Search results for "quantization"
showing 10 items of 253 documents
Experimental Realization of a Dirac Monopole through the Decay of an Isolated Monopole
2017
We experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually evolves into a spin configuration hosting a Dirac monopole in its synthetic magnetic field. We characterize in detail the Dirac monopole by measuring the particle densities of the spin states projected along different quantization axes. Importantly, we observe the spontaneous emergence of nodal lines in the condensate density that accompany the Dirac monopole. We also demonstrate that the monopole decay accelerates in weaker magnetic field gradients.
More wavelet-like orthonormal bases for the lowest Landau level: Some considerations
1994
In a previous work, Antoine and I (1994) have discussed a general procedure which 'projects' arbitrary orthonormal bases of L2(R) into orthonormal bases of the lowest Landau level. In this paper, we apply this procedure to a certain number of examples, with particular attention to the spline bases. We also discuss Haar, Littlewood-Paley and Journe bases.
Modular Structures on Trace Class Operators and Applications to Landau Levels
2009
The energy levels, generally known as the Landau levels, which characterize the motion of an electron in a constant magnetic field, are those of the one-dimensional harmonic oscillator, with each level being infinitely degenerate. We show in this paper how the associated von Neumann algebra of observables displays a modular structure in the sense of the Tomita–Takesaki theory, with the algebra and its commutant referring to the two orientations of the magnetic field. A Kubo–Martin–Schwinger state can be built which, in fact, is the Gibbs state for an ensemble of harmonic oscillators. Mathematically, the modular structure is shown to arise as the natural modular structure associated with the…
Quantization of the elastic modes in an isotropic plate
2006
We quantize the elastic modes in a plate. For this, we find a complete, orthogonal set of eigenfunctions of the elastic equations and we normalize them. These are the phonon modes in the plate and their specific forms and dispersion relations are manifested in low temperature experiments in ultra-thin membranes.
Coherent states: a contemporary panorama
2012
Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schr?dinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably…
Deformation Quantization by Moyal Star-Product and Stratonovich Chaos
2012
We make a deformation quantization by Moyal star-product on a space of functions endowed with the normalized Wick product and where Stratonovich chaos are well defined.
Cost-driven framework for progressive compression of textured meshes
2019
International audience; Recent advances in digitization of geometry and radiometry generate in routine massive amounts of surface meshes with texture or color attributes. This large amount of data can be compressed using a progressive approach which provides at decoding low complexity levels of details (LoDs) that are continuously refined until retrieving the original model. The goal of such a progressive mesh compression algorithm is to improve the overall quality of the transmission for the user, by optimizing the rate-distortion trade-off. In this paper, we introduce a novel meaningful measure for the cost of a progressive transmission of a textured mesh by observing that the rate-distor…
New techniques for visualization of losses due to image compression in grayscale medical still images
2003
To evaluate the visual influence of irreversible compression on medical images, changes of the images have to be visualized. The authors have explored alternative techniques to be used instead of the usual side-by-side comparison, where the information contained in both images is perceived in a single image, preserving the context between compression errors and image structures. Thus fast and easy comparison can be done. These techniques make use of the human ability to perceive information also in the dimensions of color, space, and time. A study was performed with JPEG-compressed coronary angiographic images. Changes in the resulting images for six compression factors from 7 to 30 were sc…
Invisible Graffiti on Your Buildings: Blind and Squaring-Proof Watermarking of Geographical Databases
2007
Due to the ease of digital copy, watermarking is crucial to protect the intellectual property of rights owners. We propose an effective watermarking method for vectorial geographical databases, with the focus on the buildings layer. Embedded watermarks survive common geographical filters, including the essential squaring and simplification transformations, as well as deliberate removal attempts, e.g. by noise addition, cropping or over-watermarking. Robustness against the squaring transformation is not adressed by existing approaches. The impact on the quality of the datasets, defined as a composition of point accuracy and angular quality, is assessed through an extensive series of experime…
Observer-Based Stabilization of Stochastic Systems with Limited Communication
2012
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2012/781542 Open Access This paper studies the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A communication channel exists between the output of the plant and the input of the dynamic controller, which is considered network-induced delays, data packet dropouts, and measurement quantization. A new stability criterion is derived for the stochastic nonlinear system by using the Lyapunov functional approach. Based on this, the design procedure of observer-based controller is presented,which ensures asy…