provided in a previous work of ours. We also show
that in any dimension $d$, for the existence of a quasi-periodic solution with
the same frequency vector as the forcing term, the standard Diophantine
condition can be weakened into the Bryuno condition. In all cases, under a
suitable positivity condition, the quasi-periodic solution is proved to
describe a local attractor.
|
0604162v1
|
2006-06-30
|
Uniform attractors for non-autonomous wave equations with nonlinear damping
|
We consider dynamical behavior of non-autonomous wave-type evolutionary
equations with nonlinear damping, critical nonlinearity, and time-dependent
external forcing which is translation bounded but not translation compact
(i.e., external forcing is not necessarily time-periodic, quasi-periodic or
almost periodic). A sufficient and necessary condition for the existence of
uniform attractors is established using the concept of uniform asymptotic
compactness. The required compactness for the existence of uniform attractors
is then fulfilled by some new a priori estimates for concrete wave type
equations arising from applications. The structure of uniform attractors is
obtained by constructing a skew product flow on the extended phase space for
the norm-to-weak continuous process.
|
0606776v1
|
2001-04-17
|
Scattering and radiation damping in gyroscopic Lorentz electrodynamic
|
Relativistic massive Lorentz electrodynamics (LED) is studied in a
``gyroscopic setup'' where the electromagnetic fields and the particle spin are
the only dynamical degrees of freedom.
A rigorous proof of the global existence and uniqueness of the dynamics is
given for essentially the whole range of field strengths reasonable for a
classical theory.
For a class of rotation-reflection symmetric field data it is shown that the
dynamics also satisfies the world-line equations for a non-moving Lorentz
electron, thus furnishing rigorous solutions of the full system of nonlinear
equations of LED.
The previously proven soliton dynamics of the Lorentz electron is further
illucidated by showing that rotation-reflection symmetric deviations from the
soliton state of the renormalized particle die out exponentially fast through
radiation damping if the electrostatic mass is smaller than the bare rest mass.
|
0104023v2
|
2002-06-18
|
Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory
|
The phase space of $N$ damped linear oscillators is endowed with a bilinear
map under which the evolution operator is symmetric. This analog of
self-adjointness allows properties familiar from conservative systems to be
recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey
sum rules, initial-value problems are readily solved and perturbation theory
applies to the_complex_ eigenvalues. These concepts are conveniently
represented in a biorthogonal basis.
|
0206026v2
|
2002-06-17
|
Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points
|
The eigenvector expansion developed in the preceding paper for a system of
damped linear oscillators is extended to critical points, where eigenvectors
merge and the time-evolution operator $H$ assumes a Jordan-block structure. The
representation of the bilinear map is obtained in this basis. Perturbations
$\epsilon\Delta H$ around an $M$-th order critical point generically lead to
eigenvalue shifts $\sim\epsilon^{1/M}$ dependent on only_one_ matrix element,
with the $M$ eigenvalues splitting in equiangular directions in the complex
plane. Small denominators near criticality are shown to cancel.
|
0206027v2
|
2002-06-22
|
Yank and Hooke's constant group theoretically
|
We study the second central extension of the (1+1) Aristotle Lie.We find that
the first central extension admit four orbits on the dual of second central
extension of the (1+1) Aristotle Lie group.The generic orbit is characterised
by a Hooke's constant k and a yank y.If the physics of the orbit is studied
with respect the evolution in time,it represents an elementary system with
internal energy U in a posotion-momentum under the conjugation of a Hooke's
force and a damping one proportional to the velocity as in particle
mechanics.If the physics of the orbit is studied with respect the evolution in
space, it represents an elementary system with an internal momentum P under the
conjugation of a kind of Hooke's force and a damping one proportional to a
slowness, slowness usually used in time travel waves.
|
0206038v1
|
2004-02-24
|
Classical harmonic oscillator with Dirac-like parameters and possible applications
|
We obtain a class of parametric oscillation modes that we call K-modes with
damping and absorption that are connected to the classical harmonic oscillator
modes through the "supersymmetric" one-dimensional matrix procedure similar to
relationships of the same type between Dirac and Schroedinger equations in
particle physics. When a single coupling parameter, denoted by K, is used, it
characterizes both the damping and the dissipative features of these modes.
