2,807 research outputs found
On the Fredholm property of bisingular pseudodifferential operators
For operators belonging either to a class of global bisingular
pseudodifferential operators on or to a class of bisingular
pseudodifferential operators on a product of two closed smooth
manifolds, we show the equivalence of their ellipticity (defined by the
invertibility of certain associated homogeneous principal symbols) and their
Fredholm mapping property in associated scales of Sobolev spaces. We also prove
the spectral invariance of these operator classes and then extend these results
to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added
reference
Gauged O(n) spin models in one dimension
We consider a gauged O(n) spin model, n >= 2, in one dimension which contains
both the pure O(n) and RP(n-1) models and which interpolates between them. We
show that this model is equivalent to the non-interacting sum of the O(n) and
Ising models. We derive the mass spectrum that scales in the continuum limit,
and demonstrate that there are two universality classes, one of which contains
the O(n) and RP(n-1) models and the other which has a tuneable parameter but
which is degenerate in the sense that it arises from the direct sum of the O(n)
and Ising models.Comment: 9 pages, no figures, LaTeX sourc
On the relevance of large scale pulsed-laser deposition: Evidence of structural heterogeneities in ZnO thin films
Pulsed-laser deposition is known as a well-suited method for growing thin films of oxide compounds presenting a wide range of functional properties. A limitation of this method for industrial process is the very anisotropic expansion dynamics of the plasma plume, which induces difficulties to grow on large scale films with homogeneous thickness and composition. The specific aspect of the crystalline or orientation uniformity has not been investigated, despite its important role on oxide films properties. In this work, the crystalline parameters and the texture of zinc oxide films are studied as a function of position with respect to the central axis of the plasma plume. We demonstrate the existence of large non-uniformities in the films. The stoichiometry, the lattice parameter, and the distribution of crystallites orientations drastically depend on the position with respect to the plume axis, i.e., on the oblique incidence of the ablated species. The origin of these non-uniformities, in particular, the unexpected tilted orientation of the ZnO c-axis may be attributed to the combined effects of the oblique incidence and of the ratio between oxygen and zinc fluxes reaching the surface of the growing film
Simulating nonequilibrium quantum fields with stochastic quantization techniques
We present lattice simulations of nonequilibrium quantum fields in
Minkowskian space-time. Starting from a non-thermal initial state, the
real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic
process in an additional (5th) ``Langevin-time''. For the example of a
self-interacting scalar field we show how to resolve apparent unstable Langevin
dynamics, and compare our quantum results with those obtained in classical
field theory. Such a direct simulation method is crucial for our understanding
of collision experiments of heavy nuclei or other nonequilibrium phenomena in
strongly coupled quantum many-body systems.Comment: 4 pages, 4 figures, PRL version, minor change
The Complex Langevin method: When can it be trusted?
We analyze to what extent the complex Langevin method, which is in principle
capable of solving the so-called sign problems, can be considered as reliable.
We give a formal derivation of the correctness and then point out various
mathematical loopholes. The detailed study of some simple examples leads to
practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and
minor corrections added, to appear in PR
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