Reproducing Kernels in Coherent States, Wavelets, and Quantization

2015 ◽  
pp. 111-125 ◽  
Author(s):  
Syed Twareque Ali
Keyword(s):  
Coherent States ◽  
Reproducing Kernels

Reproducing Kernels and Coherent States on Julia Sets

2007 ◽  
Vol 10 (4) ◽  
pp. 297-312
Author(s):  
K. Thirulogasanthar ◽  
A. Krzyżak ◽  
G. Honnouvo
Keyword(s):  
Coherent States ◽  
Julia Sets ◽  
Reproducing Kernels

scholarly journals Generalized coherent states, reproducing kernels, and quantum support vector machines

2017 ◽  
Vol 17 (15&16) ◽  
pp. 1292-1306 ◽  
Author(s):  
Rupak Chatterjee ◽  
Ting Yu
Keyword(s):  
Hilbert Space ◽  
Coherent States ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Feature Space ◽  
Reproducing Kernels ◽  
Kernel Functions ◽  
Support Vector ◽  
Machine Learning Classification ◽  
Generalized Coherent States

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that these algorithms when executed on a classical computer do not scale well with the size of the feature space both in terms of data points and dimensionality. One of the most significant limitations of classical algorithms using non-linear kernels is that the kernel function has to be evaluated for all pairs of input feature vectors which themselves may be of substantially high dimension. This can lead to computationally excessive times during training and during the prediction process for a new data point. Here, we propose using both canonical and generalized coherent states to calculate specific nonlinear kernel functions. The key link will be the reproducing kernel Hilbert space (RKHS) property for SVMs that naturally arise from canonical and generalized coherent states. Specifically, we discuss the evaluation of radial kernels through a positive operator valued measure (POVM) on a quantum optical system based on canonical coherent states. A similar procedure may also lead to calculations of kernels not usually used in classical algorithms such as those arising from generalized coherent states.

Gazeau- Klouder Coherent states on a sphere

2019 ◽  
Vol 19 (2) ◽  
pp. 379-390
Author(s):  
Z Heibati ◽  
A Mahdifar ◽  
E Amooghorban ◽  
◽  
◽  
...  
Keyword(s):  
Coherent States

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

sl(2)-modules bysl(2)-coherent states

2016 ◽  
Vol 57 (9) ◽  
pp. 091704 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Coherent States
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