Generalizations to several K parameters are also possible and lead to
analytical results. If the problem is passed to the physical optics (and/or
acoustics) context by switching from the oscillator equation to the
corresponding Helmholtz equation, one may hope to detect the K-modes as
waveguide modes of specially designed waveguides and/or cavities
|
0402065v2
|
2000-02-22
|
Front motion for phase transitions in systems with memory
|
We consider the Allen-Cahn equations with memory (a partial
integro-differential convolution equation). The prototype kernels are
exponentially decreasing functions of time and they reduce the
integrodifferential equation to a hyperbolic one, the damped Klein-Gordon
equation. By means of a formal asymptotic analysis we show that to the leading
order and under suitable assumptions on the kernels, the integro-differential
equation behave like a hyperbolic partial differential equation obtained by
considering prototype kernels: the evolution of fronts is governed by the
extended, damped Born-Infeld equation. We also apply our method to a system of
partial integro-differential equations which generalize the classical phase
field equations with a non-conserved order parameter and describe the process
of phase transitions where memory effects are present.
|
0002039v1
|
2002-03-01
|
Excitation of travelling multibreathers in anharmonic chains
|
We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam
(FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with
wavenumber p and oscillates sinusoidally in time with the frequency omega. When
omega is in the phonon band, the p-mode becomes modulationally unstable above a
critical forcing, which we determine analytically in terms of the parameters of
the system. For omega above the phonon band, the instability of the p-mode
leads to the formation of a travelling multibreather, that, in the
low-amplitude limit could be described in terms of soliton solutions of a
suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar
mechanisms of instability could show up in easy-axis magnetic structures, that
are governed by such NLS equations.
|
0203002v1
|
2003-01-15
|
Resonant triad dynamics in weakly damped Faraday waves with two-frequency forcing
|
Many of the interesting patterns seen in recent multi-frequency Faraday
experiments can be understood on the basis of three-wave interactions (resonant
triads). In this paper we consider two-frequency forcing and focus on a
resonant triad that occurs near the bicritical point where two pattern-forming
modes with distinct wavenumbers emerge simultaneously. This triad has been
observed directly (in the form of rhomboids) and has also been implicated in
the formation of quasipatterns and superlattices. We show how the symmetries of
the undamped unforced problem (time translation, time reversal, and Hamiltonian
structure) can be used, when the damping is weak, to obtain general scaling
laws and additional qualitative properties of the normal form coefficients
governing the pattern selection process near onset; such features help to
explain why this particular triad is seen only for certain "low" forcing
ratios, and predict the existence of drifting solutions and heteroclinic
cycles. We confirm the anticipated parameter dependence of the coefficients and
investigate its dynamical consequences using coefficients derived numerically
from a quasipotential formulation of the Faraday problem due to Zhang and
Vinals.
|
0301015v1
|
2003-03-21
|
Global well-posedness and multi-tone solutions of a class of nonlinear nonlocal cochlear models in hearing
|
We study a class of nonlinear nonlocal cochlear models of the transmission
line type, describing the motion of basilar membrane (BM) in the cochlea. They
are damped dispersive partial differential equations (PDEs) driven by time
dependent boundary forcing due to the input sounds. The global well-posedness
in time follows from energy estimates. Uniform bounds of solutions hold in case
of bounded nonlinear damping. When the input sounds are multi-frequency tones,
and the nonlinearity in the PDEs is cubic, we construct smooth quasi-periodic
solutions (multi-tone solutions) in the weakly nonlinear regime, where new
frequencies are generated due to nonlinear interaction. When the input is two
tones at frequencies $f_1$, $f_2$ ($f_1 < f_2$), and high enough intensities,
numerical results illustrate the formation of combination tones at $2 f_1 -f_2$
and $2f_2 -f_1$, in agreement with hearing experiments. We visualize the
frequency content of solutions through the FFT power spectral density of
displacement at selected spatial locations on BM.
|
0303048v1
|
2004-05-11
|
Analytical approach to soliton ratchets in asymmetric potentials
|
We use soliton perturbation theory and collective coordinate ansatz to
investigate the mechanism of soliton ratchets in a driven and damped asymmetric
double sine-Gordon equation. We show that, at the second order of the
perturbation scheme, the soliton internal vibrations can couple {\it
effectively}, in presence of damping, to the motion of the center of mass,
giving rise to transport. An analytical expression for the mean velocity of the
soliton is derived. The results of our analysis confirm the internal mode
mechanism of soliton ratchets proposed in [Phys. Rev. E {\bf 65} 025602(R)
(2002)].
|
0405023v1
|
2005-02-16
|
Controlling soliton explosions
|
We investigate the dynamics of solitons in generalized Klein-Gordon equations
in the presence of nonlinear damping and spatiotemporal perturbations. We will
present different mechanisms for soliton explosions. We show (both analytically
and numerically) that some space-dependent perturbations or nonlinear damping
can make the soliton internal mode unstable leading to soliton explosion. We
will show that, in some cases, while some conditions are satisfied, the soliton
explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We
believe these mechanisms can explain some of the phenomena that recently have
been reported to occur in excitable media. We present a method for controlling
soliton explosions.
