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2011-02-02
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Harmonic Oscillator in Heat Bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark statistics
|
The stochastic dynamics of the damped harmonic oscillator in a heat bath is
simulated with an algorithm that is exact for time steps of arbitrary size.
Exact analytical results are given for correlation functions and power spectra
in the form they acquire when computed from experimental time-lapse recordings.
Three applications are discussed: (i) Effects of finite sampling-rate and
-time, described exactly here, are similar for other stochastic dynamical
systems-e.g. motile micro-organisms and their time-lapse recorded trajectories.
(ii) The same statistics is satisfied by any experimental system to the extent
it is interpreted as a damped harmonic oscillator at finite temperature-such as
an AFM cantilever. (iii) Three other models of fundamental interest are
limiting cases of the damped harmonic oscillator at finite temperature; it
consequently bridges their differences and describes effects of finite sampling
rate and sampling time for these models as well. Finally, we give a brief
discussion of nondimensionalization.
|
1102.0524v1
|
2011-02-04
|
A symmetry trip from Caldirola to Bateman damped systems
|
For the Caldirola-Kanai system, describing a quantum damped harmonic
oscillator, a couple of constant-of-motion operators generating the Heisenberg
algebra can be found. The inclusion of the standard time evolution symmetry in
this algebra for damped systems, in a unitary manner, requires a non-trivial
extension of this basic algebra and hence the physical system itself.
Surprisingly, this extension leads directly to the so-called Bateman's dual
system, which now includes a new particle acting as an energy reservoir. The
group of symmetries of the dual system is presented, as well as a quantization
that implies, in particular, a first-order Schr\"odinger equation. The usual
second-order equation and the inclusion of the original Caldirola-Kanai model
in Bateman's system are also discussed.
|
1102.0990v1
|
2011-03-03
|
Determination of the pairing state in iron-based superconductors through neutron scattering
|
We calculate the spin susceptibility in the s_{+-} and s_{++} superconducting
states of the iron pnictides using the effective five orbital model and
considering the quasiparticle damping. For the experimentally evaluated
magnitude of the quasiparticle damping and the superconducting gap, the results
at the wave vector ~ (pi,0) show that the s_{+-} state is more consistent with
the neutron scattering experiments, while for larger quasiparticle damping and
the superconducting gap, the s_{++} state can be more consistent. To
distinguish between two cases that reproduce the experiments at the wave vector
~ (pi,0), we propose to investigate experimentally the wave vector ~ (pi,pi).
|
1103.0586v2
|
2011-03-03
|
Transmission of classical and quantum information through a quantum memory channel with damping
|
We consider the transfer of classical and quantum information through a
memory amplitude damping channel. Such a quantum channel is modeled as a damped
harmonic oscillator, the interaction between the information carriers - a train
of qubits - and the oscillator being of the Jaynes-Cummings kind. We prove that
this memory channel is forgetful, so that quantum coding theorems hold for its
capacities. We analyze entropic quantities relative to two uses of this
channel. We show that memory effects improve the channel aptitude to transmit
both classical and quantum information, and we investigate the mechanism by
which memory acts in changing the channel transmission properties.
|
1103.0747v2
|
2011-03-08
|
Steady states of the parametric rotator and pendulum
|
We discuss several steady-state rotation and oscillation modes of the planar
parametric rotator and pendulum with damping. We consider a general elliptic
trajectory of the suspension point for both rotator and pendulum, for the
latter at an arbitrary angle with gravity, with linear and circular
trajectories as particular cases. We treat the damped, non-linear equation of
motion of the parametric rotator and pendulum perturbatively for small
parametric excitation and damping, although our perturbative approach can be
extended to other regimes as well. Our treatment involves only ordinary
second-order differential equations with constant coefficients, and provides
numerically accurate perturbative solutions in terms of elementary functions.
Some of the steady-state rotation and oscillation modes studied here have not
been discussed in the previous literature. Other well-known ones, such as
parametric resonance and the inverted pendulum, are extended to elliptic
parametric excitation tilted with respect to gravity. The results presented
here should be accessible to advanced undergraduates, and of interest to
graduate students and specialists in the field of non-linear mechanics.
|
1103.1413v1
|
2011-03-18
|
Time-periodic solitons in a damped-driven nonlinear Schrödinger equation
|
Time-periodic solitons of the parametrically driven damped nonlinear
Schr\"odinger equation are obtained as solutions of the boundary-value problem
on a two-dimensional spatiotemporal domain. We follow the transformation of the
periodic solitons as the strength of the driver is varied. The resulting
bifurcation diagrams provide a natural explanation for the overall form and
details of the attractor chart compiled previously via direct numerical
simulations. In particular, the diagrams confirm the occurrence of the
period-doubling transition to temporal chaos for small values of dissipation
and the absence of such transitions for larger dampings. This difference in the
soliton's response to the increasing driving strength can be traced to the
difference in the radiation frequencies in the two cases. Finally, we relate
the soliton's temporal chaos to the homoclinic bifurcation.
|
1103.3604v1
|
2011-03-28
|
Motion of position-dependent mass as a damping-antidamping process: Application to the Fermi gas and to the Morse potential
|
The object of this paper is to investigate, classically and quantum
mechanically, the relation existing between the position-dependent effective
mass and damping-antidamping dynamics. The quantization of the equations of
motion is carried out using the geometric interpretation of the motion, and we
compare it with the one based on the ordering ambiguity scheme. Furthermore, we
apply the obtained results to a Fermi gas of damped-antidamped particles, and
we solve the Schr\"odinger equation for an exponentially increasing
(decreasing) mass in the presence of the Morse potential.
|
1103.5440v3
|
2011-04-30
|
Resonantly Damped Propagating Kink Waves in Longitudinally Stratified Solar Waveguides
|
It has been shown that resonant absorption is a robust physical mechanism to
explain the observed damping of magnetohydrodynamic (MHD) kink waves in the
solar atmosphere due to naturally occurring plasma inhomogeneity in the
direction transverse to the direction of the magnetic field. Theoretical
studies of this damping mechanism were greatly inspired by the first
observations of post-flare standing kink modes in coronal loops using the
Transition Region And Coronal Explorer (TRACE). More recently, these studies
have been extended to explain the attenuation of propagating coronal kink waves
observed by the Coronal Multi-Channel Polarimeter (CoMP). In the present study,
for the first time we investigate the properties of propagating kink waves in
solar waveguides including the effects of both longitudinal and transverse
plasma inhomogeneity. Importantly, it is found that the wavelength is only
dependent on the longitudinal stratification and the amplitude is simply a
product of the two effects. In light of these results the advancement of solar
atmospheric magnetoseismology by exploiting high spatial/temporal resolution
observations of propagating kink waves in magnetic waveguides to determine the
length scales of the plasma inhomogeneity along and transverse to the direction
of the magnetic field is discussed.
|
1105.0067v1
|
2011-05-05
|
The effect of twisted magnetic field on the resonant absorption of MHD waves in coronal loops
|
The standing quasi modes in a cylindrical incompressible flux tube with
magnetic twist that undergoes a radial density structuring is considered in
ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a
linearly varying density profile. Using the relevant connection formulae, the
dispersion relation for the MHD waves is derived and solved numerically to
obtain both the frequencies and damping rates of the fundamental and
first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was
found that a magnetic twist will increase the frequencies, damping rates and
the ratio of the oscillation frequency to the damping rate of these modes. The
period ratio P_1/P_2 of the fundamental and its first-overtone surface waves
for kink (m=1) and fluting (m=2,3) modes is lower than 2 (the value for an
untwisted loop) in the presence of twisted magnetic field. For the kink modes,
particularly, the magnetic twists B_{\phi}/B_z=0.0065 and 0.0255 can achieve
deviations from 2 of the same order of magnitude as in the observations.
Furthermore, for the fundamental kink body waves, the frequency bandwidth
increases with increasing the magnetic twist.
|
1105.1120v1
|
2011-05-05
|
Interpreting Graph Cuts as a Max-Product Algorithm
|
The maximum a posteriori (MAP) configuration of binary variable models with
submodular graph-structured energy functions can be found efficiently and
exactly by graph cuts. Max-product belief propagation (MP) has been shown to be
suboptimal on this class of energy functions by a canonical counterexample
where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008).
In this work, we show that under a particular scheduling and damping scheme,
MP is equivalent to graph cuts, and thus optimal. We explain the apparent
contradiction by showing that with proper scheduling and damping, MP always
converges to an optimal fixed point. Thus, the canonical counterexample only
shows the suboptimality of MP with a particular suboptimal choice of schedule
and damping. With proper choices, MP is optimal.
|
1105.1178v1
|
2011-05-14
|
Crossovers in the non-Markovian dynamics of two-qubit entanglements
|
We study the entanglement dynamics of two non-interacting, spatially
separated qubits subject to local environment noises. Based on exactly solvable
models for non-Markovian amplitude damping and phase damping noises, we are
able to analyze the entanglement dynamics of the two qubits for different
coupling bandwidths and different detunings. We show that entanglement
oscillations can occur for both amplitude and phase damping noises. Moreover,
we demonstrate that changing the coupling bandwidth can lead to crossover
between dissipative and non-dissipative entanglement dynamics, while varying
the detuning controls the crossover between strong and weak coupling limits.
Our findings can help provide a synthesized picture for the entanglement
dynamics of two qubits subject to local environment noises.
|
1105.2859v2
|
2011-06-17
|
Controlling Excitations Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator
|
We investigate the action of time dependent detunings upon the excitation
inversion of a Cooper pair box interacting with a nanomechanical resonator. The
method employs the Jaynes-Cummings model with damping, assuming different decay
rates of the Cooper pair box and various fixed and t-dependent detunings. It is
shown that while the presence of damping plus constant detunings destroy the
collapse/revival effects, convenient choices of time dependent detunings allow
one to reconstruct such events in a perfect way. It is also shown that the mean
excitation of the nanomechanical resonator is more robust against damping of
the Cooper pair box for convenient values of t-dependent detunings.
|
1106.3379v1
|
2011-06-22
|
Tunable Magnonic Frequency and Damping in [Co/Pd]8 Multilayers with Variable Co Layer Thickness
|
We report the experimental observation of collective picosecond magnetization
dynamics in [Co/Pd]8 multilayers with perpendicular magnetic anisotropy. The
precession frequency shows large and systematic variation from about 5 GHz to
about 90 GHz with the decrease in the Co layer thickness from 1.0 nm to 0.22 nm
due to the linear increase in the perpendicular magnetic anisotropy. The
damping coefficient 'alpha' is found to be inversely proportional to the Co
layer thickness and a linear relation between the perpendicular magnetic
anisotropy and 'alpha' is established. We discuss the possible reasons behind
the enhanced damping as the d-d hybridization at the interface and spin
pumping. These observations are significant for the applications of these
materials in spintronics and magnonic crystals.
|
1106.4491v1
|
2011-07-04
|
An HI column density threshold for cold gas formation in the Galaxy
|
We report the discovery of a threshold in the HI column density of Galactic
gas clouds below which the formation of the cold phase of HI is inhibited. This
threshold is at $N_{HI} = 2 \times 10^{20}$ per cm$^{2}$; sightlines with lower
HI column densities have high spin temperatures (median $T_s \sim 1800$ K),
indicating low fractions of the cold neutral medium (CNM), while sightlines
with $N_{HI} \ge 2 \times 10^{20}$ per cm$^{2}$ have low spin temperatures
(median $T_s \sim 240$ K), implying high CNM fractions. The threshold for CNM
formation is likely to arise due to inefficient self-shielding against
ultraviolet photons at lower HI column densities. The threshold is similar to
the defining column density of a damped Lyman-$\alpha$ absorber; this indicates
a physical difference between damped and sub-damped Lyman-$\alpha$ systems,
with the latter class of absorbers containing predominantly warm gas.
|
1107.0744v2
|
2011-07-11
|
One-dimensional vertical dust strings in a glass box
|
The oscillation spectrum of a one-dimensional vertical dust string formed
inside a glass box on top of the lower electrode in a GEC reference cell was
studied. A mechanism for creating a single vertical dust string is described.
