Integrable Quantum Systems| Integrable Quantum Systems |
In General
> s.a. coherent states; integrable classical systems;
non-commutative theories; special potentials
[exactly solvable, etc].
* Idea: Quantum systems
for which the energy spectrum can be explicitly computed.
* Energy eigenvalues:
The energies of the tori whose actions in the semiclassical limit are
of the form (n + k/8) h, with n
arbitrary and k some fixed integer [KAM theory; & Einstein;
Brillouin; Keller; Maslov].
@ General references: Kundu ht/96,
ht/97-conf [rev];
Prykarpatsky & Mykytiuk 98 [geometric];
Hikami & Wadati JMP(03);
Clemente-Gallardo & Marmo IJGMP(09)-a0808 [towards a definition];
issue JMP(09)#9;
Doikou et al IJMPA(10)-a0912
[introduction, and quantum groups and the quantum inverse scattering method];
Lamers PoS-a1501 [and high-energy physics];
Combot a1609
[general definition of integrability and classification].
@ Quantization of classical integrable systems:
Garay & van Straten a0802 [sufficient condition];
Marino & Nekhoroshev a1001,
a1001;
Sharygin & Talalaev a1210 [deformation quantization].
@ Related topics: Baldo & Raciti qp/95 [eigenstates along trajectories];
Scotti & Ushveridze JMP(97)qp/96 [non-linear quantization];
Kay PRA(04) [wave functions];
> s.a. Inverse Scattering.
Types and Examples
* Examples: Calogero-type
(rational) & Sutherland-type (trigonometric).
@ Calogero-Sutherland: Garcia et al JPA(01)mp [raising/lowering];
Langmann CMP(04)mp/01 [second quantization].
@ Bi-Hamiltonian systems: Cariñena et al IJMPA(00)mp/06;
Marmo et al JPA(05),
TMP(05)mp,
NdM(04)mp/05 [and compatible Hermitian structures];
> s.a. symplectic structures.
@ Other examples: Calogero & van Diejen JMP(96);
Haschke & Ruehl LNP(00)ht/98 [construction];
Rodriguez & Winternitz JMP(02)mp/01 [in En];
Yonezawa & Tsutsui JMP(06) [N = 3 Calogero, inequivalent];
Danilov & Nagaitsev a1111 [and Ermakov transfrmations].
@ Field theories: Schroer a1109 [dynamical and kinematical integrability];
Bostelmann & Cadamuro CMP(15)-a1402 [characterization of local observables];
Lamers PoS-a1506 [pedagogical, and high-energy physics].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 oct 2018