610 research outputs found
Real symmetric random matrices and replicas
Various ensembles of random matrices with independent entries are analyzed by
the replica formalism in the large-N limit. A result on the Laplacian random
matrix with Wigner-rescaling is generalized to arbitrary probability
distribution.Comment: 17 page
Random Hydrophilic-Hydrophobic Copolymers
We study a single statistical amphiphilic copolymer chain AB in a selective
solvent (e.g.water). Two situations are considered. In the annealed case,
hydrophilic (A) and hydrophobic (B) monomers are at local chemical equilibrium
and both the fraction of A monomers and their location along the chain can
vary, whereas in the quenched case (which is relevant to proteins), the
chemical sequence along the chain is fixed by synthesis. In both cases, the
physical behaviour depends on the average hydrophobicity of the polymer chain.
For a strongly hydrophobic chain (large fraction of B), we find an ordinary
continuous collapse, with a large conformational entropy in the
collapsed phase. For a weakly hydrophobic, or a hydrophilic chain, there is an
unusual first-order collapse transition. In particular, for the case of
Gaussian disorder, this discontinuous transition is driven by a change of sign
of the third virial coefficient. The entropy of this collapsed phase is
strongly reduced with respect to the collapsed phase. Email contact:
[email protected]: Saclay-T94/077 Email: [email protected]
Manning condensation in two dimensions
We consider a macroion confined to a cylindrical cell and neutralized by
oppositely charged counterions. Exact results are obtained for the
two-dimensional version of this problem, in which ion-ion and ion-macroion
interactions are logarithmic. In particular, the threshold for counterion
condensation is found to be the same as predicted by mean-field theory. With
further increase of the macroion charge, a series of single-ion condensation
transitions takes place. Our analytical results are expected to be exact in the
vicinity of these transitions and are in very good agreement with recent
Monte-Carlo simulation data.Comment: 4 pages, 4 figure
Enumeration of RNA structures by Matrix Models
We enumerate the number of RNA contact structures according to their genus,
i.e. the topological character of their pseudoknots. By using a recently
proposed matrix model formulation for the RNA folding problem, we obtain exact
results for the simple case of an RNA molecule with an infinitely flexible
backbone, in which any arbitrary pair of bases is allowed. We analyze the
distribution of the genus of pseudoknots as a function of the total number of
nucleotides along the phosphate-sugar backbone.Comment: RevTeX, 4 pages, 2 figure
Asymptotic Freedom of Elastic Strings and Barriers
We study the problem of a quantized elastic string in the presence of an
impenetrable wall. This is a two-dimensional field theory of an N-component
real scalar field which becomes interacting through the restriction that
the magnitude of is less than , for a spherical wall of
radius . The N=1 case is a string vibrating in a plane between
two straight walls. We review a simple nonperturbative argument that there is a
gap in the spectrum, with asymptotically-free behavior in the coupling (which
is the reciprocal of ) for N greater than or equal to one. This
scaling behavior of the mass gap has been disputed in some of the recent
literature. We find, however, that perturbation theory and the 1/N expansion
each confirms that these theories are asymptotically free. The large N limit
coincides with that of the O(N) nonlinear sigma model. A theta parameter exists
for the N=2 model, which describes a string confined to the interior of a
cylinder of radius .Comment: Text slightly improved, bibilography corrected, more typos corrected,
still Latex 7 page
Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions
We study, by incorporating short-range ion-surface interactions, ionic
profiles of electrolyte solutions close to a non-charged interface between two
dielectric media. In order to account for important correlation effects close
to the interface, the ionic profiles are calculated beyond mean-field theory,
using the loop expansion of the free energy. We show how it is possible to
overcome the well-known deficiency of the regular loop expansion close to the
dielectric jump, and treat the non-linear boundary conditions within the
framework of field theory. The ionic profiles are obtained analytically to
one-loop order in the free energy, and their dependence on different
ion-surface interactions is investigated. The Gibbs adsorption isotherm, as
well as the ionic profiles are used to calculate the surface tension, in
agreement with the reverse Hofmeister series. Consequently, from the
experimentally-measured surface tension, one can extract a single adhesivity
parameter, which can be used within our model to quantitatively predict hard to
measure ionic profiles.Comment: 14 pages, 6 figure
Bridge Hopping on Conducting Polymers in Solution
Configurational fluctuations of conducting polymers in solution can bring
into proximity monomers which are distant from each other along the backbone.
Electrons can hop between these monomers across the "bridges" so formed. We
show how this can lead to (i) a collapse transition for metallic polymers, and
(ii) to the observed dramatic efficiency of acceptor molecules for quenching
fluorescence in semiconducting polymers.Comment: RevTeX 12 pages + 2 Postscript figure
Topological Wilson-loop area law manifested using a superposition of loops
We introduce a new topological effect involving interference of two meson
loops, manifesting a path-independent topological area dependence. The effect
also draws a connection between quark confinement, Wilson-loops and topological
interference effects. Although this is only a gedanken experiment in the
context of particle physics, such an experiment may be realized and used as a
tool to test confinement effects and phase transitions in quantum simulation of
dynamic gauge theories.Comment: Superceding arXiv:1206.2021v1 [quant-ph
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