621 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
Continuous-Discrete Path Integral Filtering
A summary of the relationship between the Langevin equation,
Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral
descriptions of stochastic processes relevant for the solution of the
continuous-discrete filtering problem is provided in this paper. The practical
utility of the path integral formula is demonstrated via some nontrivial
examples. Specifically, it is shown that the simplest approximation of the path
integral formula for the fundamental solution of the FPKfe can be applied to
solve nonlinear continuous-discrete filtering problems quite accurately. The
Dirac-Feynman path integral filtering algorithm is quite simple, and is
suitable for real-time implementation.Comment: 35 pages, 18 figures, JHEP3 clas
Opening address
In 1526, almost five hundred years ago, somebody from the neighbourhood of Tongeren was standing here as the central authority at the occasion of the inauguration of this freshly finished new building. It was Mary of Hamal. Hamal is a hamlet just south of Tongeren. It was she who ordered to build a church and convent on this very spot and who supervised the day by day progress of the construction works. She could be very proud of the result, indeed: in less than five years she succeeded in creating a charming small monastery and a magnificent church in this location.
The former convent is now converted into a library. It constitutes the newest accomplishment in the building programme of the K.U.Leuven. The university is very proud with this result: it is a project with a rich cultural-historical value, with an impressive modern architectural value and a clear educational-scientific value as a modern scientific library for the university community. I would like to say a few words about all three aspects
Gravitational anomalies in a dispersive approach
The gravitational anomalies in two dimensions, specifically the Einstein
anomaly and the Weyl anomaly, are fully determined by means of dispersion
relations. In this approach the anomalies originate from the peculiar infrared
feature of the imaginary part of the relevant formfactor which approaches a
-function singularity at zero momentum squared when .Comment: 10 page
Path-integral evolution of multivariate systems with moderate noise
A non Monte Carlo path-integral algorithm that is particularly adept at
handling nonlinear Lagrangians is extended to multivariate systems. This
algorithm is particularly accurate for systems with moderate noise.Comment: 15 PostScript pages, including 7 figure
Direct evidence for stability of tetrahedral interstitial Er in Si up to 900C
Conversion electron emission channeling from the isotope Er (2.28 s), which is the decay product of radioactive Tm (9.25 d), offers a means of monitoring the lattice sites of Er in single crystals. We have used this method to determine the lattice location of Er in Si directly following room temperature implantation of Tm, after subsequent annealing steps, and also in situ during annealing up to 900°C. Following the recovery of implantation damage around 600°C, about 90% of Er occupies near-tetrahedral interstitial sites in both FZ and CZ Si. While in FZ Si Er was found to be stable on these sites even at 900°C, the tetrahedral Er fraction in CZ Si decreased considerably after annealing for 10 min at 800°C and above
Quantum calcium-ion interactions with EEG
Previous papers have developed a statistical mechanics of neocortical
interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated
Annealing (ASA) has been developed to perform fits to such nonlinear stochastic
systems. An N-dimensional path-integral algorithm for quantum systems,
qPATHINT, has been developed from classical PATHINT. Both fold short-time
propagators (distributions or wave functions) over long times. Previous papers
applied qPATHINT to two systems, in neocortical interactions and financial
options. \textbf{Objective}: In this paper the quantum path-integral for
Calcium ions is used to derive a closed-form analytic solution at arbitrary
time that is used to calculate interactions with classical-physics SMNI
interactions among scales. Using fits of this SMNI model to EEG data, including
these effects, will help determine if this is a reasonable approach.
\textbf{Method}: Methods of mathematical-physics for optimization and for path
integrals in classical and quantum spaces are used for this project. Studies
using supercomputer resources tested various dimensions for their scaling
limits. In this paper the quantum path-integral is used to derive a closed-form
analytic solution at arbitrary time that is used to calculate interactions with
classical-physics SMNI interactions among scales. \textbf{Results}: The
mathematical-physics and computer parts of the study are successful, in that
there is modest improvement of cost/objective functions used to fit EEG data
using these models. \textbf{Conclusion}: This project points to directions for
more detailed calculations using more EEG data and qPATHINT at each time slice
to propagate quantum calcium waves, synchronized with PATHINT propagation of
classical SMNI.Comment: published in Sc
Fluctuation relations and rare realizations of transport observables
Fluctuation relations establish rigorous identities for the nonequilibrium
averages of observables. Starting from a general transport master equation with
time-dependent rates, we employ the stochastic path integral approach to study
statistical fluctuations around such averages. We show how under nonequilibrium
conditions, rare realizations of transport observables are crucial and imply
massive fluctuations that may completely mask such identities. Quantitative
estimates for these fluctuations are provided. We illustrate our results on the
paradigmatic example of a mesoscopic RC circuit.Comment: 4 pages, 3 figures; v2: minor changes, published versio
Loop calculations in quantum-mechanical non-linear sigma models
By carefully analyzing the relations between operator methods and the
discretized and continuum path integral formulations of quantum-mechanical
systems, we have found the correct Feynman rules for one-dimensional path
integrals in curved spacetime. Although the prescription how to deal with the
products of distributions that appear in the computation of Feynman diagrams in
configuration space is surprising, this prescription follows unambiguously from
the discretized path integral. We check our results by an explicit two-loop
calculation.Comment: 17 pages, LaTeX, and one figur
Dynamic charge density correlation function in weakly charged polyampholyte globules
We study solutions of statistically neutral polyampholyte chains containing a
large fraction of neutral monomers. It is known that, even if the quality of
the solvent with respect to the neutral monomers is good, a long chain will
collapse into a globule. For weakly charged chains, the interior of this
globule is semi-dilute. This paper considers mainly theta-solvents, and we
calculate the dynamic charge density correlation function g(k,t) in the
interior of the globules, using the quadratic approximation to the
Martin-Siggia-Rose generating functional. It is convenient to express the
results in terms of dimensionless space and time variables. Let R be the blob
size, and let T be the characteristic time scale at the blob level. Define the
dimensionless wave vector q = R k, and the dimensionless time s = t/T. We find
that for q<1, corresponding to length scales larger than the blob size, the
charge density fluctuations relax according to g(q,s) = q^2(1-s^(1/2)) at short
times s < 1, and according to g(q,s) = q^2 s^(-1/2) at intermediate times 1 < s
0.1, where
entanglements are unimportant.Comment: 12 pages RevTex, 1 figure ps, PACS 61.25.Hq, reason replacement:
Expression for dynamic corr. function g(k,t) in old version was incorrect
(though expression for Fourier transform g(k,w) was correct, so the major
part of the calculation remains.) Also major textual chang
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