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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 quantum-classical correspondence for the oscillator cranking model is established through a set of coherent states of the Heisenberg symplectic group N(2)(X)Sp(4,R).
Abstract: The oscillator cranking-model wavefunction can be identified with a set of coherent states of the symplectic group Sp(4,R). A quantum-classical correspondence for the model is, however, established through a set of coherent states of the Heisenberg symplectic group N(2)(X)Sp(4,R). The properties of these states and their usefulness in various fields of physics are studied in detail. Interesting and useful generalisations of these coherent states are also discussed.
6 citations
TL;DR: In this article, the notion of atomic coherent states is extended to the multilevel case, and it is used to define a holomorphic representation for atomic states and operators in the theory of cascade superfluorescence and superradiant lasing.
Abstract: The notion of atomic coherent states is extended to the multilevel case. Since the representation based on coherent states is convenient in treating collective interactions of atoms with photons, and since many optical processes involve atoms of three or more levels, it is expected that this extension will play a role in the theory of such processes as cascade superfluorescence and superradiant lasing. Like their bosonic counterparts, atomic coherent states may be used to define a holomorphic representation for atomic states and operators. We discuss this in detail and give examples to illustrate applications.
6 citations
TL;DR: In this article, a parameterized family of Toeplitz operators in the context of affine coherent states based on the Calderon reproducing formula and specific admissible wavelets related to Laguerre functions is studied.
Abstract: We study a parameterized family of Toeplitz operators in the context of affine coherent states based on the Calderon reproducing formula (= resolution of unity on ) and the specific admissible wavelets (= affine coherent states in ) related to Laguerre functions. Symbols of such Calderon–Toeplitz operators as individual coordinates of the affine group (= upper half-plane with the hyperbolic geometry) are considered. In this case, a certain class of pseudo-differential operators, their properties and their operator algebras are investigated. As a result of this study, the Fredholm symbol algebras of the Calderon–Toeplitz operator algebras for these particular cases of symbols are described.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
6 citations
6 citations
TL;DR: In this paper, a theoretical analysis of the k-boson nonlinear coherent states of a two-level trapped ion interacting with two laser fields is presented, which are both the zero-energy state of the interaction Hamiltonian and the eigenstates of a deformed annihilation operator.
6 citations