264 research outputs found
Prescription-induced jump distributions in multiplicative Poisson processes
Generalized Langevin equations (GLE) with multiplicative white Poisson noise
pose the usual prescription dilemma leading to different evolution equations
(master equations) for the probability distribution. Contrary to the case of
multiplicative gaussian white noise, the Stratonovich prescription does not
correspond to the well known mid-point (or any other intermediate)
prescription. By introducing an inertial term in the GLE we show that the Ito
and Stratonovich prescriptions naturally arise depending on two time scales,
the one induced by the inertial term and the other determined by the jump
event. We also show that when the multiplicative noise is linear in the random
variable one prescription can be made equivalent to the other by a suitable
transformation in the jump probability distribution. We apply these results to
a recently proposed stochastic model describing the dynamics of primary soil
salinization, in which the salt mass balance within the soil root zone requires
the analysis of different prescriptions arising from the resulting stochastic
differential equation forced by multiplicative white Poisson noise whose
features are tailored to the characters of the daily precipitation. A method is
finally suggested to infer the most appropriate prescription from the data
Finite groups with all minimal subgroups solitary
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order
Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions,
i.e., including a linear pseudoscalar potential and quadratic scalar and vector
potentials which have equal or opposite signs. We consider positive and
negative quadratic potentials and discuss in detail their bound-state solutions
for fermions and antifermions. The main features of these bound states are the
same as the ones of the generalized three-dimensional relativistic harmonic
oscillator bound states. The solutions found for zero pseudoscalar potential
are related to the spin and pseudospin symmetry of the Dirac equation in 3+1
dimensions. We show how the charge conjugation and chiral
transformations relate the several spectra obtained and find that for massless
particles the spin and pseudospin symmetry related problems have the same
spectrum, but different spinor solutions. Finally, we establish a relation of
the solutions found with single-particle states of nuclei described by
relativistic mean-field theories with scalar, vector and isoscalar tensor
interactions and discuss the conditions in which one may have both nucleon and
antinucleon bound states.Comment: 33 pages, 10 figures, uses revtex macro
Multiple G-It\^{o} integral in the G-expectation space
In this paper, motivated by mathematic finance we introduce the multiple
G-It\^{o} integral in the G-expectation space, then investigate how to
calculate. We get the the relationship between Hermite polynomials and multiple
G-It\^{o} integrals which is a natural extension of the classical result
obtained by It\^{o} in 1951.Comment: 9 page
Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential
We present a formalism for obtaining the statistical properties of
functionals and inverse functionals of the paths of a particle diffusing in a
one-dimensional quenched random potential. We demonstrate the implementation of
the formalism in two specific examples: (1) where the functional corresponds to
the local time spent by the particle around the origin and (2) where the
functional corresponds to the occupation time spent by the particle on the
positive side of the origin, within an observation time window of size . We
compute the disorder average distributions of the local time, the inverse local
time, the occupation time and the inverse occupation time, and show that in
many cases disorder modifies the behavior drastically.Comment: Revtex two column 27 pages, 10 figures, 3 table
The Local Time Distribution of a Particle Diffusing on a Graph
We study the local time distribution of a Brownian particle diffusing along
the links on a graph. In particular, we derive an analytic expression of its
Laplace transform in terms of the Green's function on the graph. We show that
the asymptotic behavior of this distribution has non-Gaussian tails
characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included
Approximation of Feynman path integrals with non-smooth potentials
We study the convergence in of the time slicing approximation of
Feynman path integrals under low regularity assumptions on the potential.
Inspired by the custom in Physics and Chemistry, the approximate propagators
considered here arise from a series expansion of the action. The results are
ultimately based on function spaces, tools and strategies which are typical of
Harmonic and Time-frequency analysis.Comment: 18 page
The Dirac-Dowker Oscillator
The oscillator-like interaction is introduced in the equation for the
particle of arbitrary spin, given by Dirac and re-written to a matrix form by
Dowker.Comment: LaTeX file, 4pp. Preprint EFUAZ 94-0
Comment on ``the Klein-Gordon Oscillator''
The different ways of description of the particle with oscillator-like
interaction are considered. The results are in conformity with the previous
paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p
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