17,611 research outputs found
Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data
We study the averaging behavior of nonlinear uniformly elliptic partial
differential equations with random Dirichlet or Neumann boundary data
oscillating on a small scale. Under conditions on the operator, the data and
the random media leading to concentration of measure, we prove an almost sure
and local uniform homogenization result with a rate of convergence in
probability
Nonequilibrium quantum phase transition in itinerant electron systems
We study the effect of the voltage bias on the ferromagnetic phase transition
in a one-dimensional itinerant electron system. The applied voltage drives the
system into a nonequilibrium steady state with a non-zero electric current. The
bias changes the universality class of the second order ferromagnetic
transition. While the equilibrium transition belongs to the universality class
of the uniaxial ferroelectric, we find the mean-field behavior near the
nonequilibrium critical point.Comment: Final version as accepted to Phys. Rev. Let
Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems
It is known that perturbation theory converges in fermionic field theory at
weak coupling if the interaction and the covariance are summable and if certain
determinants arising in the expansion can be bounded efficiently, e.g. if the
covariance admits a Gram representation with a finite Gram constant. The
covariances of the standard many--fermion systems do not fall into this class
due to the slow decay of the covariance at large Matsubara frequency, giving
rise to a UV problem in the integration over degrees of freedom with Matsubara
frequencies larger than some Omega (usually the first step in a multiscale
analysis). We show that these covariances do not have Gram representations on
any separable Hilbert space. We then prove a general bound for determinants
associated to chronological products which is stronger than the usual Gram
bound and which applies to the many--fermion case. This allows us to prove
convergence of the first integration step in a rather easy way, for a
short--range interaction which can be arbitrarily strong, provided Omega is
chosen large enough. Moreover, we give - for the first time - nonperturbative
bounds on all scales for the case of scale decompositions of the propagator
which do not impose cutoffs on the Matsubara frequency.Comment: 29 pages LaTe
Destruction of bulk ordering by surface randomness
We demonstrate that the arbitrarily weak quenched disorder on the surface of
a system of continuous symmetry destroys long range order in the bulk, and,
instead, quasi-long range order emerges. Correlation functions are calculated
exactly for the two- and three-dimensional XY model with surface randomness via
the functional renormalization group. Even at strong quenched disorder the
three-dimensional XY model possesses topological order. We also determine
roughness of a domain wall in the presence of surface disorder.Comment: 4 pages Revtex; Eq. (12) correcte
No quasi-long-range order in strongly disordered vortex glasses: a rigorous proof
The paper contains a rigorous proof of the absence of quasi-long-range order
in the random-field O(N) model for strong disorder in the space of an arbitrary
dimensionality. This result implies that quasi-long-range order inherent to the
Bragg glass phase of the vortex system in disordered superconductors is absent
as the disorder or external magnetic field is strong.Comment: 3 pages, Revte
Earth resources evaluation for New Mexico by LANDSAT-2
The author has identified the following significant results. The Middle Rio Grande project has not yet progressed to the point where mineral exploration sites can be chosen; however, there does appear to be some correlation between the known structure and mineral deposits and the LANDSAT lineament map. A circular feature identified in the southern Magdalena Mountains on LANDSAT-1 imagery agrees well with the location of a newly proposed caldron complex. Several recognized and unrecognized circular features were identified on imagery of the Mogollon-Datil volcanic field. A check of aeromagnetic maps for New Mexico found that the circular features on the LANDSAT imagery showed up as areas of generally high magnetic intensity
- …