9,730 research outputs found
An Infinite Dimensional Approach to the Third Fundamental Theorem of Lie
We revisit the third fundamental theorem of Lie (Lie III) for finite
dimensional Lie algebras in the context of infinite dimensional matrices.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
We develop in detail a new formalism [as a sequel to the work of T. Champel
and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for
treating quantum problems involving slowly-varying potentials at high magnetic
fields in two-dimensional electron gases. For an arbitrary smooth potential we
show that electronic Green's function is fully determined by closed recursive
expressions that take the form of a high magnetic field expansion in powers of
the magnetic length l_B. For illustration we determine entirely Green's
function at order l_B^3, which is then used to obtain quantum expressions for
the local charge and current electronic densities at equilibrium. Such results
are valid at high but finite magnetic fields and for arbitrary temperatures, as
they take into account Landau level mixing processes and wave function
broadening. We also check the accuracy of our general functionals against the
exact solution of a one-dimensional parabolic confining potential,
demonstrating the controlled character of the theory to get equilibrium
properties. Finally, we show that transport in high magnetic fields can be
described hydrodynamically by a local equilibrium regime and that dissipation
mechanisms and quantum tunneling processes are intrinsically included at the
microscopic level in our high magnetic field theory. We calculate microscopic
expressions for the local conductivity tensor, which possesses both transverse
and longitudinal components, providing a microscopic basis for the
understanding of dissipative features in quantum Hall systems.Comment: small typos corrected; published versio
Phase space gaps and ergodicity breaking in systems with long range interactions
We study a generalized isotropic XY-model which includes both two-spin and
four-spin mean-field interactions. This model can be solved in the
microcanonical ensemble. It is shown that in certain parameter regions the
model exhibits gaps in the magnetization at fixed energy, resulting in
ergodicity breaking. This phenomenon has previously been reported in
anisotropic and discrete spin models. The entropy of the model is calculated
and the microcanonical phase diagram is derived, showing the existence of first
order phase transitions from the ferromagnetic to a paramagnetic disordered
phase. It is found that ergodicity breaking takes place both in the
ferromagnetic and the paramagnetic phases. As a consequence, the system can
exhibit a stable ferromagnetic phase within the paramagnetic region, and
conversely a disordered phase within the magnetically ordered region
Generating Focussed Molecule Libraries for Drug Discovery with Recurrent Neural Networks
In de novo drug design, computational strategies are used to generate novel
molecules with good affinity to the desired biological target. In this work, we
show that recurrent neural networks can be trained as generative models for
molecular structures, similar to statistical language models in natural
language processing. We demonstrate that the properties of the generated
molecules correlate very well with the properties of the molecules used to
train the model. In order to enrich libraries with molecules active towards a
given biological target, we propose to fine-tune the model with small sets of
molecules, which are known to be active against that target.
Against Staphylococcus aureus, the model reproduced 14% of 6051 hold-out test
molecules that medicinal chemists designed, whereas against Plasmodium
falciparum (Malaria) it reproduced 28% of 1240 test molecules. When coupled
with a scoring function, our model can perform the complete de novo drug design
cycle to generate large sets of novel molecules for drug discovery.Comment: 17 pages, 17 figure
Strong and weak semiclassical limits for some rough Hamiltonians
We present several results concerning the semiclassical limit of the time
dependent Schr\"odinger equation with potentials whose regularity doesn't
guarantee the uniqueness of the underlying classical flow. Different topologies
for the limit are considered and the situation where two bicharateristics can
be obtained out of the same initial point is emphasized
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