123,551 research outputs found
Time-resolved spectra of polar-polarizable chromophores in solution
A recently proposed model for steady-state spectra of polar-polarizable
chromophores is extended to describe time-resolved spectra. The model, based on
a two-state picture for the solute and on a continuum overdamped description
for the (polar) solvent, grasps the essential physics of solvation dynamics, as
demonstrated by the comparison with experimental spectra. The solute
(hyper)polarizability is responsible for spectroscopic features that cannot be
rationalized within the standard picture based on a linear perturbative
treatment of the solute-solvent interaction. In particular, the temporal
evolution of band-shapes and the appearance of temporary isosbestic points, two
common puzzling features of observed spectra, are natural consequences of the
molecular hyperpolarizability and of the consequent coupling between solvation
and vibrational degrees of freedom.Comment: 14pages, including 7 figure
Analogue neural networks on correlated random graphs
We consider a generalization of the Hopfield model, where the entries of
patterns are Gaussian and diluted. We focus on the high-storage regime and we
investigate analytically the topological properties of the emergent network, as
well as the thermodynamic properties of the model. We find that, by properly
tuning the dilution in the pattern entries, the network can recover different
topological regimes characterized by peculiar scalings of the average
coordination number with respect to the system size. The structure is also
shown to exhibit a large degree of cliquishness, even when very sparse.
Moreover, we obtain explicitly the replica symmetric free energy and the
self-consistency equations for the overlaps (order parameters of the theory),
which turn out to be classical weighted sums of 'sub-overlaps' defined on all
possible sub-graphs. Finally, a study of criticality is performed through a
small-overlap expansion of the self-consistencies and through a whole
fluctuation theory developed for their rescaled correlations: Both approaches
show that the net effect of dilution in pattern entries is to rescale the
critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure
The Three-Loop Lattice Free Energy
We calculate the free energy of SU(N) gauge theories on the lattice, to three
loops. Our result, combined with Monte Carlo data for the average plaquette,
gives a more precise estimate of the gluonic condensate.Comment: 5 pages + 2 figures (PostScript); report no. IFUP-TH 17/9
Tunnelling rates for the nonlinear Wannier-Stark problem
We present a method to numerically compute accurate tunnelling rates for a
Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii
equation. Our method is based on a sophisticated real-time integration of the
complex-scaled Gross-Pitaevskii equation, and it is capable of finding the
stationary eigenvalues for the Wannier-Stark problem. We show that even weak
nonlinearities have significant effects in the vicinity of very sensitive
resonant tunnelling peaks, which occur in the rates as a function of the Stark
field amplitude. The mean-field interaction induces a broadening and a shift of
the peaks, and the latter is explained by analytic perturbation theory
Supramolecular interactions in clusters of polar and polarizable molecules
We present a model for molecular materials made up of polar and polarizable
molecular units. A simple two state model is adopted for each molecular site
and only classical intermolecular interactions are accounted for, neglecting
any intermolecular overlap. The complex and interesting physics driven by
interactions among polar and polarizable molecules becomes fairly transparent
in the adopted model. Collective effects are recognized in the large variation
of the molecular polarity with supramolecular interactions, and cooperative
behavior shows up with the appearance, in attractive lattices, of discontinuous
charge crossovers. The mean-field approximation proves fairly accurate in the
description of the gs properties of MM, including static linear and non-linear
optical susceptibilities, apart from the region in the close proximity of the
discontinuous charge crossover. Sizeable deviations from the excitonic
description are recognized both in the excitation spectrum and in linear and
non-linear optical responses. New and interesting phenomena are recognized near
the discontinuous charge crossover for non-centrosymmetric clusters, where the
primary photoexcitation event corresponds to a multielectron transfer.Comment: 14 pages, including 11 figure
