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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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TL;DR: In this paper, a class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained, and the coefficients that expand them into number states are Bessel functions.
Abstract: A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.
16 citations
TL;DR: In this paper, the Segal-Bargmann representation space of the one-mode interacting Fock space was given and the generalized coherent vector associated with the Szego-Jacobi parameters was defined.
Abstract: In this paper, we shall give the Segal–Bargmann representation space of the one-mode interacting Fock space. For this purpose, we shall define the generalized coherent vector associated with the Szego–Jacobi parameters and introduce the associated integral transformation.
16 citations
TL;DR: In this paper, a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(2) coherent states, with a special case of SU(1) states presented as a special special case, and realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose-Einstein condensates.
Abstract: We show that a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(3) coherent states, with a superposition of two SU(2) coherent states presented as a special case. A phase space representation is depicted by projecting the multi-dimensional $Q$-symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose--Einstein condensates.
15 citations
TL;DR: In this paper, Rydberg atom coherent states are constructed for the Coulomb problem and the relationship between decorrelation in time and delocalization in space is elucidated, and the connection with sharp Gaussian wave packets used to explain pump-probe experiments is made.
Abstract: Generalized coherent states are constructed for the Coulomb problem. Following a construction procedure proposed by Klauder @J. Phys. A 29, L293 ~1996!#, Rydberg atom coherent states are defined and analyzed. The relationship between decorrelation in time and delocalization in space is elucidated. Keplerian orbits are discussed. The connection with sharp Gaussian wave packets used to explain pump-probe experiments is made. This is achieved by introducing genuine Gaussian Klauder coherent states that are overcomplete, and permit a resolution of the identity operator. They decorrelate comparatively slowly, and remain spatially localized for many Keplerian periods. @S1050-2947~99!05605-X#
15 citations
15 citations