9,329 research outputs found
A Uniform Approximation for the Coherent State Propagator using a Conjugate Application of the Bargmann Representation
We propose a conjugate application of the Bargmann representation of quantum
mechanics. Applying the Maslov method to the semiclassical connection formula
between the two representations, we derive a uniform semiclassical
approximation for the coherent state propagator which is finite at phase space
caustics.Comment: 4 pages, 1 figur
A New Form of Path Integral for the Coherent States Representation and its Semiclassical Limit
The overcompleteness of the coherent states basis leads to a multiplicity of
representations of Feynman's path integral. These different representations,
although equivalent quantum mechanically, lead to different semiclassical
limits. Two such semiclassical formulas were derived in \cite{Bar01} for the
two corresponding path integral forms suggested by Klauder and Skagerstan in
\cite{Klau85}. Each of these formulas involve trajectories governed by a
different classical representation of the Hamiltonian operator: the P
representation in one case and the Q representation in other. In this paper we
construct a third representation of the path integral whose semiclassical limit
involves directly the Weyl representation of the Hamiltonian operator, i.e.,
the classical Hamiltonian itself.Comment: 16 pages, no figure
Energy Dissipation Via Coupling With a Finite Chaotic Environment
We study the flow of energy between a harmonic oscillator (HO) and an
external environment consisting of N two-degrees of freedom non-linear
oscillators, ranging from integrable to chaotic according to a control
parameter. The coupling between the HO and the environment is bilinear in the
coordinates and scales with system size with the inverse square root of N. We
study the conditions for energy dissipation and thermalization as a function of
N and of the dynamical regime of the non-linear oscillators. The study is
classical and based on single realization of the dynamics, as opposed to
ensemble averages over many realizations. We find that dissipation occurs in
the chaotic regime for a fairly small N, leading to the thermalization of the
HO and environment a Boltzmann distribution of energies for a well defined
temperature. We develop a simple analytical treatment, based on the linear
response theory, that justifies the coupling scaling and reproduces the
numerical simulations when the environment is in the chaotic regime.Comment: 7 pages, 10 figure
Modular structure in C. elegans neural network and its response to external localized stimuli
Synchronization plays a key role in information processing in neuronal
networks. Response of specific groups of neurons are triggered by external
stimuli, such as visual, tactile or olfactory inputs. Neurons, however, can be
divided into several categories, such as by physical location, functional role
or topological clustering properties. Here we study the response of the
electric junction C. elegans network to external stimuli using the partially
forced Kuramoto model and applying the force to specific groups of neurons.
Stimuli were applied to topological modules, obtained by the ModuLand
procedure, to a ganglion, specified by its anatomical localization, and to the
functional group composed of all sensory neurons. We found that topological
modules do not contain purely anatomical groups or functional classes,
corroborating previous results, and that stimulating different classes of
neurons lead to very different responses, measured in terms of synchronization
and phase velocity correlations. In all cases, however, the modular structure
hindered full synchronization, protecting the system from seizures. More
importantly, the responses to stimuli applied to topological and functional
modules showed pronounced patterns of correlation or anti-correlation with
other modules that were not observed when the stimulus was applied to ganglia.Comment: 23 pages, 6 figure
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