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 $\Lambda \subset \mathbb{Z}^d$. It is well known that for small values of activity there exist the infinite volume ($\Lambda \to \mathbb{Z}^d$) limiting Gibbs distribution and the infinite volume correlation functions. In this paper we consider the converse problem - we show that given $\rho_1$ and $\rho_2(x)$, where $\rho_1$ is a constant and $\rho_2(x)$ is a function on $\mathbb{Z}^d$, which are sufficiently small, there exist a pair potential and a value of activity, for which $\rho_1$ is the density and $\rho_2(x)$ 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 $C^\infty$ 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 $\tau=1$ (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 $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially in a bound state produced by the binding potential $-2\delta (x)$. We prove that this probability goes to zero as $t\to\infty$ for almost all values of $r$, $\omega$, and $a$. The decay is initially exponential followed by a $t^{-3}$ law if $\omega$ is not close to resonances and $r$ is small; otherwise the exponential disappears and Fermi's golden rule fails. For exceptional sets of parameters $r,\omega$ and $a$ 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