194 research outputs found
Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation
The kangaroo process (KP) is characterized by various forms of the covariance
and can serve as a useful model of random noises. We discuss properties of that
process for the exponential, stretched exponential and algebraic (power-law)
covariances. Then we apply the KP as a model of noise in the generalized
Langevin equation and simulate solutions by a Monte Carlo method. Some results
appear to be incompatible with requirements of the fluctuation-dissipation
theorem because probability distributions change when the process is inserted
into the equation. We demonstrate how one can construct a model of noise free
of that difficulty. This form of the KP is especially suitable for physical
applications.Comment: 22 pages (RevTeX) and 4 figure
Adiabatic Output Coupling of a Bose Gas at Finite Temperatures
We develop a general theory of adiabatic output coupling from trapped atomic
Bose-Einstein Condensates at finite temperatures. For weak coupling, the output
rate from the condensate, and the excited levels in the trap, settles in a time
proportional to the inverse of the spectral width of the coupling to the output
modes. We discuss the properties of the output atoms in the quasi-steady-state
where the population in the trap is not appreciably depleted. We show how the
composition of the output beam, containing condensate and thermal component,
may be controlled by changing the frequency of the output coupler. This
composition determines the first and second order coherence of the output beam.
We discuss the changes in the composition of the bose gas left in the trap and
show how nonresonant output coupling can stimulate either the evaporation of
thermal excitations in the trap or the growth of non-thermal excitations, when
pairs of correlated atoms leave the condensate.Comment: 22 pages, 6 Figs. To appear in Physical Review A All the typos from
the previous submission have been fixe
Langevin Simulation of Thermally Activated Magnetization Reversal in Nanoscale Pillars
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model
incorporating thermal fluctuations and dipole-dipole interactions (calculated
by the Fast Multipole Method) are presented for systems composed of nanoscale
iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated
under sinusoidally varying fields are obtained, while the coercive field is
estimated to be 1979 14 Oe using linear field sweeps at T=0 K. Thermal
effects are essential to the relaxation of magnetization trapped in a
metastable orientation, such as happens after a rapid reversal of an external
magnetic field less than the coercive value. The distribution of switching
times is compared to a simple analytic theory that describes reversal with
nucleation at the ends of the nanomagnets. Results are also presented for
arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a
separation of 300 nm, where the field from neighboring pillars is only 1
Oe, the interactions have a significant effect on the switching of the magnets.Comment: 19 pages RevTeX, including 12 figures, clarified discussion of
numerical technique
Inflationary perturbation theory is geometrical optics in phase space
A pressing problem in comparing inflationary models with observation is the
accurate calculation of correlation functions. One approach is to evolve them
using ordinary differential equations ("transport equations"), analogous to the
Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this
approach to the complete set of momentum space correlation functions. A formal
solution can be obtained using raytracing techniques adapted from geometrical
optics. We reformulate inflationary perturbation theory in this language, and
show that raytracing reproduces the familiar "delta N" Taylor expansion. Our
method produces ordinary differential equations which allow the Taylor
coefficients to be computed efficiently. We use raytracing methods to express
the gauge transformation between field fluctuations and the curvature
perturbation, zeta, in geometrical terms. Using these results we give a compact
expression for the nonlinear gauge-transform part of fNL in terms of the
principal curvatures of uniform energy-density hypersurfaces in field space.Comment: 22 pages, plus bibliography and appendix. v2: minor changes, matches
version published in JCA
Langevin equations for interacting fermions and Cooper-like pairing in trapped one-dimensional fermions
Momentum correlations in a one-dimensional equilibrium ensemble of trapped fermions, with a point interaction between particles of opposite spin have been studied. In the degenerate regime correlations were observed between fermions with opposite spins and momenta, similar to Cooper pairing. These correlations appear as soon as the temperature is below the Fermi energy, which is a much less stringent condition than that of the BCS transition proper. Calculations are carried out in both perturbative and non-perturbative regimes. To achieve the latter. it is shown that interacting fermionic dynamics may be solved as a stochastic linear transformation of Grassmann algebra generators, much in the way random c-number paths are introduced in the conventional quantum stochastics of bosons. Importantly, the method thus emerging is inherently free of the sign problem
Validity and reliability of a sensor based electronic spinal mobility index for Axial Spondyloarthritis
