Coherent States: Types of Systems

In General > s.a. generalized-modified states; geometric quantization; semiclassical quantum mechanics; Squeezed States; systems.
@ For discrete spectrum: Klauder qp/98-in.
@ On circle: Kowalski et al JPA(96)qp/98; González & del Olmo JPA(98)qp; Kowalski & Rembielinski JPA(02)qp [and squeezed]; Ruzzi et al JPA(06)qp; Bahr & Korsch JPA(07)qp/06 [Husimi distributions].
@ On spheres: Kowalski & Rembielinski JPA(00)qp/99; Hall & Mitchell JMP(02)qp/01, qp/02-in [on S^d]; Mathur & Paul JPA(05) [carrying SU(2) and SU(3) charges].
@ On different spaces: Klauder PRA(86) [half-line]; Kowalski & Rembielinski JMP(93) [quantum C]; Berceanu JGP(97) [homogeneous manifold]; Kowalski & Rembielinski PRA(07)-a0712 [torus], JPA(08) [review].
@ Harmonic oscillator: Johansen PLA(04)qp/03 [non-classical properties]; > s.a. modified coherent states; oscillator; semiclassical quantum theory.
@ Non-linear oscillator: Molski JPA(09)-a0706; Midya et al PS-a0911 [and revival dynamics].
@ Other oscillators: Benatti & Floreanini JPA(00)ht [damped]; Quesne AP(01)qp, qp/01-in [C_-extended]; Choi PLA(04) [time-dependent]; Borzov TMP(07) [generalized]; Li RPMP(08) [forced and damped]; > s.a. 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); Unal PRA(01); Nouri PRA(02) [1D Coulomb]; Thaik & Inomata 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].
@ Finite-dimensional Hilbert spaces: Galetti & Marchiolli AP(96); Miranowicz et al qp/01-in, Leonski & Miranowicz qp/01-in; Borzov & Damaskinsky qp/06; Dömötör & Benedict a0709, Muñoz et al IJQI-a0809 [N qubits].
@ Integrable: Haba qp/95; Samsomov JMP(98)qp/97; Song & Park IJMPA(02)qp/01 [Calogero-Sutherland].
@ Various potentials: & Nonnenmacher & Voros JPA(97)cd/96 [inverted oscillator, H = (P² – Q²)]; Martin Nieto MPLA(01)qp [analytic potentials]; Shreecharan et al PRA(04) [exactly solvable]; Belloni et al PS(05) [infinite wall].
@ Particle in a magnetic field: Kowalski & Rembielinski 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].
@ PT-symmetric systems: Bagchi & Quesne MPLA(01)qp [oscillator]; Roy & Roy PLA(06)qp.
@ Related topics: Kar & Ghosh JPA(96) [quons]; Jellal MPLA(02)ht/01 [generalized Laguerre functions]; Zak JPA(01) [on von Neumann lattice]; Lev et al PRA(02)qp [spin-0 particle, non-linear coherent states]; Fan & Chen PLA(02) [entangled states]; 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 cs]; > s.a. spinors in field theory.

Constrained Systems > s.a. quantum constrained systems.
* Idea: One can start with a _coh in _kin and apply a group averaging procedure to implement the Dirac prescription, or construct a coherent state directly in _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]; Ashtekar et al PRD(05)gq; Shvedov mp/05-in, a0812.

In Quantum Field Theory > s.a. states in quantum field theory; QED; minisuperspace quantum gravity.
* 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 _z is a Poisson distribution with mean z z*.
@ Maxwell theory: 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].
@ 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.
@ Klein-Gordon theory: Haghighat & Dadkhah PLA(03)qp [with V]; Mostafazadeh & Zamani AP(06)qp.
@ Gravity: Dasgupta JCAP(03)ht [for black holes]; > s.a. semiclassical quantum gravity.
@ Related topics: Calucci JPA(87) [generalization]; Manka & Yassin CQG(95) [Einstein-Yang-Mills]; Zhang ht/99-in.

main page – abbreviations – journals – comments – other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 13 nov 2009