Coherent States: Types of Systems  

In General > s.a. generalized coherent states [including de Sitter space]; geometric quantization; semiclassical quantum mechanics; Squeezed States; systems.
@ Free particle: de la Torre & Goyeneche a1004 [and Husimi distribution]; Bagrov et al PU(14)-a1502 [and semiclassical states].
@ For discrete spectrum: Klauder qp/98-proc.
@ On a circle: Kowalski et al JPA(96)qp/98; González & del Olmo JPA(98)qp; Kowalski & Rembieliński JPA(02)qp [and squeezed]; Ruzzi et al JPA(06)qp; Bahr & Korsch JPA(07)qp/06 [Husimi distributions]; Chadzitaskos et al JPCS(11)-a1101 [or on an infinite 1D lattice]; Gazeau & Kanamoto JPCS(12)-a1110, Aremua et al JPA(12)-a1111 [action-angle coherent states]; Chadzitaskos et al JPA(12)-a1201; Giesel & Winnekens a2001.
@ On spheres: Kowalski & Rembieliński JPA(00)qp/99; Hall & Mitchell JMP(02)qp/01, in(02)qp [on Sd]; Mathur & Paul JPA(05) [carrying SU(2) and SU(3) charges]; Fakhri & Mojaveri IJMPA(10)-a1404 [for spherical harmonics]; Hall & Mitchell JPA(12)-a1112 [with a magnetic field, complexifier approach]; > s.a. Segal-Bargmann Transform.
@ On different spaces: Klauder PRA(86) [half-line]; Kowalski & Rembieliński JMP(93) [quantum complex plane]; Berceanu JGP(97) [homogeneous manifold]; Kowalski & Rembieliński PRA(07)-a0712 [torus], JPA(08) [review]; Prudêncio & Cirilo-Lombardo MPLA(13)-a1306 [Möbius strip].
@ Harmonic oscillator: Johansen PLA(04)qp/03 [non-classical properties]; Kowalski & Rembieliński a1308 [on a cylinder, evolution]; > s.a. modified coherent states; No-Cloning Theorem; oscillator; semiclassical quantum theory.
@ Non-linear oscillator: Molski JPA(09)-a0706; Midya et al PS(09)-a0911 [and revival dynamics]; Ghosh JMP(12)-a1111.
@ Other oscillators: Benatti & Floreanini JPA(00)ht [damped]; Quesne AP(01)qp, in(02)qp/01 [Cλ-extended]; Choi PLA(04) [time-dependent]; Borzov TMP(07) [generalized]; Li RPMP(08) [forced and damped]; > s.a. Pais-Uhlenbeck Model; quantum oscillator.
@ Degenerate spectra: Fox & Choi PRA(01); Curado et al PhyA(06) [H atom, and classical-like behavior]; Dello Sbarba & Hussin JMP(07) [discrete spectra].
@ H atom: Klauder JPA(96)qp/95; Majumdar & Sharatchandra PRA(97)qp; Fox PRA(99); Pol'shin JPA(00)qp, JPA(01)qp; Xu et al PRA(00); Ünal PRA(01); Nouri PRA(02) [1D Coulomb]; Thaik & Inomata JPA(05)qp/04 [radial, constant curvature space].
@ For spin: Aravind AJP(99)oct [and geometric phase]; Novaes PRA(05)qp [semiclassical propagation]; Tyc et al FP(07) [fermions]; Braun & Garg JMP(07) [many spins, semiclassical propagator]; Muminov & Yousefi a1103; Yu et al PRA(11) [many entangled spins]; Combescure & Robert JPA(12) [fermionic, using Grassmann numbers]; Francisco JPA(12) [and number theory]; Baecklund & Bengtsson PS(14)-a1312-conf [remarks]; Oeckl JPA(15)-a1408 [fermions]; Oeckl a1708-proc [in fermionic Fock-Krein spaces]; Chryssomalakos et al a1710 [geometry].
@ Finite-dimensional Hilbert spaces: Galetti & Marchiolli AP(96); Miranowicz et al in(01)qp, Leoński & Miranowicz in(01)qp; Borzov & Damaskinsky qp/06; Dömötör & Benedict PLA(08)-a0709, Muñoz et al IJQI(09)-a0809, JPA(12)-a1206 [for N qubits]; Coftas & Dragoman JPA(12)-a1205 [Wigner quasi-distribution and the discrete-continuous transition]; Alam et al a1712 [finite dimensional systems, different definitions].
@ Integrable: Haba MPLB(95)qp; Samsomov JMP(98)qp/97; Song & Park IJMPA(02)qp/01 [Calogero-Sutherland].
@ Various potentials: & Nonnenmacher & Voros JPA(97)cd/96 [inverted oscillator, H = \(1\over2\)(P2Q2)]; Martin Nieto MPLA(01)qp [analytic potentials]; Shreecharan et al PRA(04) [exactly solvable]; Belloni et al PS(05) [infinite wall]; Contreras-Astorga et al JPA(11)-a1009, Bagrov et al BJP(15)-a1502 [quadratic]; Román-Ancheyta et al JPA(11)-a1503 [trigonometric Pöschl-Teller potential].
@ Particle in an electromagnetic field: Kowalski & Rembieliński JPA(05)qp [uniform B field]; Herrera et al EJP(08) [and Husimi function]; Gazeau et al PLA(09)-a0902 [and Stieltjes moment problem]; Mantoiu et al a0911 [variable field]; Bagrov et al JPA(11)-a1008 [magnetic-solenoid field]; Díaz-Bautista & Fernández EPJP(17)-a1703 [Dirac electron in graphene placed in a magnetic field]; Dodonov a1711-proc [rev, and generalizations]; Pereira BJP(18)-a1711; Adorno & Pereira RPJ(18)-a1805.
@ Non-Hermitian systems: Bagchi & Quesne MPLA(01)qp [oscillator]; Roy & Roy PLA(06)qp; Dey et al a1801-proc [with minimal length].
@ Non-linear coherent states: Lev et al PRA(02)qp [spin-0 particle]; Eftekhari & Tavassoly IJMPA(10)-a1011, Tavassoly OC(10)-a1011 [quantum statistics and non-classical properties]; de los Santos-Sánchez & Récamier JPA(11), Román-Ancheyta & Récamier AQC(15)-a1503 [non-linear systems].
@ Multipartite: Lee et al PRA(13)-a1309 [composite bosons of distinguishable particles]; Bruschi et al PRA(17)-a1607 [bi-squeezed tripartite Gaussian states].
@ Related topics: Kar & Ghosh JPA(96) [quons]; Jellal MPLA(02)ht/01 [generalized Laguerre functions]; Zak JPA(01) [on von Neumann lattice]; Novaes et al JPA(03) [double well, generalized coherent states]; Holschneider & Teschke JMP(06) [optimally localized].