|
0502033v1
|
2005-07-22
|
Global existence in infinite lattices of nonlinear oscillators: The Discrete Klein-Gordon equation
|
Pointing out the difference between the Discrete Nonlinear Schr\"odinger
equation with the classical power law nonlinearity-for which solutions exist
globally, independently of the sign and the degree of the nonlinearity, the
size of the initial data and the dimension of the lattice-we prove either
global existence or nonexistence in time, for the Discrete Klein-Gordon
equation with the same type of nonlinearity (but of ``blow-up'' sign), under
suitable conditions on the initial data, and some times on the dimension of the
lattice. The results, consider both the conservative and the linearly damped
lattice. Similarities and differences with the continuous counterparts, are
remarked. We also make a short comment, on the existence of excitation
thresholds, for forced solutions of damped and parametrically driven,
Klein-Gordon lattices.
|
0507044v5
|
1992-12-14
|
Poisson and Porter-Thomas Fluctuations in off-Yrast Rotational Transitions
|
Fluctuations associated with stretched E2 transitions from high spin levels
in nuclei around $^{168}$Yb are investigated by a cranked shell model extended
to include residual two-body interactions. It is found that the gamma-ray
energies behave like random variables and the energy spectra show the Poisson
fluctuation, in the cranked mean field model without the residual interaction.
With two-body residual interaction included, discrete transition pattern with
unmixed rotational bands is still valid up to around 600 keV above yrast, in
good agreement with experiments. At higher excitation energy, a gradual onset
of rotational damping emerges. At 1.8 MeV above yrast, complete damping is
observed with GOE type fluctuations for both energy levels and transition
strengths(Porter-Thomas fluctuations).
|
9212006v1
|
1993-11-25
|
Microscopic analysis of two-body correlations in light nuclei
|
Within a nonperturbative dynamical two-body approach - based on coupled
equations of motion for the one-body density matrix and the two-body
correlation function - we study the distribution of occupation numbers in a
correlated system close to the groundstate, the relaxation of single-particle
excitations and the damping of collective modes. For this purpose the nonlinear
equations of motion are solved numerically within a finite oscillator basis for
the first time adopting short-range repulsive and long-range attractive
two-body forces. We find in all cases that the formation of long- and
short-range correlations and their mixing is related to the long- and
short-range part of the nucleon-nucleon interaction which dominate the
resummation of loop or ladder diagrams, respectively. However, the proper
description of relaxation or damping phenomena is found to require both types
of diagrams as well as the mixed terms simultaneously.
|
9311031v1
|
1997-03-26
|
A self-consistent treatment of damped motion for stable and unstable collective modes
|
We address the dynamics of damped collective modes in terms of first and
second moments. The modes are introduced in a self-consistent fashion with the
help of a suitable application of linear response theory. Quantum effects in
the fluctuations are governed by diffusion coefficients D_{\mu\nu}. The latter
are obtained through a fluctuation dissipation theorem generalized to allow for
a treatment of unstable modes. Numerical evaluations of the D_{\mu\nu} are
presented. We discuss briefly how this picture may be used to describe global
motion within a locally harmonic approximation. Relations to other methods are
discussed, like "dissipative tunneling", RPA at finite temperature and
generalizations of the "Static Path Approximation".
|
9703056v1
|
1997-04-24
|
A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum
|
Simple states, such as isobaric analog states or giant resonances, embedded
into continuum are typical for mesoscopic many-body quantum systems. Due to the
coupling to compound states in the same energy range, a simple mode acquires a
damping width ("internal" dynamics). When studied experimentally with the aid
of various reactions, such states reveal enhanced cross sections in specific
channels at corresponding resonance energies ("external" dynamics which include
direct decay of a simple mode and decays of intrinsic compound states through
their own channels). We consider the interplay between internal and external
dynamics using a general formalism of the effective nonhermitian hamiltonian
and looking at the situation both from "inside" (strength functions and
spreading widths) and from "outside" (S-matrix, cross sections and delay
times). The restoration of isospin purity and disappearance of the collective
strength of giant resonances at high excitation energy are discussed as
important particular manifestations of this complex interplay.
|
9704055v1
|
1998-02-27
|
New collective mode due to collisional coupling
|
Starting from a nonmarkovian conserving relaxation time approximation for
collisions we derive coupled dispersion relations for asymmetric nuclear
matter. The isovector and isoscalar modes are coupled due to asymmetric nuclear
meanfield acting on neutrons and protons differently. A further coupling is
observed by collisional correlations. The latter one leads to the appearance of
a new soft mode besides isoscalar and isovector modes in the system. We suggest
that this mode might be observable in asymmetric systems. This soft mode
approaches the isovector mode for high temperatures. At the same time the
isovector mode remains finite and approaches a constant value at higher
temperatures showing a transition from zero sound like damping to first sound.
