10,371 research outputs found
Quantum chaotic resonances from short periodic orbits
We present an approach to calculating the quantum resonances and resonance
wave functions of chaotic scattering systems, based on the construction of
states localized on classical periodic orbits and adapted to the dynamics.
Typically only a few of such states are necessary for constructing a resonance.
Using only short orbits (with periods up to the Ehrenfest time), we obtain
approximations to the longest living states, avoiding computation of the
background of short living states. This makes our approach considerably more
efficient than previous ones. The number of long lived states produced within
our formulation is in agreement with the fractal Weyl law conjectured recently
in this setting. We confirm the accuracy of the approximations using the open
quantum baker map as an example.Comment: 4 pages, 4 figure
Polymers as compressible soft spheres
We consider a coarse-grained model in which polymers under good-solvent
conditions are represented by soft spheres whose radii, which should be
identified with the polymer radii of gyrations, are allowed to fluctuate. The
corresponding pair potential depends on the sphere radii. This model is a
single-sphere version of the one proposed in Vettorel et al., Soft Matter 6,
2282 (2010), and it is sufficiently simple to allow us to determine all
potentials accurately from full-monomer simulations of two isolated polymers
(zero-density potentials). We find that in the dilute regime (which is the
expected validity range of single-sphere coarse-grained models based on
zero-density potentials) this model correctly reproduces the density dependence
of the radius of gyration. However, for the thermodynamics and the
intermolecular structure, the model is largely equivalent to the simpler one in
which the sphere radii are fixed to the average value of the radius of gyration
and radiiindependent potentials are used: for the thermodynamics there is no
advantage in considering a fluctuating sphere size.Comment: 21 pages, 7 figure
Predicting the thermodynamics by using state-dependent interactions
We reconsider the structure-based route to coarse graining in which the
coarse-grained model is defined in such a way to reproduce some distributions
functions of the original system as accurately as possible. We consider
standard expressions for pressure and chemical potential applied to this family
of coarse-grained models with density-dependent interactions and show that they
only provide approximations to the pressure and chemical potential of the
underlying original system. These approximations are then carefully compared in
two cases: we consider a generic microscopic system in the low-density regime
and polymer solutions under good-solvent conditions. Moreover, we show that the
state-dependent potentials depend on the ensemble in which they have been
derived. Therefore, care must be used in applying canonical state-dependent
potentials to predict phase lines, which is typically performed in other
ensembles.Comment: 29 pages, 1 figure; To appear in J. Chem. Phy
A multi-blob representation of semi-dilute polymer solutions
A coarse-grained multi-blob description of polymer solutions is presented,
based on soft, transferable effective interactions between bonded and
non-bonded blobs. The number of blobs is chosen such that the blob density does
not exceed their overlap threshold, allowing polymer concentrations to be
explored deep into the semi-dilute regime. This quantitative multi-blob
description is shown to preserve known scaling laws of polymer solutions and
provides accurate estimates of amplitudes, while leading to orders of magnitude
increase of simulation efficiency and allowing analytic calculations of
structural and thermodynamic properties.Comment: 4 pages, 4 figure
Multi-scale coarse-graining of diblock copolymer self-assembly: from monomers to ordered micelles
Starting from a microscopic lattice model, we investigate clustering,
micellization and micelle ordering in semi-dilute solutions of AB diblock
copolymers in a selective solvent. To bridge the gap in length scales, from
monomers to ordered micellar structures, we implement a two-step coarse
graining strategy, whereby the AB copolymers are mapped onto ``ultrasoft''
dumbells with monomer-averaged effective interactions between the centres of
mass of the blocks. Monte Carlo simulations of this coarse-grained model yield
clear-cut evidence for self-assembly into micelles with a mean aggregation
number n of roughly 100 beyond a critical concentration. At a slightly higher
concentration the micelles spontaneously undergo a disorder-order transition to
a cubic phase. We determine the effective potential between these micelles from
first principles.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett
Consistent coarse-graining strategy for polymer solutions in the thermal crossover from Good to Theta solvent
We extend our previously developed coarse-graining strategy for linear
polymers with a tunable number n of effective atoms (blobs) per chain [D'Adamo
et al., J. Chem. Phys. 137, 4901 (2012)] to polymer systems in thermal
crossover between the good-solvent and the Theta regimes. We consider the
thermal crossover in the region in which tricritical effects can be neglected,
i.e. not too close to the Theta point, for a wide range of chain volume
fractions Phi=c/c* (c* is the overlap concentration), up to Phi=30. Scaling
crossover functions for global properties of the solution are obtained by
Monte-Carlo simulations of the Domb-Joyce model. They provide the input data to
develop a minimal coarse-grained model with four blobs per chain. As in the
good-solvent case, the coarse-grained model potentials are derived at zero
density, thus avoiding the inconsistencies related to the use of
state-dependent potentials. We find that the coarse-grained model reproduces
the properties of the underlying system up to some reduced density which
increases when lowering the temperature towards the Theta state. Close to the
lower-temperature crossover boundary, the tetramer model is accurate at least
up to Phi<10, while near the good-solvent regime reasonably accurate results
are obtained up to Phi<2. The density region in which the coarse-grained model
is predictive can be enlarged by developing coarse-grained models with more
blobs per chain. We extend the strategy used in the good-solvent case to the
crossover regime. This requires a proper treatment of the length rescalings as
before, but also a proper temperature redefinition as the number of blobs is
increased. The case n=10 is investigated. Comparison with full-monomer results
shows that the density region in which accurate predictions can be obtained is
significantly wider than that corresponding to the n=4 case.Comment: 21 pages, 14 figure
Phase diagram of mixtures of colloids and polymers in the thermal crossover from good to solvent
We determine the phase diagram of mixtures of spherical colloids and neutral
nonadsorbing polymers in the thermal crossover region between the
point and the good-solvent regime. We use the generalized free-volume theory
(GFVT), which turns out to be quite accurate as long as
( is the radius of gyration of the polymer and is the colloid
radius). Close to the point the phase diagram is not very sensitive to
solvent quality, while, close to the good-solvent region, changes of the
solvent quality modify significantly the position of the critical point and of
the binodals. We also analyze the phase behavior of aqueous solutions of
charged colloids and polymers, using the extension of GFVT proposed by Fortini
et al., J. Chem. Phys. 128, 024904 (2008)
Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures
The free-carrier screening of macroscopic polarization fields in wurtzite
GaN/InGaN quantum wells lasers is investigated via a self-consistent
tight-binding approach. We show that the high carrier concentrations found
experimentally in nitride laser structures effectively screen the built-in
spontaneous and piezoelectric polarization fields, thus inducing a
``field-free'' band profile. Our results explain some heretofore puzzling
experimental data on nitride lasers, such as the unusually high lasing
excitation thresholds and emission blue-shifts for increasing excitation
levels.Comment: RevTeX 4 pages, 4 figure
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