Relativistic Systems > s.a. deformed special relativity; semiclassical general relativity.
@ Oscillators: Aldaya & Guerrero JMP(95), erratum JMP(03)mp; Tang PLA(96).
@ Spinning particle: Anastopoulos JPA(04)qp/03 [generalized coherent states]; > s.a. spinors in field theory.

Constrained Systems > s.a. quantum constrained systems.
* Idea: One can start with a \(\psi_{\rm coh}\) in \(\cal H_{\rm kin}\) and apply a group averaging procedure to implement the Dirac prescription, or construct a coherent state directly in \(\cal H_{\rm phy}\).
@ References: Klauder & Whiting JPA(93) [and coherent states with additional variables]; Ashworth qp/96 [first-class], PRA(98)qp/96 [time reparametrization]; Nakamura & Kojima NCB(01); Date & Singh qp/01 [algebraic quantization]; Bolen et al CQG(04)gq [Bianchi I models]; Ashtekar et al PRD(05)gq; Shvedov mp/05-talk, a0812.

In Quantum Field Theory > s.a. modified coherent states; states in quantum field theory.
* Motivation: Given a classical field, there is no unique quantum state one can associate with it, but the most natural or "likely" one is the coherent state, since it corresponds to the state of a quantum field after a classical source has been turned on for some time [1.02.85, from a meeting with Rafael].
* Interpretation: The probability of finding n quanta in the state \(\psi_z\) is a Poisson distribution with mean z z*.
@ General references: Ashtekar & Magnon Pra(80).
@ Maxwell theory / quantum optics: Glauber PR(63) [electromagnetic field]; Zavatta et al PRA(05)qp [+ single photon]; Dai & Jing IJTP(08) [photon-added]; Zavatta et al NJP(08) [single-photon annihilation]; Gabriel et al a0901 [squeezing experiments]; Barnich GRG(10)-a1001 [Coulomb solution and unphysical photons]; Sondermann & Leuchs JEOS(13)-a1306 [phase shift induced by a single atom]; Joye & Merkli CMP(16)-a1508 [infinite coherent states]; Malpani et al a1808 [photon-added and subtracted, non-classical properties]; Gazeau in(19)-a1810 [rev]; > s.a. optics; QED.
@ Gauge theories: Hall RVMP(01)qp/00 [1+1 Yang-Mills theory]; Thiemann CQG(01)ht/00, & Winkler CQG(01)ht/00, CQG(01)ht/00, CQG(01)ht/00; Matsumoto IJMPB(14)-a1303 [labeled by Euler angles].
@ Klein-Gordon theory: Haghighat & Dadkhah PLA(03)qp [with V]; Mostafazadeh & Zamani AP(06)qp.
@ Gravity: Manka & Yassin CQG(95) [Einstein-Yang-Mills theory]; Dasgupta JCAP(03)ht [for black holes]; Long & Bodendorfer a2006 [lqg, any dimensionality]; Calcinari et al a2009 [based on twisted geometries]; > s.a. minisuperspace; semiclassical quantum gravity.
@ Related topics: Calucci JPA(87) [generalization]; Zhang ht/99-in.

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