Quantum Systems| Quantum Systems |
In General > s.a. deformation
quantization \ quantum foundations [concept of system].
* Unstable: Used as a model for
time-irreversible system; For example, the Friedrichs model or the Lee model;
> s.a. particle effects [decay].
@ Embedded eigenvalues: Hiroshima JPA(02) [functional integral].
@ Simplest systems: Bondar et al AJP(11)apr [free particle, from properties of the Dirac delta function];
in Nauenberg AJP(16)nov [charged particle in a homogeneous electric field];
Bergeron et al a1701 [pedagogical, Euclidean plane as real Hilbert space].
@ Unstable systems: Bunge & Kálnay NCB(83);
Horwitz & Piron HPA(93);
Horwitz FP(95) [in relativistic quantum mechanics];
Urbanowski OSID(13)-a1408 [effective Hamiltonians];
Giacosa a1708-proc [some theoretical aspects and predictions];
Giacosa a2001-proc [Lee model];
> s.a. arrow of time [Brussels school].
@ Potential reconstruction: Lemm et al PRL(00)cm/99 [Bayesian],
qp/03 [using path integrals];
Alhaidari & Ismail JMP(15)-a1408.
@ With symmetries: Divakaran PRL(97) [specified by symmetries];
Zeier & Schulte-Herbrüggen JMP(11)-a1012 [symmetry principles];
Chubb & Flammia JMP(17)-a1608 [approximate symmetries, and ground space structure].
@ Related topics: Anderson PLB(93) [equivalent systems];
DeWitt IJMPA(98) [isolated; including decoherence];
Barreto & Fidaleo m.OA/05 [disordered];
Koslowski gq/06 [reduction of a theory];
Bolonek & Kosiński qp/07,
JPA(07) [non-local];
Wu et al IJTP(09)-a0909 [non-conservative];
Eisele a1204 [antilinear terms in the Hamiltonian];
Shapere & Wilczek PRL(12)-a1207 [Lagrangians with branched Hamiltonians];
Gudder a2009 [parts and composites].
Systems with Non-Trivial Topology
> s.a. physical systems [dimensionality].
* Idea: An example is
the Berry-Hannay model on the 2n-dimensional torus; Several
quantizations are possible, depending on the choice of values for
topological factors; > s.a. topological phase;
theta sectors.
@ Bounded / confined systems: Barton et al AJP(90)aug [influence of distant boundaries];
Garbaczewski & Karwowski mp/01;
Dias et al CPAM(11)-a0707 [self-adjoint Hamiltonians];
Belgiorno & Gallone JMP(09) [and non-confined limit];
Bernard & Lew Yan Voon EJP(13) [particle constrained to a curved surface];
Ciaglia et al IJGMP(17)-a1705 [manifolds with boundaries and corners].
@ Constrained systems: Bloch & Rojo PRL(08) [non-holonomic];
> s.a. first-class and second-class constraints;
types of states [totally constrained systems].
@ On a circle: Fülöp & Tsutsui PLA(00)qp/99 [with point interaction];
Scardicchio PLA(02)qp/01;
Zhang & Vourdas JMP(03)qp/05 [phase space approach];
Ben Geloun & Klauder PS(13)-a1206,
Ben Geloun a1210-conf [enhanced quantization];
Przanowski et al AP(14)-a1311 [Weyl quantization and number-phase Wigner functions].
@ On Sn:
Dita PRA(97);
Ikemori et al MPLA(98) [and meron solution],
MPLA(00) [and Berry connection];
Aldaya et al JPA(16)-a1607 [S3, non-canonical approach];
> s.a. canonical quantization
[particle on S2, group quantization].
@ Time-dependent boundaries:
Di Martino & Facchi IJGMP(15)-a1501;
Ginzburg a1807 [transition probabilities];
> s.a. special potentials [infinite wells].
@ Other compact configuration spaces:
Rubin & Lesniewski qp/98,
Gurevich & Hadani mp/03 [T2];
Gurevich & Hadani mp/04 [Berry-Hannay model on T2n];
Asorey et al IJMPA(05)ht/04;
Oriti & Raasakka PRD(11)-a1103 [on SO(3)];
Dolbeault et al a1303;
Biswas & Ghosh EPL-a1908 [non-trivial torus knot].
@ On a half-line: Gazeau & Murenzi JMP(16)-a1512,
Gouba JHEPGC-a2005 [affine quantization];
Al-Hashimi & Wiese a2103;
> see Polymer Representation.
@ Other non-trivial topology: Marques & Bezerra qp/01 [on topological defect];
Kowalski et al PRA(02)qp [pointed plane];
Exner RPMP(05) [configuration spaces of mixed dimensionality];
Dürr et al JPA(07)qp/05 [and pilot-wave theory];
Filgueiras & Moraes AP(08) [conical surface];
Cirilo-Lombardo JPA(12)-a1204 [on a Möbius strip];
Filgueiras et al JMP(12)-a1205 [on a cone];
Gubbiotti & Nucci a1607 [double cone];
> s.a. Weyl Quantization.
Other Types > see composite systems [including subsystems, atoms, many-body systems and particle + field]; discrete and finite systems [including qubits]; dissipative systems; ergodic theory and open systems; macroscopic systems [including mesoscopic, hybrid, classically chaotic]; systems with special potentials; thermodynamical systems; types of quantum field theories [coupled to atoms].
Related Topics > see analysis [fractional derivatives]; anomaly; coherent states; Crum's Theorem; curves [length]; Damped Systems; Degeneracy; quantum chaos [including Baker's map]; higher-order lagrangian theories; histories formulations [closed systems]; number theory; Stückelberg Model; Thermal Bath.
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