Huygens' principle and Dirac-Weyl equation

We investigate the validity of Huygens' principle for forward propagation in the massless Dirac-Weyl equation. The principle holds for odd space dimension n, while it is invalid for even n. We explicitly solve the cases n=1,2 and 3 and discuss generic $n$. We compare with the massless Klein-Gordon equation and comment on possible generalizations and applications.Comment: 7 pages, 1 figur

Speaker Diarization Based on Intensity Channel Contribution

The time delay of arrival (TDOA) between multiple microphones has been used since 2006 as a source of information (localization) to complement the spectral features for speaker diarization. In this paper, we propose a new localization feature, the intensity channel contribution (ICC) based on the relative energy of the signal arriving at each channel compared to the sum of the energy of all the channels. We have demonstrated that by joining the ICC features and the TDOA features, the robustness of the localization features is improved and that the diarization error rate (DER) of the complete system (using localization and spectral features) has been reduced. By using this new localization feature, we have been able to achieve a 5.2% DER relative improvement in our development data, a 3.6% DER relative improvement in the RT07 evaluation data and a 7.9% DER relative improvement in the last year's RT09 evaluation data

Representation of non-semibounded quadratic forms and orthogonal additivity

In this article we give a representation theorem for non-semibounded Hermitean quadratic forms in terms of a (non-semibounded) self-adjoint operator. The main assumptions are closability of the Hermitean quadratic form, the direct integral structure of the underlying Hilbert space and orthogonal additivity. We apply this result to several examples, including the position operator in quantum mechanics and quadratic forms invariant under a unitary representation of a separable locally compact group. The case of invariance under a compact group is also discussed in detail

A Hodge - De Rham Dirac operator on the quantum SU(2){\rm SU}(2)

We describe how it is possible to describe irreducible actions of the Hodge - de Rham Dirac operator upon the exterior algebra over the quantum spheres ${\rm SU}_q(2)$ equipped with a three dimensional left covariant calculus.Comment: 18 page

On global approximate controllability of a quantum particle in a box by moving walls

We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any target state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schr\"odinger equation and use a stability theorem for the time-dependent Schr\"odinger equation.Comment: 25 pages, 1 figur

On a sharper bound on the stability of non-autonomous Schr\"odinger equations and applications to quantum control

We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their Hamiltonians. The stability theorem obtained in this article provides a sharper bound than those previously obtained in the literature. This makes it a potentially useful tool for time-dependent problems in Quantum Physics, in particular for Quantum Control. We apply this result to prove two theorems about global approximate controllability of infinite-dimensional quantum systems. These results improve and generalise existing results on infinite-dimensional quantum control.Comment: arXiv admin note: text overlap with arXiv:2108.0049