SU(1,1) coherent states and associated Wick symbol calculus

AbstractWe prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative $$L^p$$ L p -estimate, for any $$p \ge 1$$ p ≥ 1 , is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.

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Fermionic coherent states

Introduction to Quantum Fields on a Lattice ◽

10.1017/cbo9780511583971.012 ◽

2002 ◽

pp. 242-252

Keyword(s):

Coherent States

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Gazeau- Klouder Coherent states on a sphere

Iranian Journal of Physics Research ◽

10.29252/ijpr.19.2.379 ◽

2019 ◽

Vol 19 (2) ◽

pp. 379-390

Author(s):

Z Heibati ◽

A Mahdifar ◽

E Amooghorban ◽

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...

Keyword(s):

Coherent States

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

Open Systems & Information Dynamics ◽

10.1142/s1230161215500213 ◽

2015 ◽

Vol 22 (04) ◽

pp. 1550021 ◽

Cited By ~ 1

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.

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

Entropy ◽

10.3390/e21030250 ◽

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.

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