22,845 research outputs found
Symmetric path integrals for stochastic equations with multiplicative noise
A Langevin equation with multiplicative noise is an equation schematically of
the form dq/dt = - F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose
amplitude e(q) depends on q itself. I show how to convert such equations into
path integrals. The definition of the path integral depends crucially on the
convention used for discretizing time, and I specifically derive the correct
path integral when the convention used is the natural, time-symmetric one that
time derivatives are (q_t - q_{t-\Delta t}) / \Delta t and coordinates are (q_t
+ q_{t-\Delta t}) / 2. [This is the convention that permits standard
manipulations of calculus on the action, like naive integration by parts.] It
has sometimes been assumed in the literature that a Stratanovich Langevin
equation can be quickly converted to a path integral by treating time as
continuous but using the rule \theta(t=0) = 1/2. I show that this prescription
fails when the amplitude e(q) is q-dependent.Comment: 8 page
Rocket- and aircraft-borne trace gas measurements in the winter polar stratosphere
In January and February 1987 stratospheric rocket- and aircraft-borne trace gas measurements were done in the North Polar region using ACIMS (Active Chemical Ionization Mass Spectrometry) and PACIMS (PAssive Chemical Ionization Mass Spectrometry) instruments. The rocket was launched at ESRANGE (European Sounding Rocket Launching Range) (68 N, 21 E, Northern Sweden) and the twin-jet research aircraft operated by the DFVLR (Deutsche Forschungs- und Versuchs-anstalt fuer Luft- und Raumfahrt), and equipped with a mass spectrometer laboratory was stationed at Kiruna airport. Various stratospheric trace gases were measured including nitric acid, sulfuric acid, non-methane hydrocarbons (acetone, hydrogen cyanide, acetonitrile, methanol etc.), and ambient cluster ions. The experimental data is presented and possible implications for polar stratospheric ozone discussed
Measurement of temperature profiles in hot gases by emission-absorption spectroscopy Final report
Measurement of spectral radiances and absorptances in hot gase
Real-World Repetition Estimation by Div, Grad and Curl
We consider the problem of estimating repetition in video, such as performing
push-ups, cutting a melon or playing violin. Existing work shows good results
under the assumption of static and stationary periodicity. As realistic video
is rarely perfectly static and stationary, the often preferred Fourier-based
measurements is inapt. Instead, we adopt the wavelet transform to better handle
non-static and non-stationary video dynamics. From the flow field and its
differentials, we derive three fundamental motion types and three motion
continuities of intrinsic periodicity in 3D. On top of this, the 2D perception
of 3D periodicity considers two extreme viewpoints. What follows are 18
fundamental cases of recurrent perception in 2D. In practice, to deal with the
variety of repetitive appearance, our theory implies measuring time-varying
flow and its differentials (gradient, divergence and curl) over segmented
foreground motion. For experiments, we introduce the new QUVA Repetition
dataset, reflecting reality by including non-static and non-stationary videos.
On the task of counting repetitions in video, we obtain favorable results
compared to a deep learning alternative
Pesin's Formula for Random Dynamical Systems on
Pesin's formula relates the entropy of a dynamical system with its positive
Lyapunov exponents. It is well known, that this formula holds true for random
dynamical systems on a compact Riemannian manifold with invariant probability
measure which is absolutely continuous with respect to the Lebesgue measure. We
will show that this formula remains true for random dynamical systems on
which have an invariant probability measure absolutely continuous to the
Lebesgue measure on . Finally we will show that a broad class of
stochastic flows on of a Kunita type satisfies Pesin's formula.Comment: 35 page
Low-lying bifurcations in cavity quantum electrodynamics
The interplay of quantum fluctuations with nonlinear dynamics is a central
topic in the study of open quantum systems, connected to fundamental issues
(such as decoherence and the quantum-classical transition) and practical
applications (such as coherent information processing and the development of
mesoscopic sensors/amplifiers). With this context in mind, we here present a
computational study of some elementary bifurcations that occur in a driven and
damped cavity quantum electrodynamics (cavity QED) model at low intracavity
photon number. In particular, we utilize the single-atom cavity QED Master
Equation and associated Stochastic Schrodinger Equations to characterize the
equilibrium distribution and dynamical behavior of the quantized intracavity
optical field in parameter regimes near points in the semiclassical
(mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that
the semiclassical limit sets are qualitatively preserved in the quantum
stationary states, although quantum fluctuations apparently induce phase
diffusion within periodic orbits and stochastic transitions between attractors.
We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR
Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
We compute the shift of the transition temperature for a homogenous weakly
interacting Bose gas in leading order in the scattering length a for given
particle density n. Using variational perturbation theory through six loops in
a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c =
1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.Comment: 4 pages; omega' corrected: final result changes slightly to
1.25+/-0.13; references added; several minor change
Poisson Structures for Aristotelian Model of Three Body Motion
We present explicitly Poisson structures, for both time-dependent and
time-independent Hamiltonians, of a dynamical system with three degrees of
freedom introduced and studied by Calogero et al [2005]. For the
time-independent case, new constant of motion includes all parameters of the
system. This extends the result of Calogero et al [2009] for semi-symmetrical
motion. We also discuss the case of three bodies two of which are not
interacting with each other but are coupled with the interaction of third one
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