Quantum Systems

Finite-Dimensional and Discrete Systems > s.a. spin models.
* Qubits: A qubit is 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. Qudits: A qudit is a quantum system with d-dimensional Hilbert space.
@ 1 qubit / two-level: Urbantke AJP(91) [phases and holonomy]; Slater qp/97 [statistical thermodynamics], qp/00 [and information theory]; Ralph et al FP(98) [solution]; Sassaroli AJP(99) [ 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-in [Holevo capacity from Voronoi diagrams].
@ 2 qubits: Kummer IJTP(01); Abouraddy et al PRA(01) [decomposition and entanglement]; Avron et al JMP(07); > s.a. composite.
@ N qubits: Wootters qp/03-in [generalized Wigner function]; Rigetti et al QIP(04)qp/03 [and info].
@ Three-level: Slater JGP(01)qp/00 [Bures geometry]; Rau & Zhao PRA(05)qp [complete treatment].
@ Discrete and finite-dimensional : Sánchez JPA(94) [3D 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)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 & Veselic a0709; > s.a. Cellular Automaton, graph theory, wigner functions.

Special Potentials > s.a. Bloch Theory; hilbert space; oscillator; potential; Rotor; schrödinger equation; wigner function.
@ Central: Ciftci et al JPA(03) [Coulomb + power law]; Martin qp/04 [near r = 0]; > s.a. relativistic quantum mechanics, states [bound].
@ Infinite well: Leyvraz et al AJP(97) [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)mp/03; García de León et al PLA(08) [coherent state approach]; > s.a. path integrals.
@ Finite square well: Bender et al JPA(99) [complex]; Blümel JPA(05) [analytical solution].
@ 2D billiard: Cohen & Wisniacki PRE(03)nl/02 [moving walls]; Gutkin JPA(03) [plane waves and solutions].
@ Double well: Holstein AJP(88) [semiclassical]; Razavy NCB(01) [Heisenberg equation of motion]; Friedberg et al qp/01; Roy & Bhattacharjee PLA(01)qp [chaos]; > s.a. coherent states, pilot wave.
@ Periodic: Holstein AJP(88) [semiclassical]; Khare & Sukhatme qp/04 [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 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 a0705 [in Schwarzschild metric]; Martínez-y-Romero AJP(07) [with group theory methods]; > s.a. born-infeld theory, topological defects.
@ In E field: Matteucci EJP(07) [intro].
@ In B 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]; > s.a. aharonov-bohm.
@ Singular: Gosdzinsky & Tarrach AJP(91) [ 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) [ potential, bound states]; Tsutsui & Fulop qp/03-in [defects etc]; Alberg et al PRA(05)qp/04 [1/r⁴, renormalization]: Fulop a0708-in [ambiguity in self-adjoint Hamiltonian]; > s.a. perturbation methods.
@ Random potentials: Yannacopoulos et al PS(02) [2D]; Germinet & Klein mp/05, mp/06 [localization].
@ Other: Ahmed PLA(96) [potential step]; Karasev & Osborn JMP(02)qp/00 [in electromagnetic fields]; Damanik et al mp/04 [finitely many bound states]; Schwartz mp/06 [He atom, ground state].

Integrable System > s.a. coherent states; integrable classical system; non-commutative theories; potential [solvable, etc].
* Examples: Calogero-type (rational) & Sutherland-type (trigonometric).
* Energy eigenvalues: The E's of the tori whose actions in the semicl limit are of the form (n+k/8) h, n arbitrary, k some fixed integer [KAM theory; & Einstein; Brillouin; Keller; Maslov].
@ Reviews: Kundu ht/96, ht/97-in; Hikami & Wadati JMP(03).
@ 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.
@ Calogero-Sutherland: Garcia et al JPA(01)mp [raising/lowering]; Langmann CMP(04)mp/01 [second quantization].
@ 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].
@ Related topics: Baldo & Raciti qp/95 [eigenstates along trajectories]; Scotti & Ushveridze JMP(97)qp/96 [non-linear quantization]; Kay PRA(04) [wave functions]; Garay & van Straten a0802 [sufficient condition]; > s.a. Inverse Scattering.

Other Types and General Topics > s.a. anomaly; deformation; number theory; quantum foundations [concept of system]; systems.
* 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. phase, theta.
* Damped: They give rise to complex spectra and corresponding resonant states; > s.a. Lindblad Theory, quantum states.
* Unstable: Used as a model for time-irreversible system; For example, the Friedrichs model; > s.a. particles [decay].
@ Embedded eigenvalues: Hiroshima JPA(02) [functional integral].
@ Dissipative: Feynman & Vernon AP(63), reprint AP(00) [and influence functionals]; Rajagopal & Rendell qp/01; Rau & Wendell PRL(02)qp; > s.a. oscillator, modified quantum mechanics [non-Hamiltonian].
@ On a circle: Fulop & Tsutsui qp/99 [with interaction]; Scardicchio PLA(02)qp/01; Zhang & Vourdas JMP(03)qp/05 [phase space approach].
@ On Sⁿ: Dita PRA(97); Ikemori et al MPLA(98) [and meron solution], MPLA(00) [and Berry connection].
@ Other non-trivial topology: Rubin & Lesniewski qp/98 [T²]; Garbaczewski & Karwowski mp/01 [bounded C]; 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 qp/05 [and pilot wave]; Dias & Prata a0707 [with boundaries, Hamiltonian].
@ Damped systems: Caldeira Leggett PRA(85) [effect on interference]; Chruscinski JMP(03) [resonant states and irreversibility].
@ 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.
@ Subsystems: Zanardi et al PRL(04) [partition induced by observables]; Petz RPMP(07) [complementary].
@ Potential reconstruction: Lemm et al PRL(00)cm/99 [Bayesian], qp/03 [using path integrals].
@ Related topics: Barton et al AJP(90) [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 & Kosinski qp/07, JPA(07) [non-local].
> Related topics: see analysis [fractional derivatives], composite [including many-body and particle + field]; Degeneracy; ergodic and Open Systems, quantum chaos [including Baker's map]; histories [closed systems]; higher-order lagrangian theories; relation with classical theory [macroscopic, hybrid, classically chaotic systems]; Stückelberg; Thermal Bath; thermodynamics; types of quantum field theories [coupled to atoms].

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