The damping of the new soft mode is first sound like at all temperatures.
|
9802083v1
|
1998-10-12
|
Response function beyond mean field of neutron-rich nuclei
|
The damping of single-particle and collective motion in exotic isotopes is a
new topic and its study may shed light on basic problems of nuclear dynamics.
For instance, it is known that nuclear structure calculations are not able, as
a rule, to account completely for the empirical single-particle damping. In
this contribution, we present calculations of the single-particle self-energy
in the case of the neutron-rich light nucleus $^{28}$O, by taking proper care
of the continuum, and we show that there are important differences with the
case of nuclei along the valley of stability.
|
9810033v1
|
1999-04-14
|
Scaling Analysis of Fluctuating Strength Function
|
We propose a new method to analyze fluctuations in the strength function
phenomena in highly excited nuclei. Extending the method of multifractal
analysis to the cases where the strength fluctuations do not obey power scaling
laws, we introduce a new measure of fluctuation, called the local scaling
dimension, which characterizes scaling behavior of the strength fluctuation as
a function of energy bin width subdividing the strength function. We discuss
properties of the new measure by applying it to a model system which simulates
the doorway damping mechanism of giant resonances. It is found that the local
scaling dimension characterizes well fluctuations and their energy scales of
fine structures in the strength function associated with the damped collective
motions.
|
9904037v1
|
1999-07-07
|
Pair creation: back-reactions and damping
|
We solve the quantum Vlasov equation for fermions and bosons, incorporating
spontaneous pair creation in the presence of back-reactions and collisions.
Pair creation is initiated by an external impulse field and the source term is
non-Markovian. A simultaneous solution of Maxwell's equation in the presence of
feedback yields an internal current and electric field that exhibit plasma
oscillations with a period tau_pl. Allowing for collisions, these oscillations
are damped on a time-scale, tau_r, determined by the collision frequency.
Plasma oscillations cannot affect the early stages of the formation of a
quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD
approx 1 fm/c.
|
9907027v1
|
2000-10-23
|
Barrier penetration and rotational damping of thermally excited superdeformed nuclei
|
We construct a microscopic model of thermally excited superdeformed states
that describes both the barrier penetration mechanism, leading to the decay-out
transitions to normal deformed states, and the rotational damping causing
fragmentation of rotational E2 transitions. We describe the barrier penetration
by means of a tunneling path in the two-dimensional deformation energy surface,
which is calculated with the cranked Nilsson-Strutinsky model. The individual
excited superdeformed states and associated E2 transition strengths are
calculated by the shell model diagonalization of the many-particle many-hole
excitations interacting with the delta-type residual two-body force. The effect
of the decay-out on the excited superdeformed states are discussed in detail
for $^{152}$Dy, $^{143}$Eu and $^{192}$Hg.
|
0010074v1
|
1996-02-22
|
Stability of Travelling Waves for a Damped Hyperbolic Equation
|
We consider a nonlinear damped hyperbolic equation in $\real^n$, $1 \le n \le
4$, depending on a positive parameter $\epsilon$. If we set $\epsilon=0$, this
equation reduces to the well-known Kolmogorov-Petrovski-Piskunov equation. We
remark that, after a change of variables, this hyperbolic equation has the same
family of one-dimensional travelling waves as the KPP equation. Using various
energy functionals, we show that, if $\epsilon >0$, these fronts are locally
stable under perturbations in appropriate weighted Sobolev spaces. Moreover,
the decay rate in time of the perturbed solutions towards the front of minimal
speed $c=2$ is shown to be polynomial. In the one-dimensional case, if
$\epsilon < 1/4$, we can apply a Maximum Principle for hyperbolic equations and
prove a global stability result. We also prove that the decay rate of the
perturbated solutions towards the fronts is polynomial, for all $c > 2$.
|
9602004v1
|
1998-09-18
|
Stability of Propagating Fronts in Damped Hyperbolic Equations
|
We consider the damped hyperbolic equation in one space dimension $\epsilon
u_{tt} + u_t = u_{xx} + F(u)$, where $\epsilon$ is a positive, not necessarily
small parameter. We assume that $F(0)=F(1)=0$ and that $F$ is concave on the
interval $[0,1]$. Under these assumptions, our equation has a continuous family
of monotone propagating fronts (or travelling waves) indexed by the speed
parameter $c \ge c_*$. Using energy estimates, we first show that the
travelling waves are locally stable with respect to perturbations in a weighted
Sobolev space. Then, under additional assumptions on the non-linearity, we
obtain global stability results using a suitable version of the hyperbolic
Maximum Principle. Finally, in the critical case $c = c_*$, we use self-similar
variables to compute the exact asymptotic behavior of the perturbations as $t
\to +\infty$. In particular, setting $\epsilon = 0$, we recover several
stability results for the travelling waves of the corresponding parabolic
equation.