It is shown that the oscillation amplitudes, resonance frequencies, damping
coefficients, and oscillation phases of the dust particles separate into two
distinct groups. One group exhibits low damping coefficients, increasing
amplitudes and decreasing resonance frequencies for dust particles closer to
the lower electrode. The other group shows high damping coefficients but
anomalous resonance frequencies and amplitudes. At low oscillation frequencies,
the two groups are also separated by a {\pi}-phase difference. One possible
cause for the difference in behavior between the two groups is discussed.
|
1107.2074v1
|
2011-07-24
|
Traveling kinks in cubic nonlinear Ginzburg-Landau equations
|
Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable
are usually derived from Ginzburg-Landau free energy functionals frequently
encountered in several fields of physics. Many authors considered in the past
damped versions of such equations with the damping term added by hand
simulating the friction due to the environment. It is known that even in this
damped case kink solutions can exist. By means of a factorization method, we
provide analytic formulas for several possible kink solutions of such equations
of motion in the undriven and constant field driven cases, including the
recently introduced Riccati parameter kinks which were not considered
previously in such a context. The latter parameter controls the delay of the
switching stage of the kinks
|
1107.4773v4
|
2011-08-22
|
On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping
|
We study the asymptotic stability of a dissipative evolution in a Hilbert
space subject to intermittent damping. We observe that, even if the
intermittence satisfies a persistent excitation condition, if the Hilbert space
is infinite-dimensional then the system needs not being asymptotically stable
(not even in the weak sense). Exponential stability is recovered under a
generalized observability inequality, allowing for time-domains that are not
intervals. Weak asymptotic stability is obtained under a similarly generalized
unique continuation principle. Finally, strong asymptotic stability is proved
for intermittences that do not necessarily satisfy some persistent excitation
condition, evaluating their total contribution to the decay of the trajectories
of the damped system. Our results are discussed using the example of the wave
equation, Schr\"odinger's equation and, for strong stability, also the special
case of finite-dimensional systems.
|
1108.4327v2
|
2011-08-26
|
Aligned Major Axes in a Planetary System without Tidal Evolution: The 61 Virginis example
|
Tidal damping of one of the orbits in a planetary system can lead to aligned
major-axes (the so-called "fixed-point" condition), but currently aligned major
axes do not necessarily imply such a history. An example is the nominal orbital
solution for the 61 Virginis system where two orbits librate about alignment,
but evaluation of the eigenmodes of the secular theory shows it could not be
the result of tidal damping but rather of initial conditions. Nevertheless, the
amplitudes of the eigenmodes suggest that this system may have undergone some
degree of tidal damping.
|
1108.5369v1
|
2011-09-09
|
Optimal linear optical implementation of a single-qubit damping channel
|
We experimentally demonstrate a single-qubit decohering quantum channel using
linear optics. We implement the channel, whose special cases include both the
amplitude-damping channel and the bit-flip channel, using a single, static
optical setup. Following a recent theoretical result [M. Piani et al., Phys.
Rev. A, 84, 032304 (2011)], we realize the channel in an optimal way,
maximizing the probability of success, i.e., the probability for the photonic
qubit to remain in its encoding. Using a two-photon entangled resource, we
characterize the channel using ancilla-assisted process tomography and find
average process fidelities of 0.9808 \pm 0.0002 and 0.9762 \pm 0.0002 for
amplitude-damping and the bit-flip case, respectively.
|
1109.2070v1
|
2011-11-20
|
Detection of picosecond magnetization dynamics of 50 nm magnetic dots down to the single dot regime
|
We report an all-optical time-domain detection of picosecond magnetization
dynamics of arrays of 50 nm Ni80Fe20 (permalloy) dots down to the single
nanodot regime. In the single nanodot regime the dynamics reveals one dominant
resonant mode corresponding to the edge mode of the 50 nm dot with slightly
higher damping than that of the unpatterned thin film. With the increase in
areal density of the array both the precession frequency and damping increases
significantly due to the increase in magnetostatic interactions between the
nanodots and a mode splitting and sudden jump in apparent damping are observed
at an edge-to-edge separation of 50 nm.
|
1111.4625v1
|
2011-12-02
|
An energy-based computational method in the analysis of the transmission of energy in a chain of coupled oscillators
|
In this paper we study the phenomenon of nonlinear supratransmission in a
semi-infinite discrete chain of coupled oscillators described by modified
sine-Gordon equations with constant external and internal damping, and subject
to harmonic external driving at the end. We develop a consistent and
conditionally stable finite-difference scheme in order to analyze the effect of
damping in the amount of energy injected in the chain of oscillators; numerical
bifurcation analyses to determine the dependence of the amplitude at which
supratransmission first occurs with respect to the frequency of the driving
oscillator are carried out in order to show the consequences of damping on
harmonic phonon quenching and the delay of appearance of critical amplitude.
|
1112.0581v1
|
2012-01-09
|
Universal response of optimal granular damping devices
|
Granular damping devices constitute an emerging technology for the
attenuation of vibrations based on the dissipative nature of particle
collisions. We show that the performance of such devices is independent of the
material properties of the particles for working conditions where damping is
optimal. Even the suppression of a dissipation mode (collisional or frictional)
is unable to alter the response. We explain this phenomenon in terms of the
inelastic collapse of granular materials. These findings provide a crucial
standpoint for the design of such devices in order to achieve the desired low
maintenance feature that makes particle dampers particularly suitable to harsh
environments.
|
1201.1866v2
|
2012-01-09
|
Radiative energy loss reduction in an absorptive plasma
|
The influence of the damping of radiation on the radiative energy loss
spectrum of a relativistic charge in an infinite, absorptive plasma is studied.
We find increasing reduction of the spectrum with increasing damping. Our
studies, which represent an Abelian approximation for the colour charge
dynamics in the quark-gluon plasma, may influence the analysis of jet quenching
phenomena observed in high-energy nuclear collisions. Here, we focus on a
formal discussion of the limiting behaviour with increasing radiation
frequency. In an absorptive (and polarizable) medium, this is determined by the
behaviour of the exponential damping factor entering the spectrum and the
formation time of radiation.
|
1201.1890v1
|
2012-01-10
|
Nonequilibrium Damping of Collective Motion of Homogeneous Cold Fermi Condensates with Feshbach Resonances
|
Collisionless damping of a condensate of cold Fermi atoms, whose scattering
is controlled by a Feshbach resonance, is explored throughout the BCS and BEC
regimes when small perturbations on its phase and amplitude modes are turned on
to drive the system slightly out of equilibrium. Using a one-loop effective
action, we first recreate the known result that for a broad resonance the
amplitude of the condensate decays as $t^{-1/2}$ at late times in the BCS
regime whereas it decays as $t^{-3/2}$ in the BEC regime. We then examine the
case of an idealized narrow resonance, and find that this collective mode
decays as $t^{-3/2}$ throughout both the BCS and BEC regimes. Although this
seems to contradict earlier results that damping is identical for both broad
and narrow resonances, the breakdown of the narrow resonance limit restores
this universal behaviour. More measureably, the phase perturbation may give a
shift on the saturated value to which the collective amplitude mode decays,
which vanishes only in the deep BCS regime when the phase and amplitude modes
are decoupled.
|
1201.2019v1
|
2012-01-30
|
Modeling electricity spot prices using mean-reverting multifractal processes
|
We discuss stochastic modeling of volatility persistence and
anti-correlations in electricity spot prices, and for this purpose we present
two mean-reverting versions of the multifractal random walk (MRW). In the first
model the anti-correlations are modeled in the same way as in an
Ornstein-Uhlenbeck process, i.e. via a drift (damping) term, and in the second
model the anti-correlations are included by letting the innovations in the MRW
model be fractional Gaussian noise with H < 1/2. For both models we present
approximate maximum likelihood methods, and we apply these methods to estimate
the parameters for the spot prices in the Nordic electricity market. The
maximum likelihood estimates show that electricity spot prices are
characterized by scaling exponents that are significantly different from the
corresponding exponents in stock markets, confirming the exceptional nature of
the electricity market. In order to compare the damped MRW model with the
fractional MRW model we use ensemble simulations and wavelet-based variograms,
and we observe that certain features of the spot prices are better described by
the damped MRW model. The characteristic correlation time is estimated to
approximately half a year.
|
1201.6137v1
|
2012-05-06
|
Fractional wave equation and damped waves
|
In this paper, a fractional generalization of the wave equation that
describes propagation of damped waves is considered. In contrast to the
fractional diffusion-wave equation, the fractional wave equation contains
fractional derivatives of the same order $\alpha,\ 1\le \alpha \le 2$ both in
space and in time. We show that this feature is a decisive factor for
inheriting some crucial characteristics of the wave equation like a constant
propagation velocity of both the maximum of its fundamental solution and its
gravity and mass centers. Moreover, the first, the second, and the Smith
centrovelocities of the damped waves described by the fractional wave equation
are constant and depend just on the equation order $\alpha$. The fundamental
solution of the fractional wave equation is determined and shown to be a
spatial probability density function evolving in time that possesses finite
moments up to the order $\alpha$. To illustrate analytical findings, results of
numerical calculations and numerous plots are presented.
|
1205.1199v2
|
2012-05-14
|
Critical viscoelastic response in jammed solids
|
We determine the linear viscoelastic response of jammed packings of athermal
repulsive viscous spheres, a model for emulsions, wet foams, and soft colloidal
suspensions. We numerically measure the complex shear modulus, a fundamental
characterization of the response, and demonstrate that low frequency response
displays dynamic critical scaling near unjamming. Viscoelastic shear response
is governed by the relaxational eigenmodes of a packing. We use scaling
arguments to explain the distribution of eigenrates, which develops a
divergence at unjamming. We then derive the critical exponents characterizing
response, including a vanishing shear modulus, diverging viscosity, and
critical shear thinning regime. Finally, we demonstrate that macroscopic
rheology is sensitive to details of the local viscous force law. By varying the
ratio of normal and tangential damping coefficients, we identify and explain a
qualitative difference between systems with strong and weak damping of sliding
motion. When sliding is weakly damped there is no diverging time scale, no
diverging viscosity, and no critical shear thinning regime.
