779,445 research outputs found
On a random walk with memory and its relation to Markovian processes
We study a one-dimensional random walk with memory in which the step lengths
to the left and to the right evolve at each step in order to reduce the
wandering of the walker. The feedback is quite efficient and lead to a
non-diffusive walk. The time evolution of the displacement is given by an
equivalent Markovian dynamical process. The probability density for the
position of the walker is the same at any time as for a random walk with
shrinking steps, although the two-time correlation functions are quite
different.Comment: 10 pages, 4 figure
Space-time random walk loop measures
In this work, we investigate a novel setting of Markovian loop measures and
introduce a new class of loop measures called Bosonic loop measures. Namely, we
consider loop soups with varying intensity (chemical potential in
physics terms), and secondly, we study Markovian loop measures on graphs with
an additional "time" dimension leading to so-called space-time random walks and
their loop measures and Poisson point loop processes. Interesting phenomena
appear when the additional coordinate of the space-time process is on a
discrete torus with non-symmetric jump rates. The projection of these
space-time random walk loop measures onto the space dimensions is loop measures
on the spatial graph, and in the scaling limit of the discrete torus, these
loop measures converge to the so-called [Bosonic loop measures]. This provides
a natural probabilistic definition of [Bosonic loop measures]. These novel loop
measures have similarities with the standard Markovian loop measures only that
they give weights to loops of certain lengths, namely any length which is
multiple of a given length which serves as an additional
parameter. We complement our study with generalised versions of Dynkin's
isomorphism theorem (including a version for the whole complex field) as well
as Symanzik's moment formulae for complex Gaussian measures. Due to the lacking
symmetry of our space-time random walks, the distributions of the occupation
time fields are given in terms of complex Gaussian measures over complex-valued
random fields ([B92,BIS09]. Our space-time setting allows obtaining quantum
correlation functions as torus limits of space-time correlation functions.Comment: 3 figure
Statistics of the Mesoscopic Field
We find in measurements of microwave transmission through quasi-1D dielectric
samples for both diffusive and localized waves that the field normalized by the
square root of the spatially averaged flux in a given sample configuration is a
Gaussian random process with position, polarization, frequency, and time. As a
result, the probability distribution of the field in the random ensemble is a
mixture of Gaussian functions weighted by the distribution of total
transmission, while its correlation function is a product of correlators of the
Gaussian field and the square root of the total transmission.Comment: RevTex: 5 pages, 2 figures; to be presented at Aspects of Quantum
Chaotic Scattering (Dresden, March 7-12, 2005
Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study
The quantum dynamics of an ensemble of interacting electrons in an array of
random scatterers is treated using a new numerical approach for the calculation
of average values of quantum operators and time correlation functions in the
Wigner representation. The Fourier transform of the product of matrix elements
of the dynamic propagators obeys an integral Wigner-Liouville-type equation.
Initial conditions for this equation are given by the Fourier transform of the
Wiener path integral representation of the matrix elements of the propagators
at the chosen initial times. This approach combines both molecular dynamics and
Monte Carlo methods and computes numerical traces and spectra of the relevant
dynamical quantities such as momentum-momentum correlation functions and
spatial dispersions. Considering as an application a system with fixed
scatterers, the results clearly demonstrate that the many-particle interaction
between the electrons leads to an enhancement of the conductivity and spatial
dispersion compared to the noninteracting case.Comment: 10 pages and 8 figures, to appear in PRB April 1
Local scale-invariance and ageing in noisy systems
The influence of the noise on the long-time ageing dynamics of a quenched
ferromagnetic spin system with a non-conserved order parameter and described
through a Langevin equation with a thermal noise term and a disordered initial
state is studied. If the noiseless part of the system is Galilei-invariant and
scale-invariant with dynamical exponent z=2, the two-time linear response
function is independent of the noise and therefore has exactly the form
predicted from the local scale-invariance of the noiseless part. The two-time
correlation function is exactly given in terms of certain noiseless three- and
four-point response functions. An explicit scaling form of the two-time
autocorrelation function follows. For disordered initial states, local
scale-invariance is sufficient for the equality of the autocorrelation and
autoresponse exponents in phase-ordering kinetics. The results for the scaling
functions are confirmed through tests in the kinetic spherical model, the
spin-wave approximation of the XY model, the critical voter model and the free
random walk.Comment: Latex2e, 45 pages, no figures, final for
Moments of the Wigner delay times
The Wigner time delay is a measure of the time spent by a particle inside the
scattering region of an open system. For chaotic systems, the statistics of the
individual delay times (whose average is the Wigner time delay) are thought to
be well described by random matrix theory. Here we present a semiclassical
derivation showing the validity of random matrix results. In order to simplify
the semiclassical treatment, we express the moments of the delay times in terms
of correlation functions of scattering matrices at different energies. In the
semiclassical approximation, the elements of the scattering matrix are given in
terms of the classical scattering trajectories, requiring one to study
correlations between sets of such trajectories. We describe the structure of
correlated sets of trajectories and formulate the rules for their evaluation to
the leading order in inverse channel number. This allows us to derive a
polynomial equation satisfied by the generating function of the moments. Along
with showing the agreement of our semiclassical results with the moments
predicted by random matrix theory, we infer that the scattering matrix is
unitary to all orders in the semiclassical approximation.Comment: Refereed version. 18 pages, 5 figure
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