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 Sd]; 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.
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send feedback and suggestions to bombelli at olemiss.edu – modified 13
nov 2009