|
1205.2960v1
|
2012-06-11
|
Testing the 130 GeV gamma-ray line with high energy resolution detectors
|
Recently some hints of the existence of $\gamma$-ray line around 130 GeV are
reported according to the analysis of Fermi-LAT data. If confirmed it would be
the first direct evidence to show the existence of new physics beyond the
standard model. Here we suggest that using the forthcoming high energy
resolution $\gamma$-ray detectors, such as CALET and DAMPE, we may test whether
it is real line structure or just the background effect. For DAMPE like
detector with designed energy resolution $\sim1.5%$, a line significance will
reach $11\sigma$ for the same statistics as Fermi-LAT. For about 1.4 yr survey
observation, DAMPE may detect a $5\sigma$ signal of such a $\gamma$-ray line.
|
1206.2241v2
|
2012-06-14
|
Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction
|
We study matter-wave dark solitons in atomic Bose-Einstein condensates at
finite temperatures, under the effect of linear and periodic potentials. Our
model, namely a dissipative Gross-Pitaevskii equation, is treated analytically
by means of dark soliton perturbation theory, which results in a Newtonian
equation of motion for the dark soliton center. This reduced model, which
incorporates an effective washboard potential and an anti-damping term,
constitutes an example of an anti-damped Josephson junction. We present a
qualitative (local and global) analysis of the equation of motion. For
sufficiently small wavenumbers of the periodic potential and weak linear
potentials, the results are found to be in good agreement with pertinent ones
obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.
|
1206.2993v1
|
2012-06-15
|
Damping of giant dipole resonance in hot rotating nuclei
|
The phonon damping model (PDM) is extended to include the effect of angular
momentum at finite temperature. The model is applied to the study of damping of
giant dipole resonance (GDR) in hot and noncollectively rotating spherical
nuclei. The numerical results obtained for Mo88 and Sn106 show that the GDR
width increases with both temperature T and angular momentum M. At T > 4 MeV
and M<= 60 hbar the increase in the GDR width slows down for Sn106, whereas at
M<= 80 hbar the GDR widths in both nuclei nearly saturate. By adopting the
nuclear shear viscosity extracted from fission data at T= 0, it is shown that
the maximal value of the angular momentum for Mo88 and Sn106 should be around
46 and 55 hbar, respectively, so that the universal conjecture for the lower
bound of the specific shear viscosity for all fluids is not violated up to T= 5
MeV.
|
1206.3361v1
|
2012-06-18
|
Sampled-data design for robust control of a single qubit
|
This paper presents a sampled-data approach for the robust control of a
single qubit (quantum bit). The required robustness is defined using a sliding
mode domain and the control law is designed offline and then utilized online
with a single qubit having bounded uncertainties. Two classes of uncertainties
are considered involving the system Hamiltonian and the coupling strength of
the system-environment interaction. Four cases are analyzed in detail including
without decoherence, with amplitude damping decoherence, phase damping
decoherence and depolarizing decoherence. Sampling periods are specifically
designed for these cases to guarantee the required robustness. Two sufficient
conditions are presented for guiding the design of unitary control for the
cases without decoherence and with amplitude damping decoherence. The proposed
approach has potential applications in quantum error-correction and in
constructing robust quantum gates.
|
1206.3897v2
|
2012-06-25
|
Trap anharmonicity and sloshing mode of a Fermi gas
|
For a gas trapped in a harmonic potential, the sloshing (or Kohn) mode is
undamped and its frequency coincides with the trap frequency, independently of
the statistics, interaction and temperature of the gas. However, experimental
trap potentials have usually Gaussian shape and anharmonicity effects appear as
the temperature and, in the case of Fermions, the filling of the trap are
increased. We study the sloshing mode of a degenerate Fermi gas in an
anharmonic trap within the Boltzmann equation, including in-medium effects in
both the transport and collision terms. The calculated frequency shifts and
damping rates of the sloshing mode due to the trap anharmonicity are in
satisfactory agreement with the available experimental data. We also discuss
higher-order dipole, octupole, and bending modes and show that the damping of
the sloshing mode is caused by its coupling to these modes.
|
1206.5688v2
|
2012-09-06
|
Radiative energy loss in the absorptive QGP: taming the long formation lengths in coherent emission
|
In an absorptive plasma, damping of radiation mechanisms can influence the
bremsstrahlung formation in case of large radiation formation lengths. We study
qualitatively the influence of this effect on the gluon bremsstrahlung spectrum
off heavy quarks in the quark-gluon plasma. Independent of the heavy-quark
mass, the spectrum is found to be strongly suppressed in an intermediate gluon
energy region which grows with increasing gluon damping rate and increasing
energy of the heavy quark. Thus, just as polarization effects in the plasma
render the bremsstrahlung spectra independent of the quark mass in the soft
gluon regime, damping effects tend to have a similar impact for larger gluon
energies.
|
1209.1149v1
|
2012-09-17
|
Power spectra in the eikonal approximation with adiabatic and non-adiabatic modes
|
We use the so-called eikonal approximation, recently introduced in the
context of cosmological perturbation theory, to compute power spectra for
multi-component fluids. We demonstrate that, at any given order in standard
perturbation theory, multipoint power spectra do not depend on the large-scale
adiabatic modes. Moreover, we employ perturbation theories to decipher how
nonadiabatic modes, such as a relative velocity between two different
components, damp the small-scale matter power spectrum, a mechanism recently
described in the literature. In particular, we do an explicit calculation at
1-loop order of this effect. While the 1-loop result eventually breaks down, we
show how the damping effect can be fully captured by the help of the eikonal
approximation. A relative velocity not only induces mode damping but also
creates large-scale anisotropic modulations of the matter power spectrum
amplitude. We illustrate this for the Local Group environment.
|
1209.3662v2
|
2012-09-26
|
Linear response theory for hydrodynamic and kinetic equations with long-range interactions
|
We apply the linear response theory to systems with long-range interactions
described by hydrodynamic equations such as the Euler, Smoluchowski, and damped
Euler equations. We analytically determine the response of the system submitted
to a pulse and to a step function. We compare these results with those obtained
for collisionless systems described by the Vlasov equation. We show that, in
the linear regime, the evolution of a collisionless system (Vlasov) with the
waterbag distribution is the same as the evolution of a collision-dominated gas
without dissipation (Euler). In this analogy, the maximum velocity of the
waterbag distribution plays the role of the velocity of sound in the
corresponding barotropic gas. When submitted to a step function, these systems
exhibit permanent oscillations. Other distributions exhibit Landau damping and
relax towards a steady state. We illustrate this behaviour with the Cauchy
distribution which can be studied analytically. We apply our results to the HMF
model and obtain a generalized Curie-Weiss law for the magnetic susceptibility.
Finally, we compare the linear response theory to the initial value problem for
the linearized Vlasov equation and report a case of algebraic damping of the
initial perturbation.
|
1209.5987v1
|
2012-09-15
|
Phase mixing of propagating Alfven waves in a stratified atmosphere: Solar spicules
|
Alfvenic waves are thought to play an important role in coronal heating and
solar wind acceleration. Recent observations by Hinode/SOT showed that the
spicules mostly exhibit upward propagating high frequency waves. Here we
investigate the dissipation of such waves due to phase mixing in stratified
environment of solar spicules. Since they are highly dynamic structures with
speeds at about significant fractions of the Alfven phase speed, we take into
account the effects of steady flows. Our numerical simulations show that in the
presence of stratification due to gravity, damping takes place in space than in
time. The exponential damping low, exp(-At^3), is valid under spicule
conditions, however the calculated damping time is much longer than the
reported spicule lifetimes from observations.
|
1210.0485v1
|
2012-10-03
|
Effect of temperature and velocity on superlubricity
|
We study the effects of temperature and sliding velocity on superlubricity in
numerical simulations of the Frenkel-Kontorova model. We show that resonant
excitations of the phonons in an incommensurate sliding body lead to an
effective friction and to thermal equilibrium with energy distributed over the
internal degrees of freedom. For finite temperature, the effective friction can
be described well by a viscous damping force, with a damping coefficient that
emerges naturally from the microscopic dynamics. This damping coefficient is a
non-monotonic function of the sliding velocity which peaks around resonant
velocities and increases with temperature. At low velocities, it remains finite
and nonzero, indicating the preservation of superlubricity in the zero-velocity
limit. Finally, we propose experimental systems in which our results could be
verified.
|
1210.1124v1
|
2012-10-04
|
Basic microscopic plasma physics unified and simplified by N-body classical mechanics
|
Debye shielding, collisional transport, Landau damping of Langmuir waves, and
spontaneous emission of these waves are introduced, in typical plasma physics
textbooks, in different chapters. This paper provides a compact unified
introduction to these phenomena without appealing to fluid or kinetic models,
but by using Newton's second law for a system of $N$ electrons in a periodic
box with a neutralizing ionic background. A rigorous equation is derived for
the electrostatic potential. Its linearization and a first smoothing reveal
this potential to be the sum of the shielded Coulomb potentials of the
individual particles. Smoothing this sum yields the classical Vlasovian
expression including initial conditions in Landau contour calculations of
Langmuir wave growth or damping. The theory is extended to accommodate a
correct description of trapping or chaos due to Langmuir waves. In the linear
regime, the amplitude of such a wave is found to be ruled by Landau growth or
damping and by spontaneous emission. Using the shielded potential, the
collisional diffusion coefficient is computed for the first time by a
convergent expression including the correct calculation of deflections for all
impact parameters. Shielding and collisional transport are found to be two
related aspects of the repulsive deflections of electrons.
|
1210.1546v2
|
2012-10-11
|
Measurement of the damping of nuclear shell effect in the doubly magic $^{208}$Pb region
|
The damping of the nuclear shell effect with excitation energy has been
measured through an analysis of the neutron spectra following the triton
transfer in the $^7$Li induced reaction on $^{205}$Tl. The measured neutron
spectra demonstrate the expected large shell correction energy for the nuclei
in the vicinity of doubly magic $^{208}$Pb and a small value for $^{184}$W. A
quantitative extraction of the allowed values of the damping parameter
$\gamma$, along with those for the asymptotic nuclear level density parameter
$\tilde{a}$, has been made for the first time.
|
1210.3213v2
|
2012-10-16
|
Optimal control of laser plasma instabilities using Spike Trains of Uneven Duration and Delay (STUD pulses) for ICF and IFE
|
An adaptive method of controlling parametric instabilities in laser produced
plasmas is proposed. It involves fast temporal modulation of a laser pulse on
the fastest instability's amplification time scale, adapting to changing and
unknown plasma conditions. These pulses are comprised of on and off sequences
having at least one or two orders of magnitude contrast between them. Such
laser illumination profiles are called STUD pulses for Spike Trains of Uneven
Duration and Delay. The STUD pulse program includes scrambling the speckle
patterns spatially in between the laser spikes. The off times allow damping of
driven waves. The scrambling of the hot spots allows tens of damping times to
elapse before hot spot locations experience recurring high intensity spikes.