|
9809007v1
|
1999-05-28
|
Existence threshold for the ac-driven damped nonlinear Schrödinger solitons
|
It has been known for some time that solitons of the externally driven,
damped nonlinear Schr\"odinger equation can only exist if the driver's
strength, $h$, exceeds approximately $(2/ \pi) \gamma$, where $\gamma$ is the
dissipation coefficient. Although this perturbative result was expected to be
correct only to the leading order in $\gamma$, recent studies have demonstrated
that the formula $h_{thr}= (2 /\pi) \gamma$ gives a remarkably accurate
description of the soliton's existence threshold prompting suggestions that it
is, in fact, exact. In this note we evaluate the next order in the expansion of
$h_{thr}(\gamma)$ showing that the actual reason for this phenomenon is simply
that the next-order coefficient is anomalously small: $h_{thr}=(2/ \pi) \gamma
+ 0.002 \gamma^3$. Our approach is based on a singular perturbation expansion
of the soliton near the turning point; it allows to evaluate $h_{thr}(\gamma)$
to all orders in $\gamma$ and can be easily reformulated for other perturbed
soliton equations.
|
9906001v1
|
1996-10-01
|
Exact time evolution and master equations for the damped harmonic oscillator
|
Using the exact path integral solution for the damped harmonic oscillator it
is shown that in general there does not exist an exact dissipative Liouville
operator describing the dynamics of the oscillator for arbitrary initial bath
preparations. Exact non-stationary Liouville operators can be found only for
particular preparations. Three physically meaningful examples are examined. An
exact new master equation is derived for thermal initial conditions. Second,
the Liouville operator governing the time-evolution of equilibrium correlations
is obtained. Third, factorizing initial conditions are studied. Additionally,
one can show that there are approximate Liouville operators independent of the
initial preparation describing the long time dynamics under appropriate
conditions. The general form of these approximate master equations is derived
and the coefficients are determined for special cases of the bath spectral
density including the Ohmic, Drude and weak coupling cases. The connection with
earlier work is discussed.
|
9610001v1
|
1999-01-09
|
Cluster ionization via two-plasmon excitation
|
We calculate the two-photon ionization of clusters for photon energies near
the surface plasmon resonance. The results are expressed in terms of the
ionization rate of a double plasmon excitation, which is calculated
perturbatively. For the conditions of the experiment by Schlipper et al., we
find an ionization rate of the order of 0.05-0.10 fs^(-1). This rate is used to
determine the ionization probability in an external field in terms of the
number of photons absorbed and the duration of the field. The probability also
depends on the damping rate of the surface plasmon. Agreement with experiment
can only be achieved if the plasmon damping is considerably smaller than its
observed width in the room-temperature single-photon absorption spectrum.
|
9901008v1
|
2000-08-01
|
Rectangular Waveguide HOM Couplers for a TESLA Superstructure
|
Some modifications of a Rectangular Waveguide HOM couplers for TESLA
superstructure have been investigated. These RWG HOM couplers are to be
installed between the cavities of the superstructure and also at the both ends
of it. We investigated a RWG HOM coupler attached to the beam pipe through the
slots orientated along beam pipe axis (longitudinal slots), perpendicular to it
(azimutal slots) and at some angle to this axis. For dipole modes of both
polarizations damping two RWG in every design were used. This paper presents
the results obtained for scaled-up setup at 3 GHz at room temperature. The
advantages of HOM coupler with longitudinal slots for damping dipole modes and
compact HOM coupler with slots at some angle to the axis are shown. Arrangement
of HOM coupler in cryostat and heating due to HOM and FM losses are presented.
Calculations and design of the feeding RWG coupler for superstructure are also
presented.
|
0008001v1
|
2000-08-14
|
Design of a 3 GHz Accelerator Structure for the CLIC Test Facility (CTF 3) Drive Beam
|
For the CLIC two-beam scheme, a high-current, long-pulse drive beam is
required for RF power generation. Taking advantage of the 3 GHz klystrons
available at the LEP injector once LEP stops, a 180 MeV electron accelerator is
being constructed for a nominal beam current of 3.5 A and 1.5 microsecond pulse
length. The high current requires highly effective suppression of dipolar
wakes. Two concepts are investigated for the accelerating structure design: the
"Tapered Damped Structure" developed for the CLIC main beam, and the "Slotted
Iris - Constant Aperture" structure. Both use 4 SiC loads per cell for
effective higher-order mode damping. A full-size prototype of the TDS structure
has been built and tested successfully at full power. A first prototype of the
SICA structure is being built.
