26,295 research outputs found
Many-polaron states in the Holstein-Hubbard model
A variational approach is proposed to determine some properties of the
adiabatic Holstein-Hubbard model which describes the interactions between a
static atomic lattice and an assembly of fermionic charge carriers. The sum of
the electronic energy and the lattice elastic energy is proved to have minima
with a polaron structure in a certain domain of the phase diagram. Our
analytical work consists in the expansion of these energy minima from the zero
electronic transfer limit which remarkably holds for a finite amplitude of the
onsite Hubbard repulsion and for an unbounded lattice size.Comment: submitted to Journal of Statistical Physic
Lie Dimension Subrings
We compare, for L a Lie ring over the integers, its lower central series
(\gamma_n(L))_{n>0} and its dimension series defined by \delta_n(L):=L\cap
\varpi^n(L) in the universal enveloping algebra of L. We show that
\gamma_n(L)=\delta_n(L) for all n<4, but give an example showing that they may
differ if n=4. We introduce simplicial methods to describe these results, and
to serve as a possible tool for further study of the dimension series.Comment: Small typos fixed wrt v
Visual motion processing and human tracking behavior
The accurate visual tracking of a moving object is a human fundamental skill
that allows to reduce the relative slip and instability of the object's image
on the retina, thus granting a stable, high-quality vision. In order to
optimize tracking performance across time, a quick estimate of the object's
global motion properties needs to be fed to the oculomotor system and
dynamically updated. Concurrently, performance can be greatly improved in terms
of latency and accuracy by taking into account predictive cues, especially
under variable conditions of visibility and in presence of ambiguous retinal
information. Here, we review several recent studies focusing on the integration
of retinal and extra-retinal information for the control of human smooth
pursuit.By dynamically probing the tracking performance with well established
paradigms in the visual perception and oculomotor literature we provide the
basis to test theoretical hypotheses within the framework of dynamic
probabilistic inference. We will in particular present the applications of
these results in light of state-of-the-art computer vision algorithms
Multi-dimensional metric approximation by primitive points
We refine metrical statements in the style of the Khintchine-Groshev Theorem
by requiring certain coprimality constraints on the coordinates of the integer
solutions
Gauge Group TQFT and Improved Perturbative Yang-Mills Theory
We reinterpret the Faddeev-Popov gauge-fixing procedure of Yang-Mills
theories as the definition of a topological quantum field theory for gauge
group elements depending on a background connection. This has the advantage of
relating topological gauge-fixing ambiguities to the global breaking of a
supersymmetry. The global zero modes of the Faddeev-Popov ghosts are handled in
the context of an equivariant cohomology without breaking translational
invariance. The gauge-fixing involves constant fields which play the role of
moduli and modify the behavior of Green functions at subasymptotic scales. At
the one loop level physical implications from these power corrections are gauge
invariant.Comment: 28 pages, uuencoded and compressed tar-file, LATEX+4 PS-figures, uses
psfig.sty. New appendix and some clarifying modifications, references adde
Liquid bridging of cylindrical colloids in near-critical solvents
Within mean field theory, we investigate the bridging transition between a
pair of parallel cylindrical colloids immersed in a binary liquid mixture as a
solvent which is close to its critical consolute point . We determine the
universal scaling functions of the effective potential and of the force between
the colloids. For a solvent which is at the critical concentration and close to
, we find that the critical Casimir force is the dominant interaction at
close separations. This agrees very well with the corresponding Derjaguin
approximation for the effective interaction between the two cylinders, while
capillary forces originating from the extension of the liquid bridge turn out
to be more important at large separations. In addition, we are able to infer
from the wetting characteristics of the individual colloids the first-order
transition of the liquid bridge connecting two colloidal particles to the
ruptured state. While specific to cylindrical colloids, the results presented
here provide also an outline for identifying critical Casimir forces acting on
bridged colloidal particles as such, and for analyzing the bridging transition
between them.Comment: 23 pages, 12 figure
Relative periodic orbits in point vortex systems
We give a method to determine relative periodic orbits in point vortex
systems: it consists mainly into perform a symplectic reduction on a fixed
point submanifold in order to obtain a two-dimensional reduced phase space. The
method is applied to point vortices systems on a sphere and on the plane, but
works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method
permits also to determine some relative equilibria and heteroclinic cycles
connecting these relative equilibria.Comment: 27 pages, 17 figure
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