Search results for "Closed and exact differential forms"
showing 5 items of 5 documents
The exterior derivative as a Killing vector field
1996
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.
A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
2010
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional Brownian motions. The exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise.
Theory of ground state factorization in quantum cooperative systems.
2008
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground states in a large variety of, generally non-exactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
New insights into black bodies
2012
Planck's law describes the radiation of black bodies. The study of its properties is of special interest, as black bodies are a good description for the behavior of many phenomena. In this work a new mathematical study of Planck's law is performed and new properties of this old acquaintance are obtained. As a result, the exact form for the locus in a color-color diagrams has been deduced, and an analytical formula to determine with precision the black body temperature of an object from any pair of measurements has been developed. Thus, using two images of the same field obtained with different filters, one can compute a fast estimation of black body temperatures for every pixel in the image…
Probing Quantum Frustrated Systems via Factorization of the Ground State
2009
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physica…