5,869 research outputs found
Phase diagram for a copolymer in a micro-emulsion
In this paper we study a model describing a copolymer in a micro-emulsion.
The copolymer consists of a random concatenation of hydrophobic and hydrophilic
monomers, the micro-emulsion consists of large blocks of oil and water arranged
in a percolation-type fashion. The interaction Hamiltonian assigns energy
to hydrophobic monomers in oil and energy to hydrophilic
monomers in water, where are parameters that without loss of
generality are taken to lie in the cone . Depending on the values of these
parameters, the copolymer either stays close to the oil-water interface
(localization) or wanders off into the oil and/or the water (delocalization).
Based on an assumption about the strict concavity of the free energy of a
copolymer near a linear interface, we derive a variational formula for the
quenched free energy per monomer that is column-based, i.e., captures what the
copolymer does in columns of different type. We subsequently transform this
into a variational formula that is slope-based, i.e., captures what the polymer
does as it travels at different slopes, and we use the latter to identify the
phase diagram in the -cone. There are two regimes:
supercritical (the oil blocks percolate) and subcritical (the oil blocks do not
percolate). The supercritical and the subcritical phase diagram each have two
localized phases and two delocalized phases, separated by four critical curves
meeting at a quadruple critical point. The different phases correspond to the
different ways in which the copolymer can move through the micro-emulsion. The
analysis of the phase diagram is based on three hypotheses of percolation-type
on the blocks. We show that these three hypotheses are plausible, but do not
provide a proof.Comment: 100 pages, 16 figures. arXiv admin note: substantial text overlap
with arXiv:1204.123
Probing many-body localization with neural networks
We show that a simple artificial neural network trained on entanglement
spectra of individual states of a many-body quantum system can be used to
determine the transition between a many-body localized and a thermalizing
regime. Specifically, we study the Heisenberg spin-1/2 chain in a random
external field. We employ a multilayer perceptron with a single hidden layer,
which is trained on labeled entanglement spectra pertaining to the fully
localized and fully thermal regimes. We then apply this network to classify
spectra belonging to states in the transition region. For training, we use a
cost function that contains, in addition to the usual error and regularization
parts, a term that favors a confident classification of the transition region
states. The resulting phase diagram is in good agreement with the one obtained
by more conventional methods and can be computed for small systems. In
particular, the neural network outperforms conventional methods in classifying
individual eigenstates pertaining to a single disorder realization. It allows
us to map out the structure of these eigenstates across the transition with
spatial resolution. Furthermore, we analyze the network operation using the
dreaming technique to show that the neural network correctly learns by itself
the power-law structure of the entanglement spectra in the many-body localized
regime.Comment: 12 pages, 10 figure
A new adaptive response surface method for reliability analysis
Response surface method is a convenient tool to assess reliability for a wide range of structural mechanical problems. More specifically, adaptive schemes which consist in iteratively refine the experimental design close to the limit state have received much attention. However, it is generally difficult to take into account a lot of variables and to well handle approximation error. The method, proposed in this paper, addresses these points using sparse response surface and a relevant criterion for results accuracy. For this purpose, a response surface is built from an initial Latin Hypercube Sampling (LHS) where the most significant terms are chosen from statistical criteria and cross-validation method. At each step, LHS is refined in a region of interest defined with respect to an importance level on probability density in the design point. Two convergence criteria are used in the procedure: The first one concerns localization of the region and the second one the response surface quality. Finally, a bootstrap method is used to determine the influence of the response error on the estimated probability of failure. This method is applied to several examples and results are discussed
Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
We report an order-N approach to compute the Kubo Hall conductivity for
disorderd two-dimensional systems reaching tens of millions of orbitals, and
realistic values of the applied external magnetic fields (as low as a few
Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity
using a wavepacket propagation method and a continued fraction
expansion for the computation of diagonal and off-diagonal matrix elements of
the Green functions. The validity of the method is demonstrated by comparison
of results with brute-force diagonalization of the Kubo formula, using
(disordered) graphene as system of study. This approach to mesoscopic system
sizes is opening an unprecedented perspective for so-called reverse engineering
in which the available experimental transport data are used to get a deeper
understanding of the microscopic structure of the samples. Besides, this will
not only allow addressing subtle issues in terms of resistance standardization
of large scale materials (such as wafer scale polycrystalline graphene), but
will also enable the discovery of new quantum transport phenomena in complex
two-dimensional materials, out of reach with classical methods.Comment: submitted PRB pape
Universal Low Temperature Asymptotics of the Correlation Functions of the Heisenberg Chain
We calculate the low temperature asymptotics of a function that
generates the temperature dependence of all static correlation functions of the
isotropic Heisenberg chain.Comment: Proceedings of the International Workshop "Recent Advances in Quantum
Integrable Systems" (Annecy, France
Bunching and anti-bunching of localised particles in disordered media
We consider pairs of non-interacting quantum particles transmitted through a
disordered medium, with emphasis on the role of their quantum statistics. It is
shown that particle-number correlations measured in transmission are strikingly
sensitive to the quantum nature of the particles when they undergo Anderson
localisation, due to bosonic bunching and fermionic anti-bunching in the
scattering channels of the medium. The case of distinguishable particles is
also discussed.Comment: 5 pages, 3 figure
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