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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