3,053 research outputs found
Analysis of Nonlinear Noisy Integrate\&Fire Neuron Models: blow-up and steady states
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks
can be written as Fokker-Planck-Kolmogorov equations on the probability density
of neurons, the main parameters in the model being the connectivity of the
network and the noise. We analyse several aspects of the NNLIF model: the
number of steady states, a priori estimates, blow-up issues and convergence
toward equilibrium in the linear case. In particular, for excitatory networks,
blow-up always occurs for initial data concentrated close to the firing
potential. These results show how critical is the balance between noise and
excitatory/inhibitory interactions to the connectivity parameter
Functional characterization of generalized Langevin equations
We present an exact functional formalism to deal with linear Langevin
equations with arbitrary memory kernels and driven by any noise structure
characterized through its characteristic functional. No others hypothesis are
assumed over the noise, neither the fluctuation dissipation theorem. We found
that the characteristic functional of the linear process can be expressed in
terms of noise's functional and the Green function of the deterministic
(memory-like) dissipative dynamics. This object allow us to get a procedure to
calculate all the Kolmogorov hierarchy of the non-Markov process. As examples
we have characterized through the 1-time probability a noise-induced interplay
between the dissipative dynamics and the structure of different noises.
Conditions that lead to non-Gaussian statistics and distributions with long
tails are analyzed. The introduction of arbitrary fluctuations in fractional
Langevin equations have also been pointed out
Deconstructing double-barred galaxies in 2D and 3D. II. Two distinct groups of inner bars
The intrinsic photometric properties of inner and outer stellar bars within
17 double-barred galaxies are thoroughly studied through a photometric analysis
consisting of: i) two-dimensional multi-component photometric decompositions,
and ii) three-dimensional statistical deprojections for measuring the
thickening of bars, thus retrieving their 3D shape. The results are compared
with previous measurements obtained with the widely used analysis of integrated
light. Large-scale bars in single- and double-barred systems show similar
sizes, and inner bars may be longer than outer bars in different galaxies. We
find two distinct groups of inner bars attending to their in-plane length and
ellipticity, resulting in a bimodal behaviour for the inner/outer bar length
ratio. Such bimodality is related neither to the properties of the host galaxy
nor the dominant bulge, and it does not show a counterpart in the dimension off
the disc plane. The group of long inner bars lays at the lower end of the outer
bar length vs. ellipticity correlation, whereas the short inner bars are out of
that relation. We suggest that this behaviour could be due to either a
different nature of the inner discs from which the inner bars are dynamically
formed, or a different assembly stage for the inner bars. This last possibility
would imply that the dynamical assembly of inner bars is a slow process taking
several Gyr to happen. We have also explored whether all large-scale bars are
prone to develop an inner bar at some stage of their lives, possibility we
cannot fully confirm or discard.Comment: 14 pages, 8 figures, 1 table. Accepted for publication in MNRA
Non-equilibrium transition from dissipative quantum walk to classical random walk
We have investigated the time-evolution of a free particle in interaction
with a phonon thermal bath, using the tight-binding approach. A dissipative
quantum walk can be defined and many important non-equilibrium decoherence
properties can be investigated analytically. The non-equilibrium statistics of
a pure initial state have been studied. Our theoretical results indicate that
the evolving wave-packet shows the suppression of Anderson's boundaries
(ballistic peaks) by the presence of dissipation. Many important relaxation
properties can be studied quantitatively, such as von Neumann's entropy and
quantum purity. In addition, we have studied Wigner's function. The
time-dependent behavior of the quantum entanglement between a free particle -in
the lattice- and the phonon bath has been characterized analytically. This
result strongly suggests the non-trivial time-dependence of the off-diagonal
elements of the reduced density matrix of the system. We have established a
connection between the quantum decoherence and the dissipative parameter
arising from interaction with the phonon bath. The time-dependent behavior of
quantum correlations has also been pointed out, showing continuous transition
from quantum random walk to classical random walk, when dissipation increases.Comment: Submitted for publication. 17 pages, 6 figure
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