Quantum Systems  

Finite-Dimensional and Discrete Systems > s.a. classical systems; modified quantum mechanics [discrete underlying space].
* Qubits: A qubit is 2-state system, a quantum system with a 2D Hilbert space; Density matrices for 1 qubit are in 1-1 correspondence with points of the 3D solid ball, the Bloch sphere; An example is the two-level atom.
* Qutrits: A qutrit is a three-state quantum system; For example, a single photon passing through a system of three slits, a "Young-type" qutrit.
* Qudits: A qudit is a quantum system with d-dimensional Hilbert space.
* Spin-J system: In the Majorana representation, a state of a spin-J system can be seen as a set of 2J points on the Bloch sphere.
@ One qubit: Urbantke AJP(91)jun [phases and holonomy]; Slater qp/97 [statistical thermodynamics], qp/00 [and information theory]; Ralph et al FP(98) [solution]; Sassaroli AJP(99)oct [neutrino oscillations]; Bagrov et al JPA(01)qp [V(t)]; Barata & Cortez qp/02 [periodic driving]; An et al JOB(04)qp/05 [coupled to squeezed vacuum field]; Maioli & Sacchetti JSP(05) [+ stochastic perturbation]; Gemmer & Michel PhyE(05)qp [+ environment]; Kato et al qp/06-conf [Holevo capacity from Voronoi diagrams]; Calmet & Calmet a1201 [in quantum field theory]; Palmer et al AP(12) [in curved spacetime]; > s.a. particles; relativistic quantum mechanics.
@ Two qubits: Kummer IJTP(01); Abouraddy et al PRA(01) [decomposition and entanglement]; Avron et al JMP(07); Güngördü et al PRA(12)-a1205 [dynamical invariants of two-level systems]; > s.a. composite systems; examples of entanglement.
@ N qubits: Wootters qp/03-conf [generalized Wigner function]; Rigetti et al QIP(04)qp/03 [and information]; Klimov et al JPA(12)-a1007 [phase space]; Coecke & Duncan NJP(11) [graphical calculus]; Giorgi et al PRL(11)-a1108 [three qubits, quantum and classical correlations].
@ Three-level: Sánchez JPA(94); Slater JGP(01)qp/00 [Bures geometry]; Rau & Zhao PRA(05)qp [complete treatment]; Chruściński & Wudarski OSID(11)-a1105, Chruściński & Sarbicki a1108 [entanglement witnesses].
@ One spin: Bruno PRL(12)-a1204 + Niu Phy(12)jun [spin-J system, Majorana's stellar representation]; > s.a. spin models [more spins]; types of quantum states.
@ Discrete / finite-dimensional Hilbert space: Ruzzi & Galetti JPA(00), Ruzzi JPA(02)qp/01, & Galetti JPA(02) [and continuum]; Barker JPA(01), JMP(01) [continuum limits]; de la Torre & Goyeneche AJP(03)jan-qp/02; Brukner et al PRA(03)qp/02 [relation with continuous variables]; Gudder FP(06) [and finite group theory]; Hassan & Joag JPA(07) [combinatorial approach]; Lenz & Veselić a0709; Kornyak in(09)-a0906 [gauge invariance and continuum limit]; Planat IJGMP(11) [four and eight-level systems]; Domenech et al RPMP(11) [two-valued states over orthomodular lattices]; Vourdas JMP(12) [partial order and T0 topology]; > s.a. Cellular Automaton; graph theory; wigner functions.