Damping in the meantime will have healed the scars of past growth. Another
unique feature of STUD pulses on crossing beams is that their temporal profiles
can be interlaced or staggered, and their interactions thus controlled with an
on-off switch and a dimmer.
|
1210.4462v1
|
2012-10-28
|
Mass Dependence of Instabilities of an Oscillator with Multiplicative and Additive Noise
|
We study the instabilities of a harmonic oscillator subject to additive and
dichotomous multiplicative noise, focussing on the dependance of the
instability threshold on the mass. For multiplicative noise in the damping, the
instability threshold is crossed as the mass is decreased, as long as the
smaller damping is in fact negative. For multiplicative noise in the stiffness,
the situation is more complicated and in fact the transition is reentrant for
intermediate noise strength and damping. For multiplicative noise in the mass,
the results depend on the implementation of the noise. One can take the
velocity or the momentum to be conserved as the mass is changed. In these cases
increasing the mass destabilizes the system. Alternatively, if the change in
mass is caused by the accretion/loss of particles to the Brownian particle,
these processes are asymmetric with momentum conserved upon accretion and
velocity upon loss. In this case, there is no instability, as opposed to the
other two implementations. We also study the distribution of the energy,
finding a power-law cutoff at a value which increases with time.
|
1210.7433v1
|
2012-10-30
|
Extending the Concept of Analog Butterworth Filter for Fractional Order Systems
|
This paper proposes the design of Fractional Order (FO) Butterworth filter in
complex w-plane (w=sq; q being any real number) considering the presence of
under-damped, hyper-damped, ultra-damped poles. This is the first attempt to
design such fractional Butterworth filters in complex w-plane instead of
complex s-plane, as conventionally done for integer order filters. Firstly, the
concept of fractional derivatives and w-plane stability of linear fractional
order systems are discussed. Detailed mathematical formulation for the design
of fractional Butterworth-like filter (FBWF) in w-plane is then presented.
Simulation examples are given along with a practical example to design the FO
Butterworth filter with given specifications in frequency domain to show the
practicability of the proposed formulation.
|
1210.8194v3
|
2012-11-24
|
Effects of Quantum Error Correction on Entanglement Sudden Death
|
We investigate the effects of error correction on non-local quantum coherence
as a function of time, extending the study by Sainz and Bj\"ork. We consider
error correction of amplitude damping, pure phase damping and combinations of
amplitude and phase damping as they affect both fidelity and quantum
entanglement. Initial two-qubit entanglement is encoded in arbitrary real
superpositions of both \Phi-type and \Psi-type Bell states. Our main focus is
on the possibility of delay or prevention of ESD (early stage decoherence, or
entanglement sudden death). We obtain the onset times for ESD as a function of
the state-superposition mixing angle. Error correction affects entanglement and
fidelity differently, and we exhibit initial entangled states for which error
correction increases fidelity but decreases entanglement, and vice versa.
|
1211.5654v2
|
2012-12-04
|
Polarization dependence of phonon influences in exciton-biexciton quantum dot systems
|
We report on a strong dependence of the phonon-induced damping of Rabi
dynamics in an optically driven exciton-biexciton quantum dot system on the
polarization of the exciting pulse. While for a fixed pulse intensity the
damping is maximal for linearly polarized excitation, it decreases with
increasing ellipticity of the polarization. This finding is most remarkable
considering that the carrier-phonon coupling is spin-independent. In addition
to simulations based on a numerically exact real-time path integral approach,
we present an analysis within a weak coupling theory that allows for analytical
expressions for the pertinent damping rates. We demonstrate that an efficient
coupling to the biexciton state is of central importance for the reported
polarization dependencies. Further, we discuss influences of various system
parameters and show that for finite biexciton binding energies Rabi scenarios
differ qualitatively from the widely studied two-level dynamics.
|
1212.0642v1
|
2012-12-10
|
Heat-induced damping modification in YIG/Pt hetero-structures
|
We experimentally demonstrate the manipulation of magnetization relaxation
utilizing a temperature difference across the thickness of an yttrium iron
garnet/platinum (YIG/Pt) hetero-structure: the damping is either increased or
decreased depending on the sign of the temperature gradient. This effect might
be explained by a thermally-induced spin torque on the magnetization
precession. The heat-induced variation of the damping is detected by microwave
techniques as well as by a DC voltage caused by spin pumping into the adjacent
Pt layer and the subsequent conversion into a charge current by the inverse
spin Hall effect.
|
1212.2073v1
|
2012-12-13
|
Surface plasmon polaritons in a semi-bounded degenerate plasma: role of spatial dispersion and collisions
|
Surface plasmon polaritons (SPPs) in a semi-bounded degenerate plasma (e.g.,
a metal) are studied using the quasiclassical mean-field kinetic model, taking
into account the spatial dispersion of the plasma (due to quantum degeneracy of
electrons) and electron-ion (electron-lattice, for metals) collisions. SPP
dispersion and damping are obtained in both retarded ($\omega/k_z\sim c$) and
non-retarded ($\omega/k_z\ll c$) regions, as well as in between. It is shown
that the plasma spatial dispersion significantly affects the properties of
SPPs, especially at short wavelengths (less than the collisionless skin depth,
$\lambda\lesssim c/\omega_{pe}$). Namely, the collisionless (Landau) damping of
SPPs (due to spatial dispersion) is comparable to the purely collisional
(Ohmic) damping (due to electron-lattice collisions) in a wide range of SPP
wavelengths, e.g., from $\lambda\sim20$ nm to $\lambda\sim0.8$ nm for SPP in
gold at T=293 K, and from $\lambda\sim400$ nm to $\lambda\sim0.7$ nm for SPPs
in gold at T=100 K. The spatial dispersion is also shown to affect, in a
qualitative way, the dispersion of SPPs at short wavelengths $\lambda\lesssim
c/\omega_{pe}$.
|
1212.3040v1
|
2012-12-13
|
Branching of quasinormal modes for nearly extremal Kerr black holes
|
We show that nearly extremal Kerr black holes have two distinct sets of
quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes
(DMs). The ZDMs exist for all harmonic indices $l$ and $m \ge 0$, and their
frequencies cluster onto the real axis in the extremal limit. The DMs have
nonzero damping for all black hole spins; they exist for all counterrotating
modes ($m<0$) and for corotating modes with $0\leq \mu\lesssim \mu_c=0.74$ (in
the eikonal limit), where $\mu\equiv m/(l+1/2)$. When the two families coexist,
ZDMs and DMs merge to form a single set of quasinormal modes as the black hole
spin decreases. Using the effective potential for perturbations of the Kerr
spacetime, we give intuitive explanations for the absence of DMs in certain
areas of the spectrum and for the branching of the spectrum into ZDMs and DMs
at large spins.
|
1212.3271v1
|
2012-12-31
|
Effects of lateral device size and material properties on the ferromagnetic resonance response of spinwave eigen-modes in magnetic devices
|
We analyze the effects of lateral device size and magnetic material
parameters on the ferromagnetic resonance (FMR) response. Results presented are
directly relevant to widely used FMR experimental techniques for extracting
magnetic parameters from thin films, the results of which are often assumed to
carry over to corresponding nanometer-sized patterned devices. We show that
there can be significant variation in the FMR response with device size, and
that the extent of the variation depends on the magnetic material properties.
This explains, for example, why different experiments along these lines have
yielded different size-dependent trends from damping measurements. Observed
trends with increasing size and different material parameters are explained
through the evolution of three distinct eigen-modes, demonstrating the
respective roles of demagnetization and exchange. It is also shown that there
is a crossover of dominant eigen-modes in the response signal, accompanied by
conjugating edge-type modes, leading to evident effects in measured linewidth
and damping. Among the sizes considered, in higher saturation magnetization, we
observe as much as a 40% increase in apparent damping, due solely to device
size variation.
|
1212.6835v1
|
2013-01-16
|
Gain-tunable optomechanical cooling in a laser cavity
|
We study the optical cooling of the resonator mirror in a
cavity-optomechanical system that contains an optical gain medium. We find that
the optical damping rate is vanishingly small for an incoherently pumped laser
above threshold. In the presence of an external coherent drive however, the
optical damping rate can be enhanced substantially with respect to that of a
passive cavity. We show that the strength of the incoherent pump provides a
conduit to tune the damping rate and the minimum attainable phonon number with
the same radiation pressure force, and the latter can be lowered from that of a
passive cavity if the thermal contribution is nonnegligible. We also show that
the system can undergo a transition from the weak optomechanical coupling
regime to the strong optomechanical coupling regime as the incoherent pump
strength is varied.
|
1301.3762v2
|
2013-01-18
|
Adiabatic stability under semi-strong interactions: The weakly damped regime
|
We rigorously derive multi-pulse interaction laws for the semi-strong
interactions in a family of singularly-perturbed and weakly-damped
reaction-diffusion systems in one space dimension. Most significantly, we show
the existence of a manifold of quasi-steady N-pulse solutions and identify a
"normal-hyperbolicity" condition which balances the asymptotic weakness of the
linear damping against the algebraic evolution rate of the multi-pulses. Our
main result is the adiabatic stability of the manifolds subject to this normal
hyperbolicity condition. More specifically, the spectrum of the linearization
about a fixed N-pulse configuration contains essential spectrum that is
asymptotically close to the origin as well as semi-strong eigenvalues which
move at leading order as the pulse positions evolve. We characterize the
semi-strong eigenvalues in terms of the spectrum of an explicit N by N matrix,
and rigorously bound the error between the N-pulse manifold and the evolution
of the full system, in a polynomially weighted space, so long as the
semi-strong spectrum remains strictly in the left-half complex plane, and the
essential spectrum is not too close to the origin.
|
1301.4466v1
|
2013-01-24
|
Spin transport parameters in metallic multilayers determined by ferromagnetic resonance measurements of spin pumping
|
We measured spin transport in nonferromagnetic (NM) metallic multilayers from
the contribution to damping due to spin pumping from a ferromagnetic Co90Fe10
thin film. The multilayer stack consisted of NM1/NM2/Co90Fe10(2 nm)/NM2/NM3
with varying NM materials and thicknesses. Using conventional theory for one
dimensional diffusive spin transport in metals, we show that the effective
damping due to spin pumping can be strongly affected by the spin transport
properties of each NM in the multilayer, which permits the use of damping
measurements to accurately determine the spin transport properties of the
various NM layers in the full five-layer stack. We find that due to its high
electrical resistivity, amorphous Ta is a poor spin conductor, in spite of a
short spin-diffusion length of 1.0 nm, and that Pt is an excellent spin
conductor by virtue of its low electrical resistivity and a spin diffusion
length of only 0.5 nm. Spin Hall effect measurements may have underestimated
the spin Hall angle in Pt by assuming a much longer spin diffusion length.
|
1301.5861v1
|
2013-02-11
|
Low-damping epsilon-near-zero slabs: nonlinear and nonlocal optical properties
|
We investigate second harmonic generation, low-threshold multistability,
all-optical switching, and inherently nonlocal effects due to the free-electron
gas pressure in an epsilon-near-zero (ENZ) metamaterial slab made of
cylindrical, plasmonic nanoshells illuminated by TM-polarized light. Damping
compensation in the ENZ frequency region, achieved by using gain medium inside
the shells' dielectric cores, enhances the nonlinear properties. Reflection is
inhibited and the electric field component normal to the slab interface is
enhanced near the effective pseudo-Brewster angle, where the effective
\epsilon-near-zero condition triggers a non-resonant, impedance-matching
phenomenon. We show that the slab displays a strong effective, spatial
nonlocality associated with leaky modes that are mediated by the compensation
of damping. The presence of these leaky modes then induces further spectral and
angular conditions where the local fields are enhanced, thus opening new
windows of opportunity for the enhancement of nonlinear optical processes.
|
1302.2392v1
|
2013-02-14
|
A Matlab toolbox for fractional relaxation-oscillation equations
|
Stress relaxation and oscillation damping of complex viscoelastic media often
manifest history- and path-dependent physical behaviors and cannot accurately
be described by the classical models. Recent research found that fractional
derivative models can characterize such complex relaxation and damping.
