Search results for "Rotational invariance"
showing 7 items of 7 documents
Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation
2020
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed …
Restrictions for asymmetry and polarizations of recoil in muon capture
1975
Abstract Using the helicity formalism, we discuss muon capture by targets of spin-zero. Owing to the definite neutrino helicity, three independent observables define a complete experiment. The precise relation between asymmetry α and longitudinal polarization P L of recoil, α = 1 + 2 jP L , comes only from rotational invariance. When time-reversal invariance is inserted, there is an additional restriction between the average polarization P av and the longitudinal polarization P L . On the basis of the experimental result P av = 0.43 ± 0.10 for 12 C, we predict P L = −(0.99 +0.01 −0.04 .
Realizing total reciprocity violation in the phase for photon scattering
2017
Scientific reports 7, 43114 (2017). doi:10.1038/srep43114
Noncritical quadrature squeezing in two-transverse-mode optical parametric oscillators
2010
In this article we explore the quantum properties of a degenerate optical parametric oscillator when it is tuned to the first family of transverse modes at the down-converted frequency. Recently we found [C. Navarrete-Benlloch et al., Phys. Rev. Lett. 100, 203601 (2008)] that above threshold a TEM${}_{10}$ mode following a random rotation in the transverse plane emerges in this system (we denote it as the bright mode), breaking thus its rotational invariance. Then, owing to the mode orientation being undetermined, we showed that the phase quadrature of the transverse mode orthogonal to this one (denoted as the dark mode) is perfectly squeezed at any pump level and without an increase in the…
Analytical formula for calculating the focal shift in apodized systems
1998
We report a quite simple analytical formula for the evaluation of the focal shift in apodized systems, with or without rotational invariance. Specifically it is shown that the magnitude of the focal shift is determined by the product of the Fresnel number of the focusing geometry and the standard deviation of a mapped version of the azimuthal average of the pupil transmittance. To illustrate our approach, several examples are examined.
Rotation-Invariant Texture Retrieval via Signature Alignment Based on Steerable Sub-Gaussian Modeling
2008
This paper addresses the construction of a novel efficient rotation-invariant texture retrieval method that is based on the alignment in angle of signatures obtained via a steerable sub-Gaussian model. In our proposed scheme, we first construct a steerable multivariate sub-Gaussian model, where the fractional lower-order moments of a given image are associated with those of its rotated versions. The feature extraction step consists of estimating the so-called covariations between the orientation subbands of the corresponding steerable pyramid at the same or at adjacent decomposition levels and building an appropriate signature that can be rotated directly without the need of rotating the im…
Improved rotation invariant pattern recognition using circular harmonics of binary gray level slices
2000
We introduce a new rotation invariant pattern recognition method based on nonlinear correlation. The images are decomposed into disjoint binary slices and then correlated using the common linear correlation. This operation is very discriminant even when the target is embedded in strong noise. We extend our sliced orthogonal nonlinear generalized correlation method to rotation invariant pattern recognition by combining the information of a circular harmonic (CH) of each binary slice of the reference object with binary slices of the target. In addition to improved discrimination capability, the method avoids the time-consuming process of finding proper centers for the CHs. Results are present…