|
0008052v1
|
2000-08-17
|
Superconducting Superstructure for the TESLA Collider: New Results
|
A new cavity-chain layout has been proposed for the main linac of the TESLA
linear collider. This superstructure-layout is based upon four 7-cell
superconducting standing-wave cavities, coupled by short beam pipes. The main
advantages of the superstructure are an increase in the active accelerating
length in TESLA and a saving in rf components, especially power couplers, as
compared to the present 9-cell cavities. The proposed scheme allows to handle
the field-flatness tuning and the HOM damping at sub-unit level, in contrast to
standard multi-cell cavities. The superstructure-layout is extensively studied
at DESY since 1999. Computations have been performed for the rf properties of
the cavity-chain, the bunch-to-bunch energy spread and multibunch dynamics. A
copper model of the superstructure has been built in order to compare with the
simulations and for testing the field-profile tuning and the HOM damping
scheme. A "proof of principle" niobium prototype of the superstructure is now
under construction and will be tested with beam at the TESLA Test Facility in
2001. In this paper we present latest results of these investigations.
|
0008104v1
|
2000-08-20
|
An Investigation of Optimised Frequency Distributions for Damping Wakefields in X-Band Linacs for the NLC
|
In the NLC (Next Linear Collider) small misalignments in each of the
individual accelerator structures (or the accelerator cells) will give rise to
wakefields which kick the beam from its electrical axis. This wakefield can
cause BBU (Beam Break Up) or at the very least it will dilute the emittance of
the beam. Several Gaussian detuned structures have been designed and tested [1]
at SLAC and in this paper we explore new distributions with possibly better
damping properties. The progress of the beam through approximately 5,000
structures is monitored in phase space and results on this are presented.
[1] J.W. Wang et al, TUA03, LINAC2000
|
0008202v2
|
2001-04-14
|
Parameters for a 30 GeV Undulator Test Facility in the FFTB/LCLS
|
The parameters for a 30 GeV test beam are outlined for use with an undulator
in the FFTB tunnel where the LCLS will eventually be housed. It is proposed to
use the SLAC linac and damping rings in their present mode of operation for PEP
II injection, where 30 GeV beams are also delivered at 10 Hz to the FFTB. High
peak currents are obtained with the addition of a second bunch compressor in
the linac. In order to minimize the synchrotron radiation induced emittance
growth in the bunch compressor it is necessary to locate the new bunch
compressor at the low-energy end of the linac, just after the damping rings.
The bunch compressor is a duplicate of the LCLS chicane-style bunch compressor.
This test beam would provide an exciting possibility to test LCLS undulator
sections and provide a unique high-brightness source of incoherent X-rays and
begin developing the LCLS experimental station. The facility will also act as a
much needed accelerator test bed for the production, diagnostics and tuning of
very short bunches in preparation for the LCLS after the photo injector is
commissioned.
|
0104045v1
|
2001-10-05
|
Characterization of a Low Frequency Power Spectral Density f^(-gamma) in a Threshold Model
|
his study investigates the modifications of the thermal spectrum, at low
frequency, induced by an external damping on a system in heat contact with
internal fluctuating impurities. Those impurities can move among locations and
their oscillations are associated with a loss function depending on the model.
The fluctuation properties of the system are provided by a potential function
shaped by wells, in such a way that jumps between the stationary positions are
allowed. The power spectral density associated with this dissipation mechanism
shows a f^(-gamma)tail. The interest of this problem is that many systems are
characterized by a typical f^(-\gamma) spectral tail at low frequency. The
model presented in this article is based on a threshold type behaviour and its
generality allows applications in several fields. The effects of an external
force, introduced to produce damping, are studied by using both analytical
techniques and numerical simulations. The results obtained with the present
model show that no reduction of the power spectral density is appreciable below
the main peak of the spectral density.
|
0110019v1
|
2002-05-13
|
Damping of electromagnetic waves in low-collision electron-ion plasmas
|
Using previously developed method of two-dimensional Laplace transform we
obtain the characteristic equations k(\omega) for electromagnetic waves in
low-collision fully ionized plasma of a plane geometry. We apply here a new,
different from the one used in our previous paper, iteration procedure of
taking into account the Coulomb collisions. The waves are collisionally damping
in the same extent as electromagnetic waves. Despite the different from
previous paper form of the dispersion (poles) equation, the obtained decrements
for fast and slow wave modes coincide with results obtained in our earlier
paper, if one neglects the terms of higher orders in v^2/c^2, (v and c are
electron and light velocities). We point out how one can determine mutually
dependent boundary conditions allowing to eliminate simultaneously both the
backward and kinematical waves for transversal as well as for longitudinal
oscillations.