However, to our best knowledge, easy-to-use numerical software is not available
for fractional relaxation-oscillation (FRO) equations. This paper is to
introduce an open source free Matlab toolbox which we developed in recent years
for numerical solution of the FRO equations. This FRO toolbox uses the
predictor-corrector approach for the discretization of time fractional
derivative, and non-expert users can accurately solve fractional
relaxation-oscillation equations via a friendly graphical user interface.
Compared with experimental data, our numerical experiments show that the FRO
toolbox is highly efficient and accurate to simulate viscoelastic stress
relaxation and damped vibration. This free toolbox will help promote the
research and practical use of fractional relaxation-oscillation equations.
|
1302.3384v1
|
2013-03-11
|
The Analysis of Long-Term Frequency and Damping Wandering in Buildings Using the Random Decrement Technique
|
The characterization and monitoring of buildings is an issue that has
attracted the interest of many sectors over the last two decades. With the
increasing use of permanent, continuous and real-time networks, ambient
vibrations can provide a simple tool for the identification of dynamic building
parameters. This study is focused on the long-term variation of frequency and
damping in several buildings, using the Random Decrement Technique (RDT). RDT
provides a fast, robust and accurate long-term analysis and improves the
reliability of frequency and damping measurements for structural health
monitoring. This reveals particularly useful information in finding out
precisely how far changes in modal parameters can be related to changes in
physical properties. This paper highlights the reversible changes of the
structure's dynamic parameters, correlated with external forces, such as
temperature and exposure to the sun. Contrasting behaviors are observed,
including correlation and anti-correlation with temperature variations.
|
1303.2642v1
|
2013-03-21
|
Optimizing atomic resolution of force microscopy in ambient conditions
|
Ambient operation poses a challenge to AFM because in contrast to operation
in vacuum or liquid environments, the cantilever dynamics change dramatically
from oscillating in air to oscillating in a hydration layer when probing the
sample. We demonstrate atomic resolution by imaging of the KBr(001) surface in
ambient conditions by frequency-modulation atomic force microscopy with a
cantilever based on a quartz tuning fork (qPlus sensor) and analyze both long-
and short-range contributions to the damping. The thickness of the hydration
layer increases with relative humidity, thus varying humidity enables us to
study the in uence of the hydration layer thickness on cantilever damping.
Starting with measurements of damping versus amplitude, we analyzed the signal
and the noise characteristics at the atomic scale. We then determined the
optimal amplitude which enabled us to acquire high-quality atomically resolved
images.
|
1303.5204v2
|
2013-04-10
|
Current Sheets and Collisionless Damping in Kinetic Plasma Turbulence
|
We present the first study of the formation and dissipation of current sheets
at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence
simulation. We investigate the relative importance of dissipation associated
with collisionless damping via resonant wave-particle interactions versus
dissipation in small-scale current sheets in weakly collisional plasma
turbulence. Current sheets form self-consistently from the wave-driven
turbulence, and their filling fraction is well correlated to the electron
heating rate. However, the weakly collisional nature of the simulation
necessarily implies that the current sheets are not significantly dissipated
via Ohmic dissipation. Rather, collisionless damping via the Landau resonance
with the electrons is sufficient to account for the measured heating as a
function of scale in the simulation, without the need for significant Ohmic
dissipation. This finding suggests the possibility that the dissipation of the
current sheets is governed by resonant wave-particle interactions and that the
locations of current sheets correspond spatially to regions of enhanced
heating.
|
1304.2958v2
|
2013-04-22
|
Constant residual electrostatic electron plasma mode in Vlasov-Ampere system
|
In a collisionless Vlasov-Poisson (V-P) electron plasma system, two types of
modes for electric field perturbation exist: the exponentially Landau damped
electron plasma waves and the initial-value sensitive ballistic modes. Here,
the V-P system is modified slightly to a Vlasov-Ampere (V-A) system. A new
constant residual mode is revealed. Mathematically, this mode comes from the
Laplace transform of an initial electric field perturbation, and physically
represents that an initial perturbation (e.g., external electric field
perturbation) would not be damped away. Thus, this residual mode is more
difficult to be damped than the ballistic mode. [Physics of Plasmas 20, 112108
(2013); doi: 10.1063/1.4831761]
|
1304.5883v2
|
2013-04-23
|
Existence and non-existence of breather solutions in damped and driven nonlinear lattices
|
We investigate the existence of spatially localised solutions, in the form of
discrete breathers, in general damped and driven nonlinear lattice systems of
coupled oscillators. Conditions for the exponential decay of the difference
between the maximal and minimal amplitudes of the oscillators are provided
which proves that initial non-uniform spatial patterns representing breathers
attain exponentially fast a spatially uniform state preventing the formation
and/or preservation of any breather solution at all. Strikingly our results are
generic in the sense that they hold for arbitrary dimension of the system, any
attractive interaction, coupling strength and on-site potential and general
driving fields. Furthermore, our rigorous quantitative results establish
conditions under which discrete breathers in general damped and driven
nonlinear lattices can exist at all and open the way for further research on
the emergent dynamical scenarios, in particular features of pattern formation,
localisation and synchronisation, in coupled cell networks.
|
1304.6370v3
|
2013-06-21
|
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
|
We prove asymptotic stability of shear flows close to the planar Couette flow
in the 2D inviscid Euler equations on $\Torus \times \Real$. That is, given an
initial perturbation of the Couette flow small in a suitable regularity class,
specifically Gevrey space of class smaller than 2, the velocity converges
strongly in L^2 to a shear flow which is also close to the Couette flow. The
vorticity is asymptotically driven to small scales by a linear evolution and
weakly converges as $t \rightarrow \pm\infty$. The strong convergence of the
velocity field is sometimes referred to as inviscid damping, due to the
relationship with Landau damping in the Vlasov equations. This convergence was
formally derived at the linear level by Kelvin in 1887 and it occurs at an
algebraic rate first computed by Orr in 1907; our work appears to be the first
rigorous confirmation of this behavior on the nonlinear level.
|
1306.5028v3
|
2013-07-12
|
Spin injection from topological insulator tunnel-coupled to metallic leads
|
We study theoretically helical edge states of 2D and 3D topological
insulators (TI) tunnel-coupled to metal leads and show that their transport
properties are strongly affected by contacts as the latter play a role of a
heat bath and induce damping and relaxation of electrons in the helical states
of TI. A simple structure that produces a pure spin current in the external
circuit is proposed. The current and spin current delivered to the external
circuit depend on relation between characteristic lengths: damping length due
to tunneling, contact length and, in case of 3D TI, mean free path and spin
relaxation length caused by momentum scattering. If the damping length due to
tunneling is the smallest one, then the electric and spin currents are
proportional to the conductance quantum in 2D TI, and to the conductance
quantum multiplied by the ratio of the contact width to the Fermi wavelength in
3D TI.
|
1307.3333v1
|
2013-07-19
|
Damping and non-linearity of a levitating magnet in rotation above a superconductor
|
We study the dissipation of moving magnets in levitation above a
superconductor. The rotation motion is analyzed using optical tracking
techniques. It displays a remarkable regularity together with long damping time
up to several hours. The magnetic contribution to the damping is investigated
in detail by comparing 14 distinct magnetic configurations, and points towards
amplitude-dependent dissipation mechanisms. The non-linear dynamics of the
mechanical rotation motion is also revealed and described with an effective
Duffing model. The obtained picture of the coupling of levitating magnets to
their environment sheds light on their potential as ultra-low dissipation
mechanical oscillators for high precision physics.
|
1307.5155v1
|
2013-07-19
|
Perfect squeezing by damping modulation in circuit quantum electrodynamics
|
Dissipation-driven quantum state engineering uses the environment to steer
the state of quantum systems and preserve quantum coherence in the steady
state. We show that modulating the damping rate of a microwave resonator
generates a vacuum squeezed state of arbitrary squeezing strength, thereby
constituting a mechanism allowing perfect squeezing. Given the recent
experimental realizations in circuit QED of a microwave resonator with a
tunable damping rate [Yin et al., Phys. Rev. Lett. 110, 107001 (2013)],
superconducting circuits are an ideal playground to implement this technique.
By dispersively coupling a qubit to the microwave resonator, it is possible to
obtain qubit-state dependent squeezing.
|
1307.5311v2
|
2013-07-27
|
Charge-carrier-induced frequency renormalization, damping and heating of vibrational modes in nanoscale junctions
|
In nanoscale junctions the interaction between charge carriers and the local
vibrations results in renormalization, damping and heating of the vibrational
modes. We here formulate a nonequilibrium Green's functions based theory to
describe such effects. Studying a generic junction model with an off-resonant
electronic level, we find a strong bias dependence of the frequency
renormalization and vibrational damping accompanied by pronounced nonlinear
vibrational heating in junctions with intermediate values of the coupling to
the leads. Combining our theory with ab-initio calculations we furthermore show
that the bias dependence of the Raman shifts and linewidths observed
experimentally in an OPV3 junction [D. Ward et al., Nature Nano. 6, 33 (2011)]
may be explained by a combination of dynamic carrier screening and molecular
charging.
|
1307.7288v3
|
2013-07-30
|
Phase retrapping in a pointlike $\varphi$ Josephson junction: the Butterfly effect
|
We consider a $\varphi$ Josephson junction, which has a bistable zero-voltage
state with the stationary phases $\psi=\pm\varphi$. In the non-zero voltage
state the phase "moves" viscously along a tilted periodic double-well
potential. When the tilting is reduced quasistatically, the phase is retrapped
in one of the potential wells. We study the viscous phase dynamics to determine
in which well ($-\varphi$ or $+\varphi$) the phase is retrapped for a given
damping, when the junction returns from the finite-voltage state back to
zero-voltage state. In the limit of low damping the $\varphi$ Josephson
junction exhibits a butterfly effect --- extreme sensitivity of the destination
well on damping. This leads to an impossibility to predict the destination
well.
|
1307.8042v1
|
2013-08-10
|
CESR Test Accelerator
|
The Cornell Electron Storage Ring (CESR) was reconfigured in 2008 as a test
accelerator to investigate the physics of ultra-low emittance damping rings.
