1,050 research outputs found
Analytic linearization of nonlinear perturbations of Fuchsian systems
Nonlinear perturbation of Fuchsian systems are studied in regions including
two singularities. Such systems are not necessarily analytically equivalent to
their linear part (they are not linearizable). Nevertheless, it is shown that
in the case when the linear part has commuting monodromy, and the eigenvalues
have positive real parts, there exists a unique correction function of the
nonlinear part so that the corrected system becomes analytically linearizable
Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case
We study the time evolution of a three dimensional quantum particle,
initially in a bound state, under the action of a time-periodic zero range
interaction with ``strength'' (\alpha(t)). Under very weak generic conditions
on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t
\to \infty). We prove also that, under the same conditions, all the states of
the system are scattering states.Comment: LaTeX2e, 15 page
The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation
Given a potential of pair interaction and a value of activity, one can
consider the Gibbs distribution in a finite domain . It is well known that for small values of activity there exist
the infinite volume () limiting Gibbs distribution
and the infinite volume correlation functions. In this paper we consider the
converse problem - we show that given and , where
is a constant and is a function on , which are
sufficiently small, there exist a pair potential and a value of activity, for
which is the density and is the pair correlation function
Borel summability and Lindstedt series
Resonant motions of integrable systems subject to perturbations may continue
to exist and to cover surfaces with parametric equations admitting a formal
power expansion in the strength of the perturbation. Such series may be,
sometimes, summed via suitable sum rules defining functions of the
perturbation strength: here we find sufficient conditions for the Borel
summability of their sums in the case of two-dimensional rotation vectors with
Diophantine exponent (e. g. with ratio of the two independent
frequencies equal to the golden mean).Comment: 17 pages, 1 figur
Decay versus survival of a localized state subjected to harmonic forcing: exact results
We investigate the survival probability of a localized 1-d quantum particle
subjected to a time dependent potential of the form with
or . The particle is
initially in a bound state produced by the binding potential . We
prove that this probability goes to zero as for almost all values
of , , and . The decay is initially exponential followed by a
law if is not close to resonances and is small; otherwise
the exponential disappears and Fermi's golden rule fails. For exceptional sets
of parameters and the survival probability never decays to zero,
corresponding to the Floquet operator having a bound state. We show similar
behavior even in the absence of a binding potential: permitting a free particle
to be trapped by harmonically oscillating delta function potential
Viroporin potential of the lentivirus lytic peptide (LLP) domains of the HIV-1 gp41 protein
<p>Abstract</p> <p>Background</p> <p>Mechanisms by which HIV-1 mediates reductions in CD4+ cell levels in infected persons are being intensely investigated, and have broad implications for AIDS drug and vaccine development. Virally induced changes in membrane ionic permeability induced by lytic viruses of many families contribute to cytopathogenesis. HIV-1 induces disturbances in plasma membrane ion transport. The carboxyl terminus of TM (gp41) contains potential amphipathic α-helical motifs identified through their structural similarities to naturally occurring cytolytic peptides. These sequences have been dubbed lentiviral lytic peptides (LLP) -1, -2, and -3.</p> <p>Results</p> <p>Peptides corresponding to the LLP domains (from a clade B virus) partition into lipid membranes, fold into α-helices and disrupt model membrane permeability. A peptide corresponding to the LLP-1 domain of a clade D HIV-1 virus, LLP-1D displayed similar activity to the LLP-1 domain of the clade B virus in all assays, despite a lack of amino acid sequence identity.</p> <p>Conclusion</p> <p>These results suggest that the C-terminal domains of HIV-1 Env proteins may form an ion channel, or viroporin. Increased understanding of the function of LLP domains and their role in the viral replication cycle could allow for the development of novel HIV drugs.</p
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