|
0205035v2
|
2002-06-01
|
Intrabeam scattering analysis of measurements at KEK's ATF damping ring
|
We derive a simple relation for estimating the relative emittance growth in x
and y due to intrabeam scattering (IBS) in electron storage rings. We show that
IBS calculations for the ATF damping ring, when using the formalism of
Bjorken-Mtingwa, a modified formalism of Piwinski (where eta squared divided by
beta has been replaced by the dispersion invariant), or a simple high-energy
approximate formula all give results that agree well. Comparing theory,
including the effect of potential well bunch lengthening, with a complete set
of ATF steady-state beam size vs. current measurements we find reasonably good
agreement for energy spread and horizontal emittance. The measured vertical
emittance, however, is larger than theory in both offset (zero current
emittance) and slope (emittance change with current). The slope error indicates
measurement error and/or additional current-dependent physics at the ATF; the
offset error, that the assumed Coulomb log is correct to within a factor of
1.75.
|
0206003v1
|
2002-08-24
|
Wakefield Band Partitioning In Linac Structures
|
In the NLC project multiple bunches of electrons and positrons will be
accelerated initially to a centre of mass of 500 GeV and later to 1 TeV or
more. In the process of accelerating 192 bunches within a pulse train,
wakefields are excited which kick the trailing bunches off axis and can cause
luminosity dilution and BBU (Beam Break Up). Several structures to damp the
wakefield have been designed and tested at SLAC and KEK and these have been
found to successfully damp the wakefield [1]. However, these 2pi/3 structures
suffered from electrical breakdown and this has prompted us to explore lower
group velocity structures operating at higher fundamental mode phase advances.
The wakefield partitioning amongst the bands has been found to change markedly
with increased phase advance. Here we report on general trends in the kick
factor and associated wakefield band partitioning in dipole bands as a function
of phase advance of the synchronous mode in linacs. These results are
applicable to both TW (travelling wave) and SW (standing wave) structures [1]
R.M. Jones et al, PAC99, also SLAC-PUB-8103
|
0208086v1
|
2003-01-30
|
Calculation of the Coherent Synchrotron Radiation Impedance from a Wiggler
|
Most studies of Coherent Synchrotron Radiation (CSR) have only considered the
radiation from independent dipole magnets. However, in the damping rings of
future linear colliders, a large fraction of the radiation power will be
emitted in damping wigglers. In this paper, the longitudinal wakefield and
impedance due to CSR in a wiggler are derived in the limit of a large wiggler
parameter $K$. After an appropriate scaling, the results can be expressed in
terms of universal functions, which are independent of $K$. Analytical
asymptotic results are obtained for the wakefield in the limit of large and
small distances, and for the impedance in the limit of small and high
frequencies.
|
0301073v1
|
2003-10-02
|
Damping factors for the gap-tooth scheme
|
An important class of problems exhibits macroscopically smooth behaviour in
space and time, while only a microscopic evolution law is known. For such
time-dependent multi-scale problems, the gap-tooth scheme has recently been
proposed. The scheme approximates the evolution of an unavailable (in closed
form) macroscopic equation in a macroscopic domain; it only uses appropriately
initialized simulations of the available microscopic model in a number of small
boxes. For some model problems, including numerical homogenization, the scheme
is essentially equivalent to a finite difference scheme, provided we repeatedly
impose appropriate algebraic constraints on the solution for each box. Here, we
demonstrate that it is possible to obtain a convergent scheme without
constraining the microscopic code, by introducing buffers that "shield" over
relatively short times the dynamics inside each box from boundary effects. We
explore and quantify the behavior of these schemes systematically through the
numerical computation of damping factors of the corresponding coarse
time-stepper, for which no closed formula is available.
|
0310014v1
|
2004-07-31
|
Propagation of optical excitations by dipolar interactions in metal nanoparticle chains
|
Dispersion relations for dipolar modes propagating along a chain of metal
nanoparticles are calculated by solving the full Maxwell equations, including
radiation damping. The nanoparticles are treated as point dipoles, which means
the results are valid only for a/d <= 1/3, where a is the particle radius and d
the spacing. The discrete modes for a finite chain are first calculated, then
these are mapped onto the dispersion relations appropriate for the infinite
chain. Computed results are given for a chain of 50-nm diameter Ag spheres
spaced by 75 nm. We find large deviations from previous quasistatic results:
Transverse modes interact strongly with the light line. Longitudinal modes
develop a bandwidth more than twice as large, resulting in a group velocity
that is more than doubled. All modes for which k_mode <= w/c show strongly
enhanced decay due to radiation damping.