During the approximately 40 days/year available for dedicated operation as a
test accelerator, specialized instrumentation is used to measure growth and
mitigation of the electron cloud, emittance growth due to electron cloud,
intra-beam scattering, and ions, and single and multi-bunch instabilities
generated by collective effects. The flexibility of the CESR guide field optics
and the integration of accelerator modeling codes with the control system have
made possible an extraordinary range of experiments. Findings at CesrTA with
respect to electron cloud effects, emittance tuning techniques, and beam
instrumentation for measuring electron cloud, beam sizes, and beam positions
are the basis for much of the design of the ILC damping rings as documented in
the ILC-Technical Design Report. The program has allowed the Cornell group to
cultivate the kind of talent and expertise that will be absolutely essential to
the final engineering design, and commissioning of the damping rings for a
linear collider.
|
1308.2325v1
|
2013-09-09
|
Characterization of the International Linear Collider damping ring optics
|
A method is presented for characterizing the emittance dilution and dynamic
aperture for an arbitrary closed lattice that includes guide field magnet
errors, multipole errors and misalignments. This method, developed and tested
at the Cornell Electron Storage Ring Test Accelerator (CesrTA), has been
applied to the damping ring lattice for the International Linear Collider
(ILC). The effectiveness of beam based emittance tuning is limited by beam
position monitor (BPM) measurement errors, number of corrector magnets and
their placement, and correction algorithm. The specifications for damping ring
magnet alignment, multipole errors, number of BPMs, and precision in BPM
measurements are shown to be consistent with the required emittances and
dynamic aperture. The methodology is then used to determine the minimum number
of position monitors that is required to achieve the emittance targets, and how
that minimum depends on the location of the BPMs. Similarly, the maximum
tolerable multipole errors are evaluated. Finally, the robustness of each BPM
configuration with respect to random failures is explored.
|
1309.2248v3
|
2013-09-19
|
Van der Waals Coefficients for the Alkali-metal Atoms in the Material Mediums
|
The damping coefficients for the alkali atoms are determined very accurately
by taking into account the optical properties of the atoms and three distinct
types of trapping materials such as Au (metal), Si (semi-conductor) and
vitreous SiO2 (dielectric). Dynamic dipole polarizabilities are calculated
precisely for the alkali atoms that reproduce the damping coefficients in the
perfect conducting medium within 0.2% accuracy. Upon the consideration of the
available optical data of the above wall materials, the damping coefficients
are found to be substantially different than those of the ideal conductor. We
also evaluated dispersion coefficients for the alkali dimers and compared them
with the previously reported values. These coefficients are fitted into a
ready-to-use functional form to aid the experimentalists the interaction
potentials only with the knowledge of distances.
|
1309.4897v1
|
2013-10-13
|
What the Timing of Millisecond Pulsars Can Teach us about Their Interior
|
The cores of compact stars reach the highest densities in nature and
therefore could consist of novel phases of matter. We demonstrate via a
detailed analysis of pulsar evolution that precise pulsar timing data can
constrain the star's composition, through unstable global oscillations
(r-modes) whose damping is determined by microscopic properties of the
interior. If not efficiently damped, these modes emit gravitational waves that
quickly spin down a millisecond pulsar. As a first application of this general
method, we find that ungapped interacting quark matter is consistent with both
the observed radio and x-ray data, whereas for ordinary nuclear matter some
additional enhanced damping mechanism is required.
|
1310.3524v2
|
2013-11-28
|
Conservative effects in spin-transfer-driven magnetization dynamics
|
It is shown that under appropriate conditions spin-transfer-driven
magnetization dynamics in a single-domain nanomagnet is conservative in nature
and admits a specific integral of motion, which is reduced to the usual
magnetic energy when the spin current goes to zero. The existence of this
conservation law is connected to the symmetry properties of the dynamics under
simultaneous inversion of magnetisation and time. When one applies an external
magnetic field parallel to the spin polarization, the dynamics is transformed
from conservative into dissipative. More precisely, it is demonstrated that
there exists a state function such that the field induces a monotone relaxation
of this function toward its minima or maxima, depending on the field
orientation. These results hold in the absence of intrinsic damping effects.
When intrinsic damping is included in the description, a competition arises
between field-induced and damping-induced relaxations, which leads to the
appearance of limit cycles, that is, of magnetization self-oscillations.
|
1311.7344v1
|
2013-12-05
|
The initial condition problems of damped quantum harmonic oscillator
|
We investigate the exact dynamics of the damped quantum harmonic oscillator
under the (un)correlated initial conditions. The master equation is generalized
to the cases of the arbitrary factorized state and/or Gaussian state. We show
that the variances of the factorized Gaussian state do not sensitively depend
on the initial oscillator-bath correlation, which however can remarkably affect
the mean values even at high temperature. We also illustrate that the
correlations among the factorized states still give rise to the initial dips
during the purity evolutions, which can be smoothed out by increasing the
amount of correlation to some extent. We finally study the effects of repeated
measurements on the time evolution of the damped oscillator analytically, which
are compared with the weak coupling results to indicate that they give rather
different transient behaviors even for an intermediate coupling.
|
1312.1454v1
|
2013-12-13
|
Optical variability of quasars: a damped random walk
|
A damped random walk is a stochastic process, defined by an exponential
covariance matrix that behaves as a random walk for short time scales and
asymptotically achieves a finite variability amplitude at long time scales.
Over the last few years, it has been demonstrated, mostly but not exclusively
using SDSS data, that a damped random walk model provides a satisfactory
statistical description of observed quasar variability in the optical
wavelength range, for rest-frame timescales from 5 days to 2000 days. The
best-fit characteristic timescale and asymptotic variability amplitude scale
with the luminosity, black hole mass, and rest wavelength, and appear
independent of redshift. In addition to providing insights into the physics of
quasar variability, the best-fit model parameters can be used to efficiently
separate quasars from stars in imaging surveys with adequate long-term
multi-epoch data, such as expected from LSST.
|
1312.3966v1
|
2013-12-25
|
Non-linear damping of visco-resistive Alfven waves in solar spicules
|
Interaction of Alfven waves with plasma inhomogeneities generates phase
mixing which can lead to dissipate Alfven waves and to heat the solar plasma.
Here we study the dissipation of Alfven waves by phase mixing due to viscosity
and resistivity variations with height. We also consider nonlinear
magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms
of MHD equations include perturbed velocity, magnetic field, and density. To
investigate the damping of Alfven waves in a stratified atmosphere of solar
spicules, we solve the non-linear MHD equations in the x-z plane. Our
simulations show that the damping is enhanced due to viscosity and resistivity
gradients. Moreover, energy variations is influenced due to nonlinear terms in
MHD equations.
|
1312.7866v1
|
2013-12-31
|
A novel variability-based method for quasar selection: evidence for a rest frame ~54 day characteristic timescale
|
We compare quasar selection techniques based on their optical variability
using data from the Catalina Real-time Transient Survey (CRTS). We introduce a
new technique based on Slepian wavelet variance (SWV) that shows comparable or
better performance to structure functions and damped random walk models but
with fewer assumptions. Combining these methods with WISE mid-IR colors
produces a highly efficient quasar selection technique which we have validated
spectroscopically. The SWV technique also identifies characteristic timescales
in a time series and we find a characteristic rest frame timescale of ~54 days,
confirmed in the light curves of ~18000 quasars from CRTS, SDSS and MACHO data,
and anticorrelated with absolute magnitude. This indicates a transition between
a damped random walk and $P(f) \propto f^{-1/3}$ behaviours and is the first
strong indication that a damped random walk model may be too simplistic to
describe optical quasar variability.
|
1401.1785v1
|
2014-02-09
|
Manipulation of tripartite-to-bipartite entanglement localization under quantum noises and its application to entanglement distribution
|
This paper is to investigate the effects of quantum noises on entanglement
localization by taking an example of reducing a three-qubit
Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We
consider, respectively, two types of quantum decoherence, i.e.,
amplitude-damping and depolarizing decoherence, and explore the best von
Neumann measurements on one of three qubits of the triple GHZ state for making
the amount of entanglement of the collapsed bipartite state be as large as
possible. The results indicate that different noises have different impacts on
entanglement localization, and that the optimal strategy for reducing a
three-qubit GHZ state to a two-qubit one via local measurements and classical
communications in the amplitude-damping case is different from that in the
noise-free case. We also show that the idea of entanglement localization could
be utilized to improve the quality of bipartite entanglement distributing
through amplitude-damping channels. These findings might shed a new light on
entanglement manipulations and transformations.
|
1402.1914v2
|
2014-02-25
|
Thermodynamic anomalies in the presence of dissipation: from the free particle to the harmonic oscillator
|
A free particle coupled to a heat bath can exhibit a number of thermodynamic
anomalies like a negative specific heat or reentrant classicality. These
low-temperature phenomena are expected to be modified at very low temperatures
where finite-size effects associated with the discreteness of the energy
spectrum become relevant. In this paper, we explore in which form the
thermodynamic anomalies of the free damped particle appear for a damped
harmonic oscillator. Since the discreteness of the oscillator's energy spectrum
is fully accounted for, the results are valid for arbitrary temperatures. As
expected, they are in agreement with the third law of thermodynamics and
indicate how the thermodynamic anomalies of the free damped particle can be
reconciled with the third law. Particular attention is paid to the transition
from the harmonic oscillator to the free particle when the limit of the
oscillator frequency to zero is taken.
|
1402.6221v1
|
2014-02-26
|
Magneto-elastic modes and lifetime of magnons in thin yttrium-iron garnet films
|
We calculate the effects of the spin-lattice coupling on the magnon spectrum
of thin ferromagnetic films consisting of the magnetic insulator yttrium-iron
garnet. The magnon-phonon hybridisation generates a characteristic minimum in
the spin dynamic structure factor which quantitatively agrees with recent
Brillouin light scattering experiments. We also show that at room temperature
the phonon contribution to the magnon damping exhibits a rather complicated
momentum dependence: In the exchange regime the magnon damping is dominated by
Cherenkov type scattering processes, while in the long-wavelength dipolar
regime these processes are subdominant and the magnon damping is two orders of
magnitude smaller. We supplement our calculations by actual measurements of the
magnon relaxation in the dipolar regime. Our theory provides a simple
explanation of a recent experiment probing the different temperatures of the
magnon and phonon gases in yttrium-iron garnet.
|
1402.6575v2
|
2014-02-28
|
A new way to evaluate x-ray Brillouin scattering data
|
Making use of the classical second moment sum rule, it is possible to convert
a series of constant-Q x-ray Brillouin scattering scans (Q momentum transfer)
into a series of constant frequency scans over the measured $Q$ range. The
method is applied to literature results for the phonon dispersion in liquid
vitreous silica and in glassy polybutadiene. It turns out that the constant
frequency scans are again well fitted by the damped harmonic oscillator
function, but now in terms of a Q-independent phonon damping depending
exclusively on the frequency. At low frequency, the sound velocity and the
damping of both evaluations agree, but at higher frequencies one gets
significant differences. The results in silica suggest a new interpretation of
x-ray Brillouin data in terms of a strong mixing of longitudinal and transverse
phonons toward higher frequencies. The results in polybutadiene enlighten the
crossover from Brillouin to Umklapp scattering.