Effect of two gaps on the flux lattice internal field distribution: evidence of two length scales from muSR in Mg1-xAlxB2
We have measured the transverse field muon spin precession in the flux
lattice (FL) state of the two gap superconductor MgB2 and of the electron doped
compounds Mg1-xAlxB2 in magnetic fields up to 2.8T. We show the effect of the
two gaps on the internal field distribution in the FL, from which we determine
two coherence length parameters and the doping dependence of the London
penetration depth. This is an independent determination of the complex vortex
structure already suggested by the STM observation of large vortices in a MgB2
single crystal. Our data agrees quantitatively with STM and we thus validate a
new phenomenological model for the internal fields.Comment: now in press Phys. Rev. Lett., small modifications required by the
edito
Dielectric response of modified Hubbard models with neutral-ionic and Peierls transitions
The dipole P(F) of systems with periodic boundary conditions (PBC) in a
static electric field F is applied to one-dimensional Peierls-Hubbard models
for organic charge-transfer (CT) salts. Exact results for P(F) are obtained for
finite systems of N = 14 and 16 sites that are almost converged to infinite
chains in deformable lattices subject to a Peierls transition. The electronic
polarizability per site, \alpha_{el} = (\partial P/\partial F)_0, of rigid
stacks with alternating transfer integrals t(1 +/- \delta) diverges at the
neutral-ionic transition for \delta = 0 but remains finite for \delta > 0 in
dimerized chains. The Peierls or dimerization mode couples to charge
fluctuations along the stack and results in large vibrational contributions,
\alpha_{vib}, that are related to \partial P/\partial \delta and that peak
sharply at the Peierls transition. The extension of P(F) to correlated
electronic states yields the dielectric response \kappa of models with
neutral-ionic or Peierls transitions, where \kappa peaks >100 are found with
parameters used previously for variable ionicity \rho and vibrational spectra
of CT salts. The calculated \kappa accounts for the dielectric response of CT
salts based on substituted TTFs (tetrathiafulvalene) and substituted CAs
(chloranil). The role of lattice stiffness appears clearly in models: soft
systems have a Peierls instability at small \rho and continuous crossover to
large \rho, while stiff stacks such as TTF-CA have a first-order transition
with discontinuous \rho that is both a neutral-ionic and Peierls transition.
The transitions are associated with tuning the electronic ground state of
insulators via temperature or pressure in experiments, or via model parameters
in calculations.Comment: 10 pages, 9 figures; J.Chem.Phys., in pres
Phase transitions, double-scaling limit, and topological strings
Topological strings on Calabi--Yau manifolds are known to undergo phase
transitions at small distances. We study this issue in the case of perturbative
topological strings on local Calabi--Yau threefolds given by a bundle over a
two-sphere. This theory can be regarded as a q--deformation of Hurwitz theory,
and it has a conjectural nonperturbative description in terms of q--deformed 2d
Yang--Mills theory. We solve the planar model and find a phase transition at
small radius in the universality class of 2d gravity. We give strong evidence
that there is a double--scaled theory at the critical point whose all genus
free energy is governed by the Painlev\'e I equation. We compare the critical
behavior of the perturbative theory to the critical behavior of its
nonperturbative description, which belongs to the universality class of 2d
supergravity. We also give evidence for a new open/closed duality relating
these Calabi--Yau backgrounds to open strings with framing.Comment: 49 pages, 3 eps figures; section added on non-perturbative proposal
and 2d gravity; minor typos correcte
Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions
We give explicit numerical values with 100 decimal digits for the Mertens
constant involved in the asymptotic formula for and, as a by-product, for the Meissel-Mertens constant
defined as , for , ...,
and .Comment: 12 pages, 6 table
Gravitational-wave extraction from neutron-star oscillations
We compare different gravitational-wave extraction methods used in
three-dimensional nonlinear simulations against linear simulations of
perturbations of spherical spacetimes with matter. We present results from
fully general-relativistic simulations of a system composed by an oscillating
and non-rotating star emitting gravitational radiation. Results about the onset
of non-linear effects are also shown
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