|
0408003v2
|
2004-08-22
|
Tacoma Bridge Failure-- a Physical Model
|
The cause of the collapse of the Tacoma Narrows Bridge has been a topic of
much debate and confusion since the day it fell. Many mischaracterizations of
the observed phenomena have limited the widespread understanding of the
problem. Nevertheless, there has always been an abundance of evidence in favour
of a negative damping model. Negative damping, or positive feedback, is
responsible for many large amplitude oscillations observed in many
applications. In this paper, we will explain some well-known examples of
positive feedback. We will then present a feedback model, derived from
fundamental physics, capable of explaining a number of features observed in the
instabilities of many bridge decks. This model is supported by computational,
experimental and historical data.
|
0408101v1
|
2004-08-30
|
Short waves and cyclotron losses in the relativistic gyrokinetic theory
|
Radiation damping of the motion of charged particles in relativistic,
optically thin plasmas is described within the framework of the covariant
gyrokinetic theory. It involves description of the collisionless
single-particle dynamics as well as the Vlasov and Maxwell equations both
written in the covariant formulation. The damping causes corrections to the
phase-space trajectory of the particle, as well as to the form of the kinetic
equation itself, due to the failure of conditions of the Liouville theorem.
Both effects result independent of the gyrophase, which is retained as an
ignorable variable. In addition, the applicability range of the covariant
gyrokinetic theory is extended to describe short-wavelength perturbations with
the background of zero parallel electric field. The presented theory is
suitable for description of magnetized, relativistic, collisionless plasmas in
the context of astrophysical or laboratory problems. Non-uniquenes of the
gyrokinetic representation and consequences thereof are discussed.
|
0408128v1
|
2004-11-02
|
Supersymmetric free-damped oscillators: Adaptive observer estimation of the Riccati parameter
|
A supersymmetric class of free damped oscillators with three parameters has
been obtained in 1998 by Rosu and Reyes through the factorization of the Newton
equation. The supplementary parameter is the integration constant of the
general Riccati solution. The estimation of the latter parameter is performed
here by employing the recent adaptive observer scheme of Besancon et al., but
applied in a nonstandard form in which a time-varying quantity containing the
unknown Riccati parameter is estimated first. Results of computer simulations
are presented to illustrate the good feasibility of this approach for a case in
which the estimation is not easily accomplished by other means
|
0411019v2
|
2004-11-05
|
Wave-kinetic description of nonlinear photons
|
The nonlinear interaction, due to quantum electrodynamical (QED) effects,
between photons is investigated using a wave-kinetic description. Starting from
a coherent wave description, we use the Wigner transform technique to obtain a
set of wave-kinetic equations, the so called Wigner-Moyal equations. These
equations are coupled to a background radiation fluid, whose dynamics is
determined by an acoustic wave equation. In the slowly varying acoustic limit,
we analyse the resulting system of kinetic equations, and show that they
describe instabilities, as well as Landau-like damping. The instabilities may
lead to break-up and focusing of ultra-high intensity multi-beam systems, which
in conjunction with the damping may result in stationary strong field
structures. The results could be of relevance for the next generation of
laser-plasma systems.
|
0411058v1
|
2004-12-17
|
Optimal Determination of the Equilibrium Displacement of a Damped Harmonic Oscillator in the Presence of Thermal Noise
|
Using a matched filter technique, we derive the minimum variance, unbiased
estimator for the equilibrium displacement of a damped harmonic oscillator in
thermal equilibrium when interactions with the thermal bath are the leading
source of noise. We compare the variance in this optimal estimator with the
variance in other, commonly used estimators in the presence of pure thermal
noise and pure white noise. We also compare the variance in these estimators
for a mixture of white and thermal noise. This result has implications for
experimental design and the collection and analysis of data.
|
0412102v1
|
2006-01-13
|
Atomic collider into dual-isotope magneto-optical trap
|
When two of three pairs of the Gaussian laser beams of a traditional MOT are
misaligned in the racetrack configuration the effective coordinate-dependent
vortex force do arise. Then an atom is accelerated by this vortex force until
its velocity not balanced by the damping force. This situation may produce a
stable ring of revolving atoms of a certain radius. Due to the different
frequency and laser beams intensity dependences of the vortex, damping and
trapping forces it is possible to equalize the radii of two orbiting groups of
atoms in two-species or dual-isotope magneto-optical trap and so to arrange a
continuing collider of cooled atoms with the prescribed relative velocity. A
collider setup for atoms of two different types rotating with different angular
velocities along the same ring-like trajectory into MOT of the conventional
six-beam geometry is proposed and designed on example of two rubidium isotopes
Rb85 and Rb87.
|
0601097v1
|
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