Special Potentials > s.a. hilbert space; integrable quantum systems; oscillator; potential; schrödinger equation; wigner function.
@ Central: Ciftci et al JPA(03) [Coulomb + power law]; Martin qp/04 [near r = 0]; Hall et al PRA(09)-a0908 [soft Coulomb potential]; > s.a. relativistic quantum mechanics; quantum states [bound].
@ Potential steps: Ahmed PLA(96); Boonserm & Visser JPA(09)-a0808 [transmission probabilities]; Yearsley JPCS(09)-a0901 [propagator, path integral]; Jaffe AJP(10)jun [reflection above the barrier as tunneling in momentum space]; Garrido et al AJP(11)dec [reflection at a downward potential step].
@ Infinite well: Leyvraz et al AJP(97)nov [accidental degeneracy]; Ni qp/98 [Einstein, Pauli, Yukawa]; Colanero & Chu PRA(99)qp [oscillating]; Sankaranarayanan et al PRE(01)nl [periodic pulsing and chaos]; Waldenström et al PS(03) [revivals]; Garbaczewski & Karwowski AJP(04)jul-mp/03; García de León et al PLA(08) [coherent state approach]; Pedram & Vahabi AJP(10)aug [with a δ-function potential]; Ogren & Carlsson EJP(11)-a1103 [lower energy bound]; > s.a. path integrals.
@ Finite square well: Bender et al JPA(99) [complex]; Blümel JPA(05) [analytical solution]; > s.a. modified quantum theory [PT-symmetric].
@ 2D billiard: Cohen & Wisniacki PRE(03)nl/02 [moving walls]; Gutkin JPA(03) [plane waves and solutions].
@ Double well: Holstein AJP(88)apr [semiclassical]; Razavy NCB(01) [Heisenberg equation of motion]; Friedberg et al AP(01)qp; Roy & Bhattacharjee PLA(01)qp [chaos]; Tian a1003 [new model]; > s.a. coherent states; pilot-wave theory.
@ Periodic: Holstein AJP(88)oct [semiclassical]; Khare & Sukhatme JPA(04)qp [rev + solvable]; Pereyra AP(05) [finite-size]; > s.a. coherent states.
@ Periodic in time: Costin et al JPA(00)mp/06 [bound state survival probability], JPA(02)mp/06, JSP(04)mp/06, mp/06; López qp/06; Duclos et al RVMP(08)-a0710 [stability].
@ H atom: Hofer qp/98 [different]; Parfitt & Portnoi JMP(02)mp [2D]; Alves et al PRA(03)ht/05 [between parallel plates]; Palma & Raff CJP(06)qp [1D]; Zhao et al PRD(07)-a0705 [in Schwarzschild metric]; Martínez-y-Romero et al AJP(07)jul [with group theory methods]; Jaramillo et al PLA(09) [1D]; Machet & Vysotsky PRD(11)-a1011 [in a superstrong magnetic field]; > s.a. born-infeld theory; topological defects.
@ He atom: Schwartz mp/06 [ground state]; Withers & Nadarajah RPMP(11) [solutions of Schrödinger's equation]; Esposito & Naddeo a1207 [Majorana and the two-electron problem].
@ In an electric field: Karasev & Osborn JMP(02)qp/00 [electromagnetic fields]; Matteucci EJP(07) [intro].
@ In a magnetic field: Krause PRA(96) [constant]; Schmiedmayer & Scrinzi PRA(96) [linear current]; Thienel AP(00)qp/98; Nambu NPB(00) [2D, vortices and field]; Schuch & Moshinsky JPA(03) [coherent states]; Chiou et al mp/04 [self-linking B field]; > s.a. aharonov-bohm effect.
@ Singular: Gosdzinsky & Tarrach AJP(91)jan [δ-potential and quantum field theory model]; Esposito JPA(98)ht [scattering], FPL(00)qp/99; Landsman gq/98; Schulze-Halberg IJTP(00) [irregular singularity]; Demiralp & Beker JPA(03) [δ potential, bound states]; Tsutsui & Fülöp qp/03-proc [defects etc]; Alberg et al PRA(05)qp/04 [1/r4, renormalization]: Fülöp Sigma(07)-a0708-proc [ambiguity in self-adjoint Hamiltonian]; > s.a. perturbation methods; representations [1/r2 potential in polymer representation].
@ Random potentials: Yannacopoulos et al PS(02) [2D]; Germinet & Klein mp/05, mp/06 [localization]; Baker et al CMP(08) [deformed lattice]; > s.a. Anderson Localization.
@ Other types: Damanik et al CMP(05)mp/04 [finitely-many bound states]; Smilga JPA(09)-a0808 [exceptional points]; Fabre & Guéry-Odelin AJP(11)jul-a1012 [exactly solvable, supersymmetry and approximation schemes]; > s.a. Bloch Theory; Rotor.

Other Types and General Topics > s.a. Damped Systems; deformation quantization; physical systems [dimensionality]; quantum foundations [concept of system].
* Non-trivial topology: 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.
* Unstable: Used as a model for time-irreversible system; For example, the Friedrichs model; > s.a. particle effects [decay].
@ Embedded eigenvalues: Hiroshima JPA(02) [functional integral].
@ On a circle: Fülöp & Tsutsui qp/99 [with 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].
@ On Sn: Dita PRA(97); Ikemori et al MPLA(98) [and meron solution], MPLA(00) [and Berry connection]; > s.a. canonical quantization.
@ Bounded / confined systems: Garbaczewski & Karwowski mp/01; Dias et al CPAM(11)-a0707 [self-adjoint Hamiltonians]; Belgiorno & Gallone JMP(09) [and non-confined limit].
@ Other non-trivial topology: Rubin & Lesniewski qp/98 [T2]; Marques & Bezerra qp/01 [on topological defect]; Kowalski et al PRA(02)qp [pointed plane]; Asorey et al IJMPA(05)ht/04 [compact C]; Gurevich & Hadani mp/04 [Berry-Hannay model]; 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]; Oriti & Raasakka PRD(11)-a1103 [quantum mechanics on SO(3)]; Cirilo-Lombardo JPA(12)-a1204 [on a Möbius strip]; Filgueiras et al JMP(12)-a1205 [on a cone]; > s.a. Polymer Representation [half line].
@ Unstable systems: Bunge & Kálnay NCB(83); Horwitz & Piron HPA(93); Horwitz FP(95) [in relativistic quantum mechanics]; > s.a. arrow of time [Brussels school].
@ Constrained systems: Bloch & Rojo PRL(08) [non-holonomic]; > s.a. first-class and second-class constraints; types of states [totally constrained systems].
@ Subsystems: Zanardi et al PRL(04) [partition induced by observables]; Petz RPMP(07) [complementary]; Alicki et al PRA(09)-a0902 [formalism in terms of completely positive maps and correlation functions]; Fields a0906 [consistency of decomposition and consequences].
@ Potential reconstruction: Lemm et al PRL(00)cm/99 [Bayesian], qp/03 [using path integrals].
@ Related topics: Barton et al AJP(90)aug [influence of distant boundaries]; Anderson PLB(93) [equivalent systems]; Divakaran PRL(97) [specified by symmetries]; 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]; Zeier & Schulte-Herbrüggen JMP(11)-a1012 [symmetry principles]; Bondar et al AJP(11)apr [free particle, from properties of the Dirac delta function]; Eisele a1204 [antilinear terms in the Hamiltonian]; Shapere & Wilczek PRL(12)-a1207 [Lagrangians with branched Hamiltonians].
> Other types: see composite systems [including many-body and particle + field]; dissipative systems; ergodic theory and open systems.
> Related topics: see analysis [fractional derivatives]; anomaly; Crum's Theorem; Degeneracy; quantum chaos [including Baker's map]; higher-order lagrangian theories; histories formulations [closed systems]; macroscopic systems [including mesoscopic, hybrid, classically chaotic]; number theory; Stückelberg Model; Thermal Bath; thermodynamical systems; types of quantum field theories [coupled to atoms].

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