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Coherent states in mathematical physics

About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.


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Journal ArticleDOI
TL;DR: In this paper, it is shown on examples that the distance between nearby states is related to quantum fluctuations; in particular, in the particular case of the harmonic oscillator group the condition of zero curvature appears to be identical to that of non dispersion of wave packets.
Abstract: A metric tensor is defined from the underlying Hilbert space structure for any submanifold of quantum states. The case where the manifold is generated by the action of a Lie group on a fixed state vector (generalized coherent states manifold hereafter noted G.C.S.M.) is studied in details; the geometrical properties of some wellknown G.C.S.M. are reviewed and an explicit expression for the scalar Riemannian curvature is given in the general case. The physical meaning of such Riemannian structures (which have been recently introduced to describe collective manifolds in nuclear physics) is discussed. It is shown on examples that the distance between nearby states is related to quantum fluctuations; in the particular case of the harmonic oscillator group the condition of zero curvature appears to be identical to that of non dispersion of wave packets.

520 citations

Book
26 Oct 2009
TL;DR: In this article, the basic formalism of Probability theory has been used for the quantization of spin-coherent states in the context of quantum information and quantum physics.
Abstract: Part I: Coherent States 1. Introduction 2. The Standard Coherent States: The Basics 3. The Standard Coherent States: The (Elementary) Mathematics 4. Coherent States in Quantum Information: An Example of Experimental Manipulation 5. Coherent States: A General Construction 6. The Spin Coherent States 7. Selected Pieces of Applications of Standard and Spin Coherent States 8. SU(1,1) or SL(2,R)Coherent States 9. Another Family of SU(1,1) Coherent States for Quantum Systems 10. Squeezed States and their SU(1,1) Content 11. Fermionic Coherent States Part II: Coherent State Quantization 12. Standard Coherent Quantization: The Klauder-Berezin Approach 13. Coherent State or Frame Quantization 14. CS Quantization of Finite Set, Unit Interval, and Circle 15. CS Quantization of Motions on Circle, Interval, and Others 16. Quantization of the Motion on the Torus 17. Fuzzy Geometries: Sphere and Hyperboloid 18. Conclusion and Outlook Appendices A. The Basic Formalism of Probability Theory B. The Basics of Lie Algebra, Lie Groups, and their Representation C. SU(2)-Material D. Wigner-Eckart Theorem for CS quantized Spin Harmonics E. Symmetrization of the Commutator Bibliography

448 citations

Journal ArticleDOI
TL;DR: An improved phase estimation scheme employing entangled coherent states is presented and it is demonstrated that these states give the smallest variance in the phase parameter in comparison to NOON, "bat," and "optimal" states under perfect and lossy conditions.
Abstract: We present an improved phase estimation scheme employing entangled coherent states and demonstrate that these states give the smallest variance in the phase parameter in comparison to NOON, ``bat,'' and ``optimal'' states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.

409 citations

Journal ArticleDOI
TL;DR: In this article, a generalized Heisenberg-type uncertainty relation is obtained for two arbitrary operators both in the case of pure and of mixed states, and as a rule equality is found to hold for pure quantum state only.

265 citations

Book
05 Feb 2012
TL;DR: The standard coherent states of quantum mechanics were defined and analyzed in this article, where the Weyl symbols of the metaplectic operators were represented as Weyl-Heisenberg group.
Abstract: The standard coherent states of quantum mechanics.- The Weyl-Heisenberg group and the coherent states of arbitrary profile.- The coherent states of the Harmonic Oscillator.- From Schrodinger to Fock-Bargmann representation.- Weyl quantization and coherent states: Classical and Quantum observables.- Wigner function.- Coherent states and operator norm estimates.- Product rule and applications.- Husimi functions, frequency sets and propagation.- The Wick and anti-Wick quantization.- The generalized coherent states in the sense of Perelomov.- The SU(1,1) coherent states: Definition and properties.- The squeezed states.- The SU(2) coherent states.- The quantum quadratic Hamiltonians: The propagator of quadratic quantum Hamiltonians.- The metaplectic transformations.- The propagation of coherent states.- Representation of the Weyl symbols of the metaplectic operators.- The semiclassical evolution of coherent states.- The van Vleck and Hermann-Kluk approximations.- The semiclassical Gutzwiller trace formula using coherent states decomposition.- The hydrogen atom coherent states: Definition and properties.- The localization around Kepler orbits.- The quantum singular oscillator: The two-body case.- The N-body case.

262 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202214
20201
20182
201710
201612