 Generalized and Modified Coherent States |
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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 g ∈ G.
* 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;
Guaita et al a2012.
@ 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: Watson & Klauder JMP(00)qp;
Klauder JPA(12)-a1108.
@ Thermal coherent states:
Mann et al JMP(89);
Floquet et al IJMPA(17)-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 [z → f(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 PRD(17)-a1704 [GUP-modified];
Goldberg & Steinberg PRQ(20) [transcoherent states].
@ 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;
Mahdifar et al a1801 [on the sphere];
> 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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