Objective: To evaluate the validity and reliability of inertial measurement unit (IMU) sensors in the assessment of spinal mobility in axial Spondyloarthritis (axSpA). Methods: A repeated measures study design involving 40 participants with axSpA was used. Pairs of IMU sensors were used to measure the maximum range of movement at the cervical and lumbar spine. A composite IMU score was defined by combining the IMU measures. Conventional metrology and physical function assessment were performed. Validation was assessed considering the agreement of IMU measures with conventional metrology and correlation with physical function. Reliability was assessed using intra-class correlation coefficients (ICCs). Results: The composite IMU score correlated closely (r=0.88) with the Bath Ankylosing Spondylitis Metrology Index (BASMI). Conventional cervical rotation and lateral flexion tests correlated closely with IMU equivalents (r=0.85,0.84). All IMU movement tests correlated strongly with Bath Ankylosing Spondylitis Functional Index (BASFI) whilst this was true for only some of the BASMI tests. The reliability of both conventional and IMU tests (except for chest expansion) ranged from good to excellent. Test-retest ICCs for individual conventional tests varied between 0.57 and 0.91, in comparison to a range from 0.74 to 0.98 for each of the IMU tests. Each of the composite regional IMU scores had excellent test-retest reliability (ICCs 0.94-0.97), comparable to the reliability of the BASMI (ICC 0.96). Conclusion: Cervical and lumbar spinal mobility measured using wearable IMU sensors is a valid and reliable assessment in multiple planes (including rotation), in patients with a wide range of axSpA severity
Theory of output coupling for trapped fermionic atoms
We develop a dynamic theory of output coupling, for fermionic atoms initially
confined in a magnetic trap. We consider an exactly soluble one-dimensional
model, with a spatially localized delta-type coupling between the atoms in the
trap and a continuum of free-particle external modes. Two important special
cases are considered for the confinement potential: the infinite box and the
harmonic oscillator. We establish that in both cases a bound state of the
coupled system appears for any value of the coupling constant, implying that
the trap population does not vanish in the infinite-time limit. For weak
coupling, the energy spectrum of the outgoing beam exhibits peaks corresponding
to the initially occupied energy levels in the trap; the height of these peaks
increases with the energy. As the coupling gets stronger, the energy spectrum
is displaced towards dressed energies of the fermions in the trap. The
corresponding dressed states result from the coupling between the unperturbed
fermionic states in the trap, mediated by the coupling between these states and
the continuum. In the strong-coupling limit, there is a reinforcement of the
lowest-energy dressed mode, which contributes to the energy spectrum of the
outgoing beam more strongly than the other modes. This effect is especially
pronounced for the one-dimensional box, which indicates that the efficiency of
the mode-reinforcement mechanism depends on the steepness of the confinement
potential. In this case, a quasi-monochromatic anti-bunched atomic beam is
obtained. Results for a bosonic sample are also shown for comparison.Comment: 16 pages, 7 figures, added discussion on time-dependent spectral
distribution and corresponding figur
Non-Equilibrium Statistical Physics of Currents in Queuing Networks
We consider a stable open queuing network as a steady non-equilibrium system
of interacting particles. The network is completely specified by its underlying
graphical structure, type of interaction at each node, and the Markovian
transition rates between nodes. For such systems, we ask the question ``What is
the most likely way for large currents to accumulate over time in a network
?'', where time is large compared to the system correlation time scale. We
identify two interesting regimes. In the first regime, in which the
accumulation of currents over time exceeds the expected value by a small to
moderate amount (moderate large deviation), we find that the large-deviation
distribution of currents is universal (independent of the interaction details),
and there is no long-time and averaged over time accumulation of particles
(condensation) at any nodes. In the second regime, in which the accumulation of
currents over time exceeds the expected value by a large amount (severe large
deviation), we find that the large-deviation current distribution is sensitive
to interaction details, and there is a long-time accumulation of particles
(condensation) at some nodes. The transition between the two regimes can be
described as a dynamical second order phase transition. We illustrate these
ideas using the simple, yet non-trivial, example of a single node with
feedback.Comment: 26 pages, 5 figure
Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
Both community ecology and conservation biology seek further understanding of
factors governing the advance of an invasive species. We model biological
invasion as an individual-based, stochastic process on a two-dimensional
landscape. An ecologically superior invader and a resident species compete for
space preemptively. Our general model includes the basic contact process and a
variant of the Eden model as special cases. We employ the concept of a
"roughened" front to quantify effects of discreteness and stochasticity on
invasion; we emphasize the probability distribution of the front-runner's
relative position. That is, we analyze the location of the most advanced
invader as the extreme deviation about the front's mean position. We find that
a class of models with different assumptions about neighborhood interactions
exhibit universal characteristics. That is, key features of the invasion
dynamics span a class of models, independently of locally detailed demographic
rules. Our results integrate theories of invasive spatial growth and generate
novel hypotheses linking habitat or landscape size (length of the invading
front) to invasion velocity, and to the relative position of the most advanced
invader.Comment: The original publication is available at
www.springerlink.com/content/8528v8563r7u2742
Quantum Fluctuation Relations for the Lindblad Master Equation
An open quantum system interacting with its environment can be modeled under
suitable assumptions as a Markov process, described by a Lindblad master
equation. In this work, we derive a general set of fluctuation relations for
systems governed by a Lindblad equation. These identities provide quantum
versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response
regime, these fluctuation relations yield a fluctuation-dissipation theorem
(FDT) valid for a stationary state arbitrarily far from equilibrium. For a
closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula
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