Generalized and Modified Coherent States  

In General > s.a. coherent states; Squeezed States.
* Idea: Several have been proposed, for systems other than the harmonic oscillator, and they differ considerably; Some generalized coherent states are highly non-classical.
* Generalized: (Perelomov) A state of the form |ψg\(\rangle\) = T(g) |ψ0\(\rangle\), where T(g) is a representation of gG.
* Weak: They do not admit a resolution of unity expressed in terms of a local integral; They arise, e.g., in the case that a group acts on an inadmissible fiducial vector.

And Group Theory > s.a. types of coherent states.
@ And group representations: Perelomov CMP(72)mp/02, 86.
@ SU groups: Luo JMP(97), Basu PRS(99) [SU(1,1)]; Mathur & Sen JMP(01)qp/00 [SU(3)]; Barros e Sá JPA(01)qp/00 [SU(2)], Lachièze-Rey et al IJTP(03)mp; de Guise & Bertola JMP(02) [SU(n+1) on Tn]; Nemoto JPA(00)qp, Mathur & Mani JMP(02)qp [SU(n)]; Mathur & Paul JPA(05)qp [with SU(2) and SU(3) charges]; Sadiq & Inomata JPA(07) [polynomial su(2) algebra]; > s.a. quantum theory in phase space [qubits].
@ SO groups: Lindner et al PRA(03)qp [SO(4) states as direction indicators]; Xu & Ye IJMPA(04) [SO(2,1), for Coulomb problem].
@ Euclidean groups: Isham & Klauder JMP(91).
@ On Lie algebras: Antonsen IJTP(99)phy/97; Fujii hp/01, ht/01, qp/01-talk, YMJ(02)qp [on su(2) and su(1,1)].
@ For deformed algebras: Sunilkumar et al qp/99; El Baz et al RPMP(02)mp; Roknizadeh & Tavassoly JPA(04)mp [f-deformed Fock space]; Kowalski & Rembieliński JPA(04)qp [q-deformed on a circle]; Alvarez-Moraga JPA(05)mp [coherent and squeezed]; Skoda LMP(07) [Hopf algebras]; Ching & Ng PRD(13) [with maximum momentum].
@ Non-commutative spaces, generalized uncertainty relations: Yin & Zhang PLB(05); Naderi et al IJMPA(09); Dey & Fring PRD(12)-a1207; Dey a1609 [completeness of coherent states].
@ Non-commutative quantum mechanics: Lubo JHEP(04)ht/03; Ben Geloun & Scholtz JMP(09)-a0901 [Gazeau-Klauder coherent states].
@ Deformed oscillators: Chung IJTP(01); Nozari & Azizi IJQI(05)gq, Pedram IJMPD(13)-a1204 [harmonic oscillator with generalized uncertainty principle]; El Baz mp/05 [k-deformed fermionic-Grassmann]; Eremin & Meldianov TMP(06), a0810 [and uncertainties].
@ Related topics: Coftas & Gazeau JPA(10)-a0803 [finite groups, and crystal structure]; Mohamed et al JPA(11) [multiplicative group of non-zero \(\mathbb C\) numbers]; Bojowald & Tsobanjan CQG(14)-a1401 [effective properties of group coherent states]; Brahma et al a1612 [in de Sitter spacetime].

Other Modified Coherent States > s.a. Ladder Operators [systems with continuous spectra].
* Non-linear: Right-hand eigenstates of the product of the boson â operator and a non-linear function of the N operator.
* Vector coherent states: A generalization of ordinary coherent states for higher-rank tensor Hilbert spaces.
* Thermal: They provide a framework for generalizing the uncertainty relation to take into account both thermal and quantum fluctuations.
@ Non-linear, even / odd: de Matos & Vogel PRA(96) [non-linear]; Man'ko et al PS(97); Mancini PLA(97); Sivakumar PLA(98), JPA(00); Roy & Roy JPA(98), PLA(99), PLA(99), JPB(00), JPB(00); Wang et al IJTP(03), IJTP(03), IJTP(04); Guo et al IJTP(07).
@ Gazeau-Klauder coherent states: Gazeau & Klauder JPA(99); Yadollahi & Tavassoly OC(10)-a1011 [theoretical scheme for generating them].
@ Affine coherent states: & Klauder JMP(00)qp; Klauder JPA(12)-a1108.
@ Thermal coherent states: Mann et al JMP(89); Floquet et al a1507 [algebraic formulation].
@ Vector coherent states: Bagarello JPA(09)-a0904 [Gazeau-Klauder-type]; Aremua et al a1109 [2D and 3D harmonic oscillators]; Rowe JPA(12)-a1207.
@ Other proposals: Klauder AP(95); Brif et al qp/98-fs [group theoretic]; Penson & Solomon JMP(99); Martin Nieto & Truax OC(00)qp/99 [eigenstates of a j]; Trifonov JOSA(00)qp; Fujii ht/01; Avron et al JMP(02)mp [in time-energy plane]; Solovej & Spitzer CMP(03)mp/02, mp/02-proc [and Scott's correction]; Thirulogasanthar & Honnouvo IJTP(04)mp/03 [zf(z)]; Appl & Schiller JPA(04)qp/03 [hypergeometric]; Hartmann ht/03, Hartmann & Klauder JMP(04)ht/03 [weak]; Roknizadeh & Tavassoly JPA(04)qp, JMP(05)qp/04 [generalized from non-linear]; Hassouni et al PRA(05) [algebraic systems]; Tavassoly qp/05 [tutorial]; Popov et al IJTP(10) [of the Barut-Girardello type]; Twareque Ali et al JPA(11)-a1007 [on Hilbert modules]; Guerrero et al JPA(11)-a1010 [multi-localized]; Honarasa et al JPA(11)-a1103 [excited coherent states for continuous spectra]; Philbin AJP(14)aug-a1311 [generalized coherent states and quantum optics]; Hu et al a1512 [Laguerre polynomial excited coherent states]; Bosso et al a1704 [GUP-modified].
@ Semi-coherent: & Mathews & Eswaran (73); Dodonov & Renó JPA(06) [properties].
@ Photon-added states: Quesne PLA(01)qp [on the circle]; Górska et al JPA(10)-a1007; Windhager et al OC(11)-a1009 [interference between coherent state and single-photon state]; Barbieri et al PRA(10)-a1012 [experimental test]; Sivakumar IJTP(14)-a1402; > s.a. types of coherent states.
@ Supersymmetric coherent states: Kochetov PLA(96) [path integral]; Samsonov JMP(97); Akhtarshenas IJTP(96) [parasupersymmetric coherent states]; Fernández et al JPA(07); Kornbluth & Zypman a1203 [harmonic oscillator, generalized supercoherent states]; > s.a. modified quantum mechanics.
@ Evolution: Kovner & Rosenstein PRD(85); Nikolov & Trifonov qp/04.
@ Manifold of (generalized) coherent states: Fujiwara & Nagaoka JMP(99); Fivel PRA(02)qp.
@ Comparisons: Crawford JPA(99); Fox & Choi PRA(00) [regular vs Gaussian Klauder].
@ Related topics: Ali et al JPA(04)qp/03 [dualities and relationships]; Boixo et al EPL(07)qp/06 [for open quantum systems, and noiseless subspaces]; Bang & Berger PRA(09)-a0811, Marchiolli & Ruzzi AP(12) [discrete phase space]; Heinosaari & Pellonpää JPA(12)-a1112 [and POVMs]; Horzela & Szafraniec JPA(12) [measure-free approach]; Allevi et al JOSA(13)-a1302 [phase-averaged coherent states]; Drummond a1610 [in projected Hilbert spaces].

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