|
1402.7237v1
|
2014-03-10
|
Quantum Fisher Information of W States in Decoherence Channels
|
We study the quantum Fisher information (QFI) of W states analytically with
respect to SU(2) rotations in the basic decoherence channels i.e. depolarizing
(DPC), amplitude damping (ADC) and phase damping (PDC), and present the
interesting behavior of QFI of W states, especially when compared to that of
GHZ states [Ma et al., Phys. Rev. A, 84, 022302 (2011)]. We find that when
initially pure W states are under decoherence, i) DPC: as decoherence starts
and increases, QFI smoothly decays; ii) ADC: just as decoherence starts, QFI
exhibits a sudden drop to the shot noise level and as decoherence increases,
QFI continues to decrease to zero and then increases back to the shot noise
level; iii) PDC: just as decoherence starts, a sudden death of QFI occurs and
QFI remains zero for any rate of decoherence, therefore W states in phase
damping channel do not provide phase sensitivity. We also find that, on the
contrary to GHZ states, pure or decohered W states are not sensitive with
respect to rotations in z direction and the sensitivities with respect to
rotations in x and y directions are equal to each other, implying no sudden
change points of QFI due to competition between directions.
|
1403.2376v1
|
2014-03-14
|
Silk damping at a redshift of a billion: a new limit on small-scale adiabatic perturbations
|
We study the dissipation of small-scale adiabatic perturbations at early
times when the Universe is hotter than T ~ 0.5 keV. When the wavelength falls
below the damping scale 1/kD, the acoustic modes diffuse and thermalize,
causing entropy production. Before neutrino decoupling, kD is primarily set by
the neutrino shear viscosity, and we study the effect of acoustic damping on
the relic neutrino number, primordial nucleosynthesis, dark-matter freeze-out,
and baryogenesis. This sets a new limit on the amplitude of primordial
fluctuations of DeltaR^2 < 0.007 at 10^4/Mpc< k < 10^5/Mpc and a model
dependent limit of DeltaR^2 < 0.3 at k < 10^{20-25}/Mpc.
|
1403.3697v1
|
2014-06-02
|
CMB $μ$ distortion from primordial gravitational waves
|
We propose a new mechanism of generating the $\mu$ distortion in cosmic
microwave background (CMB) originated from primordial gravitational waves. Such
$\mu$ distortion is generated by the damping of the temperature anisotropies
through the Thomson scattering, even on scales larger than that of Silk
damping. This mechanism is in sharp contrast with that from the primordial
curvature (scalar) perturbations, in which the temperature anisotropies mainly
decay by Silk damping effects. We estimate the size of the $\mu$ distortion
from the new mechanism, which can be used to constrain the amplitude of
primordial gravitational waves on smaller scales independently from the CMB
anisotropies, giving more wide-range constraint on their spectral index by
combining the amplitude from the CMB anisotropies.
|
1406.0451v2
|
2014-06-04
|
Self-organized escape processes of linear chains in nonlinear potentials
|
An enhancement of localized nonlinear modes in coupled systems gives rise to
a novel type of escape process. We study a spatially one dimensional set-up
consisting of a linearly coupled oscillator chain of $N$ mass-points situated
in a metastable nonlinear potential. The Hamilton-dynamics exhibits breather
solutions as a result of modulational instability of the phonon states. These
breathers localize energy by freezing other parts of the chain. Eventually this
localised part of the chain grows in amplitude until it overcomes the critical
elongation characterized by the transition state. Doing so, the breathers
ignite an escape by pulling the remaining chain over the barrier. Even if the
formation of singular breathers is insufficient for an escape, coalescence of
moving breathers can result in the required concentration of energy. Compared
to a chain system with linear damping and thermal fluctuations the breathers
help the chain to overcome the barriers faster in the case of low damping. With
larger damping, the decreasing life time of the breathers effectively inhibits
the escape process.
|
1406.0938v1
|
2014-06-08
|
Dissipation-driven squeezed and sub-Poissonian mechanical states in quadratic optomechanical systems
|
In this work we study an optomechanical system in which there is a purely
quadratic optomechanical coupling between the optical and mechanical modes. The
optical mode is pumped by three coherent fields and the mechanical mode is
parametrically driven. We show that if the frequencies and amplitudes of both
optical and mechanical drivings are properly chosen, the optomechanical
interaction gives rise to an effective interaction, which, in the presence of
optical damping and in the absence of mechanical damping, has the squeezed
vacuum state and the squeezed one phonon state as dark states of the dynamics.
These states are well known for presenting quadrature squeezing and
sub-Poissonian statistics. However, even in the presence of mechanical damping
it is possible to find steady states with large degrees of quadrature squeezing
or strong sub-Poissonian statistics. Furthermore, we find a counter-intuitive
behavior in which a nonzero temperature of the mechanical environment allows
the observation of mechanical states with more pronounced sub-Poissonian
statistics.
|
1406.1987v3
|
2014-06-13
|
Frequency-dependent damping in propagating slow magneto-acoustic waves
|
Propagating slow magneto-acoustic waves are often observed in polar plumes
and active region fan loops. The observed periodicities of these waves range
from a few minutes to few tens of minutes and their amplitudes were found to
decay rapidly as they travel along the supporting structure. Previously,
thermal conduction, compressive viscosity, radiation, density stratification,
and area divergence, were identified to be some of the causes for change in the
slow wave amplitude. Our recent studies indicate that the observed damping in
these waves is frequency dependent. We used imaging data from SDO/AIA, to study
this dependence in detail and for the first time from observations we attempted
to deduce a quantitative relation between damping length and frequency of these
oscillations. We developed a new analysis method to obtain this relation. The
observed frequency dependence does not seem to agree with the current linear
wave theory and it was found that the waves observed in the polar regions show
a different dependence from those observed in the on-disk loop structures
despite the similarity in their properties.
|
1406.3565v1
|
2014-06-24
|
On finite density effects on cosmic reheating and moduli decay and implications for Dark Matter production
|
We study the damping of an oscillating scalar field in a
Friedmann-Robertson-Walker spacetime by perturbative processes, taking into
account the finite density effects that interactions with the plasma of decay
products have on the damping rate. The scalar field may be identified with the
inflaton, in which case this process leads to the reheating of the universe
after inflation. It can also resemble a modulus that dominates the energy
density of the universe at later times. We find that the finite density
corrections to the damping rate can have a drastic effect on the thermal
history and considerably increase both, the maximal temperature in the early
universe and the reheating temperature at the onset of the radiation dominated
era. As a result abundance of some Dark Matter candidates may be considerably
larger than previously estimated. We give improved analytic estimates for the
maximal and the reheating temperatures and confirm them numerically in a simple
model.
|
1406.6243v2
|
2014-08-13
|
Probing dense matter in compact star cores with radio pulsar data
|
Astrophysical observations of compact stars provide, in addition to collider
experiments, the other big source of information on matter under extreme
conditions. The largest and most precise data set about neutron stars is the
timing data of radio pulsars. We show how this unique data can be used to learn
about the ultra-dense matter in the compact star interior. The method relies on
astro-seismology based on special global oscillation modes (r-modes) that emit
gravitational waves. They would prevent pulsars from spinning with their
observed high frequencies, unless the damping of these modes, determined by the
microscopic properties of matter, can prevent this. We show that for each form
of matter there is a distinct region in a frequency/spindown-rate diagram where
r-modes can be present. We find that stars containing ungapped quark matter are
consistent with both the observed radio and x-ray data, whereas, even when
taking into account the considerable uncertainties, neutron star models with
standard viscous damping are inconsistent with both data sets and additional
damping mechanisms would be required.
|
1408.3152v1
|
2014-08-25
|
Spin-Scattering Rates in Metallic Thin Films Measured by Ferromagnetic Resonance Damping Enhanced by Spin-Pumping
|
We determined the spin-transport properties of Pd and Pt thin films by
measuring the increase in ferromagnetic resonance damping due to spin-pumping
in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM
thicknesses. The increase in damping with NM thickness depends strongly on both
the spin- and charge-transport properties of the NM, as modeled by diffusion
equations that include both momentum- and spin-scattering parameters. We use
the analytical solution to the spin-diffusion equations to obtain
spin-diffusion lengths for Pt and Pd. By measuring the dependence of
conductivity on NM thickness, we correlate the charge- and spin-transport
parameters, and validate the applicability of various models for
momentum-scattering and spin-scattering rates in these systems: constant,
inverse-proportional (Dyakanov-Perel), and linear-proportional (Elliot-Yafet).
We confirm previous reports that the spin-scattering time can be shorter than
the momentum scattering time in Pt, and the Dyakanov-Perel-like model is the
best fit to the data.
|
1408.5921v2
|
2014-08-27
|
Quasi-particle Lifetime in a Mixture of Bose and Fermi Superfluids
|
In this letter, to reveal the effect of quasi-particle interactions in a
Bose-Fermi superfluid mixture, we consider the lifetime of quasi-particle of
Bose superfluid due to its interaction with quasi-particles in Fermi
superfluid. We find that this damping rate, i.e. inverse of the lifetime, has
quite different threshold behavior at the BCS and the BEC side of the Fermi
superfluid. The damping rate is a constant nearby the threshold momentum in the
BCS side, while it increases rapidly in the BEC side. This is because in the
BCS side the decay processe is restricted by constant density-of-state of
fermion quasi-particle nearby Fermi surface, while such a restriction does not
exist in the BEC side where the damping process is dominated by bosonic
quasi-particles of Fermi superfluid. Our results are related to collective mode
experiment in recently realized Bose-Fermi superfluid mixture.
|
1408.6419v1
|
2014-09-04
|
A numerical study of the pull-in instability in some free boundary models for MEMS
|
In this work we numerically compute the bifurcation curve of stationary
solutions for the free boundary problem for MEMS in one space dimension. It has
a single turning point, as in the case of the small aspect ratio limit. We also
find a threshold for the existence of global-in-time solutions of the evolution
equation given by either a heat or a damped wave equation. This threshold is
what we term the dynamical pull-in value: it separates the stable operation
regime from the touchdown regime. The numerical calculations show that the
dynamical threshold values for the heat equation coincide with the static
values. For the damped wave equation the dynamical threshold values are smaller
than the static values. This result is in agreement with the observations
reported for a mass-spring system studied in the engineering literature. In the
case of the damped wave equation, we also show that the aspect ratio of the
device is more important than the inertia in the determination of the pull-in
value.
|
1409.1291v2
|
2014-09-15
|
Direct path from microscopic mechanics to Debye shielding, Landau damping, and wave-particle interaction
|
The derivation of Debye shielding and Landau damping from the $N$-body
description of plasmas is performed directly by using Newton's second law for
the $N$-body system. This is done in a few steps with elementary calculations
using standard tools of calculus, and no probabilistic setting. Unexpectedly,
Debye shielding is encountered together with Landau damping. This approach is
shown to be justified in the one-dimensional case when the number of particles
in a Debye sphere becomes large. The theory is extended to accommodate a
correct description of trapping and chaos due to Langmuir waves. Shielding and
collisional transport are found to be two related aspects of the repulsive
deflections of electrons, in such a way that each particle is shielded by all
other ones while keeping in uninterrupted motion.
|
1409.4323v1
|
2014-09-19
|
Damping of metallized bilayer nanomechanical resonators at room temperature
|
We investigate the influence of gold thin-films subsequently deposited on a
set of initially bare, doubly clamped, high-stress silicon nitride string
resonators at room temperature. Analytical expressions for resonance frequency,
quality factor and damping for both in- and out-of-plane flexural modes of the
bilayer system are derived, which allows for the determination of effective
elastic parameters of the composite structure from our experimental data. We
find the inverse quality factor to scale linearly with the gold film thickness,
indicating that the overall damping is governed by losses in the metal.
