Generalized
and Modified Coherent States |
|
In General > s.a. Squeezed
States.
* Idea: Several have been proposed, for systems other than the harmonic
oscillator, and they differ considerably.
* Generalized: (Perelomov) A state of the form |
g
= T(g) |
0
,
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.
@ 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,
YMJ(02)qp [on
su(2) and su(1,1)].
@ For deformed algebras: Sunilkumar et al qp/99;
El Baz et al mp/02;
Roknizadeh & Tavassoly JPA(04)mp [f-deformed
Fock space]; Kowalski & Rembielinski JPA(04)qp [q-deformed
on a circle]; Alvarez-Moraga JPA(05)mp [coherent
and squeezed]; Yin & Zhang PLB(05)
[in non-commutative space]; Skoda LMP(07) [Hopf algebras].
@ Non-commutative
quantum mechanics:
Lubo JHEP(04)ht/03;
Ben Geloun & Scholtz a0901 [Gazeau-Klauder coherent states].
@ Deformed oscillators: Chung IJTP(01);
Nozari & Azizi IJQI(05)gq [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 a0803 [finite groups, and crystal structure].
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.
* 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).
@ Proposals: Mann et al JMP(89)
[thermal coherent states]; Klauder AP(95);
Brif
et al qp/98-in
[group theoretic]; Gazeau & Klauder
JPA(99);
Penson & Solomon JMP(99);
Martin Nieto & Truax OC(00)qp/99 [eigenstates
of a j]; Trifonov
JOSA(00)qp;
Watson & Klauder JMP(00)qp [affine];
Fujii ht/01;
Avron et al JMP(02)mp [in
time-energy plane]; Solovej & Spitzer mp/02,
mp/02-in
[and Scott's correction]; Thirulogasanthar & Honnouvo IJTP(04)mp/03 [z → f(z)];
Appl & Schiller 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];
Bagarello JPA(09)-a0904 [Gazeau-Klauder-type
vector coherent states]; Naderi et al IJMPA(09) [and non-commutative geometry].
@ Semi-coherent: & Mathews & Eswaran (73); Dodonov & Renó JPA(06) [properties].
@ Photon added: Quesne PLA(01)qp [on
the circle]; > s.a. types of coherent states.
@ Supercoherent states, supersymmetric quantum mechanics: Kochetov PLA(96)
[path integral]; Samsonov JMP(97);
Akhtarshenas IJTP(96)
[parasupersymmetric coherent states]; Fernández et al JPA(07);
> s.a. modified quantum mechanics.
@ Evolution: Kovner & Rosenstein PRD(85); Nikolov & Trifonov qp/04.
@ Manifold of (generalized) coherent states: Fujiwara & Nagaoka JMP(99);
Fivel
qp/02.
@ Comparisons: Crawford JPA(99); Fox & Choi PRA(00) [regular vs
Gaussian Klauder].
@ Related topics: Nesterov & Sabinin IJTP(97)ht/00 [loops
and geometric phases]; Ali et al qp/03 [dualities
and relationships]; Boixo et al EPL(07)qp/06 [for
open quantum systems, and noiseless subspaces]; Bang & Berger a0811 [discrete
phase space].
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jun
2009