Correspondingly, the mechanical linewidth increases by more than one order of
magnitude compared to the bare silicon nitride string resonator. Furthermore,
we extract mechanical quality factors of the gold film for both flexural modes
and show that they can be enhanced by complete deposition of the metal in a
single step, suggesting that surface and interface losses play a vital role in
metal thin-films.
|
1409.5670v1
|
2014-10-09
|
Non-Fermi-liquid behavior and anomalous suppression of Landau damping in layered metals close to ferromagnetism
|
We analyse the low-energy physics of nearly ferromagnetic metals in two
spatial dimensions using the functional renormalization group technique. We
find a new low-energy fixed point, at which the fermionic (electron-like)
excitations are non-Fermi-liquid ($z_f = 13/10$) and the magnetic fluctuations
exhibit an anomalous Landau damping whose rate vanishes as $\Gamma_{\bf q} \sim
\vert {\bf q} \vert^{3/5}$ in the low-$\vert {\bf q} \vert$ limit. We discuss
this renormalization of the Landau-damping exponent, which is the major novel
prediction of our work, and highlight the possible link between that
renormalization and neutron-scattering data on UGe$_2$ and related compounds.
Implications of our analysis for YFe$_2$Al$_{10}$ are also discussed.
|
1410.2539v3
|
2014-10-09
|
Special mean motion resonance pairs: Mimas-Tethys and Titan-Hyperion
|
Five pairs of large solar system satellites occupy first order mean-motion
resonances (MMRs). Among these, the pairs of Mimas-Tethys and Titan-Hyperion
are special. They are located much deeper in resonance than the others and
their critical arguments librate with much greater amplitudes. These
characteristics are traced to the insignificant damping, over $\Gyr$
timescales, of Mimas's orbital inclination and Hyperion's orbital eccentricity.
Absent that, these resonances would not survive. Instead their librations would
be overstable and escape from resonance would occur on the relevant damping
time. Unlike the aforementioned MMRs, those involving Enceladus-Dione,
Io-Europa, and Europa-Ganymede are limited by eccentricity damping. They must
either remain at the shallow depths they currently occupy, or, if they venture
deeper, retreat after a limited time. The latter seems almost certain for
Enceladus-Dione and quite likely for the others, We examine the MMRs involving
Mimas-Tethys and Titan-Hyperion under the assumption that they formed as a
result of convergent migration. Capture probabilities are $\sim 6\%$ for the
former and $100\%$ for the latter. The possibility of collisional excitation of
their large librations is investigated but largely discounted.
|
1410.2648v1
|
2014-11-13
|
Stability and bifurcation for the Kuramoto model
|
We study the mean-field limit of the Kuramoto model of globally coupled
oscillators. By studying the evolution in Fourier space and understanding the
domain of dependence, we show a global stability result. Moreover, we can
identify function norms to show damping of the order parameter for velocity
distributions and perturbations in $\mathcal{W}^{n,1}$ for $n > 1$. Finally,
for sufficiently regular velocity distributions we can identify exponential
decay in the stable case and otherwise identify finitely many eigenmodes. For
these eigenmodes we can show a center-unstable manifold reduction, which gives
a rigorous tool to obtain the bifurcation behaviour. The damping is similar to
Landau damping for the Vlasov equation.
|
1411.3752v3
|
2014-11-26
|
A singular finite element technique for calculating continuum damping of Alfvén eigenmodes
|
Damping due to continuum resonances can be calculated using dissipation-less
ideal magnetohydrodynamics (MHD) provided that the poles due to these
resonances are properly treated. We describe a singular finite element
technique for calculating the continuum damping of Alfv\'{e}n waves. A
Frobenius expansion is used to determine appropriate finite element basis
functions on an inner region surrounding a pole due to the continuum resonance.
The location of the pole due to the continuum resonance and mode frequency are
calculated iteratively using a Galerkin method. This method is used to find the
complex frequency and mode structure of a toroidicity-induced Alfv\'{e}n
eigenmode (TAE) in a large aspect ratio circular tokamak and are shown to agree
closely with a complex contour technique.
|
1411.7111v1
|
2014-11-26
|
Energy decay for a locally undamped wave equation
|
We study the decay rate for the energy of solutions of a damped wave equation
in a situation where the Geometric Control Condition is violated. We assume
that the set of undamped trajectories is a flat torus of positive codimension
and that the metric is locally flat around this set. We further assume that the
damping function enjoys locally a prescribed homogeneity near the undamped set
in traversal directions. We prove a sharp decay estimate at a polynomial rate
that depends on the homogeneity of the damping function. Our method relies on a
refined microlocal analysis linked to a second microlocalization procedure to
cut the phase space into tiny regions respecting the uncertainty principle but
way too small to enter a standard semi-classical analysis localization. Using a
multiplier method, we obtain the energy estimates in each region and we then
patch the microlocal estimates together.
|
1411.7271v1
|
2014-12-05
|
Entanglement Dynamics of Quantum Oscillators Nonlinearly Coupled to Thermal Environments
|
We study the asymptotic entanglement of two quantum harmonic oscillators
nonlinearly coupled to an environment. Coupling to independent baths and a
common bath are investigated. Numerical results obtained using the
Wangsness-Bloch-Redfield method are supplemented by analytical results in the
rotating wave approximation. The asymptotic negativity as function of
temperature, initial squeezing and coupling strength, is compared to results
for systems with linear system-reservoir coupling. We find that due to the
parity conserving nature of the coupling, the asymptotic entanglement is
considerably more robust than for the linearly damped cases. In contrast to
linearly damped systems, the asymptotic behavior of entanglement is similar for
the two bath configurations in the nonlinearly damped case. This is due to the
two-phonon system-bath exchange causing a supression of information exchange
between the oscillators via the bath in the common bath configuration at low
temperatures.
|
1412.1999v1
|
2014-12-08
|
The dispersion modification of electrostatic geodesic acoustic mode by electron geodesic drift current
|
The past studies treated the perturbed distribution of circulating electrons
as adiabatic one when studying the dispersion relation of electrostatic
geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic
current (FEGC) is added to modify this adiabatic distribution. Based on the
drift kinetic theory, it is found that FEGC obviously increases the magnitude
of the standard GAM's frequency and reduces its damping rate. The increase of
frequency results from the contribution of FEGC to the radial flow. The reason
for the reduction of damping rate is that when the effect of FEGC counts, the
new resonant velocity becomes much larger than ions thermal velocity with
equilibrium distribution obeying Maxwellian distribution, compared with
unmodified Landau resonant velocity. Especially, FEGC changes the characters of
the frequency and damping rate of low-frequency GAM as functions of safety
factor $q$ .
|
1412.2481v1
|
2014-12-10
|
Alfvenic Turbulence Beyond the Ambipolar Diffusion Scale
|
We investigate the nature of the Alfv\'enic turbulence cascade in two fluid
MHD simulations in order to determine if turbulence is damped once the ion and
neutral species become decoupled at a critical scale called the ambipolar
diffusion scale (L$_{AD}$). Using mode decomposition to separate the three
classical MHD modes, we study the second order structure functions of the
Alfv\'en mode velocity field of both neutrals and ions in the reference frame
of the local magnetic field. On scales greater than L$_{AD}$ we confirm that
two fluid turbulence strongly resembles single fluid MHD turbulence. Our
simulations show that the behavior of two fluid turbulence becomes more complex
on scales less than L$_{AD}$. We find that Alfvenic turbulence can exist past
L$_{AD}$ when the turbulence is globally super-Alfv\'enic, with the ions and
neutrals forming separate cascades once decoupling has taken place. When
turbulence is globally sub-Alfvenic and hence strongly anisotropic with a large
separation between the parallel and perpendicular decoupling scales, turbulence
is damped at L$_{AD}$. We also find that the power spectrum of the kinetic
energy in the damped regime is consistent with a $k^{-4}$ scaling (in agreement
with the predictions of Lazarian, Vishniac & Cho 2004).
|
1412.3452v1
|
2015-01-19
|
Linear wave action decay entailed by Landau damping in inhomogeneous, nonstationary and anisotropic plasma
|
This paper addresses the linear propagation of an electron wave in a
collisionless, inhomogeneous, nonstationary and anisotropic plasma. The plasma
is characterized by its distribution function, $f_H$, at zero order in the wave
amplitude. This distribution function, from which are derived all the
hydrodynamical quantities, may be chosen arbitrarily, provided that it solves
Vlasov equation. Then, from the linearized version of the electrons equation of
motion, and from Gauss law, is derived an envelope equation for the wave
amplitude, assumed to evolve over time and space scales much larger than the
oscillation periods of the wave. The envelope equation may be cast into an
equation for the the wave action, derived from Whitham's variational principle,
that demonstrates the action decay due to Landau damping. Moreover, the Landau
damping rate is derived at first order in the variations of the wave number and
frequency. As briefly discussed, this paper generalizes numerous previous works
on the subject, provides a theoretical basis for heuristic arguments regarding
the action decay, and also addresses the propagation of an externally driven
wave.
|
1501.04485v1
|
2015-01-23
|
Response solutions for quasi-periodically forced, dissipative wave equations
|
We consider several models of nonlinear wave equations subject to very strong
damping and quasi-periodic external forcing. This is a singular perturbation,
since the damping is not the highest order term. We study the existence of
response solutions (i.e., quasi-periodic solutions with the same frequency as
the forcing). Under very general non-resonance conditions on the frequency, we
show the existence of asymptotic expansions of the response solution; moreover,
we prove that the response solution indeed exists and depends analytically on
$\varepsilon$ (where $\varepsilon$ is the inverse of the coefficient
multiplying the damping) for $\varepsilon$ in a complex domain, which in some
cases includes disks tangent to the imaginary axis at the origin. In other
models, we prove analyticity in cones of aperture $\pi/2$ and we conjecture it
is optimal. These results have consequences for the asymptotic expansions of
the response solutions considered in the literature. The proof of our results
relies on reformulating the problem as a fixed point problem, constructing an
approximate solution and studying the properties of iterations that converge to
the solutions of the fixed point problem.
|
1501.05979v1
|
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