Composite Quantum Systems  

In General > s.a. quantum states; spin models.
* Idea: A quantum system that is composed of subsystems A and B has as Hilbert space the tensor product = A B.
@ General references: Wilce IJTP(90); Coecke FP(98)qp/01, IJTP(00)qp [characterization]; Bene qp/97/PRL [macroscopic]; Kummer IJTP(99) [2 spin- particles, state space]; Aerts IJTP(00)qp/01 [paradox], & Valckenborgh IJTP(04) [failure of quantum mechanics]; Johnson mp/06 [formalism]; Blanchard & Brüning PLA(06) [structure of states, envariance]; Albeverio et al RPMP(07) [local invariants]; Blasone et al IJMPA(09) ['t Hooft's quantization proposal].
@ Subsystems: Orlov PRL(99) [measurement and indeterminism]; Zanardi et al PRL(04)qp/03 [observable-induced partition]; Jordan a0710 [maps describing evolution]; > s.a. Open Systems.
@ Discrete + continuum, particle + field: Stenholm & Paloviita JMO(97)qp; Aguiar Pinto & Thomaz JPA(03)qp/02 [decay]; Kupsch Pra(02)mp [particle + IR divergent boson]; > s.a. Dicke and Friedrichs Model; entropy in quantum theory [Wehrl entropy].
@ Correlations: Kübler & Zeh AP(73); Linden et al qp/02 [n-way].
@ Other systems: Quesne & Tkachuk a0906 [with minimal length].
> Related topics: see diffraction; entropy; observables [subdynamics]; particle statistics; renormalization; scattering.

Few-Body Problem > s.a. Born-Oppenheimer Approximation.
@ General references: Thirring 81; Glöckle 83; Parker & Doran qp/01-in [2-particle basis and entanglement].
@ Two-body problem: Droz-Vincent PLA(90) [relativistic, in constant B field].
@ Three-body problem: Mohr et al AP(06).
@ Molecules: Arndt et al Nat(99)oct + pn(99)oct [buckyballs, C60]; Armour et al PRP(05) [stability of few-charge systems].

Many Degrees of Freedom > s.a. semiclassical quantum mechanics; entanglement; quantum chaos; statistical mechanics; stochastic processes.
* History: Founded by papers by Dirac and Heisenberg on identical particles.
* Approaches: The first approximation is the mean-field theory, exact only for free systems; The next approximation uses 2-body correlations, random phase approximation, and the Bethe ansatz; The main approach is the coupled cluster method; Density-functional theory.
* Examples: Atomic or molecular clusters, atoms or molecules, nuclei, nucleons; Systems with strong pair correlations can be modeled by the exactly solvable Richardson-Gaudin models.
@ General references: Dirac PRS(29); March et al 67; Fetter & Walecka 71; Thirring 83; Strocchi 85 [infinite]; Sewell 86 [collective phenomena]; Koltun & Eisenberg 88; Korepin et al 93; Mahler & Weberruß 98 [networks]; Zagoskin 98; Hunziker & Sigal JMP(00); Fabrocini 02.
@ Condensed, macroscopic: Balucani et al PRP(03) [condensed, correlations]; Grandy FP(04), FP(04), FP(04) [time evolution]; Khrennikov FP(05)qp/04 [concept]; Pitowsky PRA(04) ["combinatorial"]; Bruus & Flensberg 04 [in condensed matter].
@ Ground state: Lenard JMP(64) [1D impenetrable bosons]; Date et al PRL(98); Van Neck et al PRA(01) [energy bound]; Ostili & Presilla NJP(04)cm [analytic].
@ Boson gas: Lieb mp/00-in [energy/particle], et al mp/02-in, mp/04-in; Vakarchuk qp/05 [self-consistent]; > s.a. gas.
@ N particles: Anastopoulos PRD(96) [and gravity]; Mirlin PRP(00) [disordered, energy levels]; Dukelsky et al RMP(04) [Richardson-Gaudin models]; Wen 04 [quantum field theory of many-body systems]; Dunn et al qp/06 [confined, wave function]; Braun & Garg JMP(07) [coherent state propagator]; Laing et al JMP(09)-a0808 [group-theoretical and graphical techniques]; Pezzotti & Pulvirenti a0810 [semiclassical, mean-field limit]; > s.a. crystals [electron states]; supersymmetry.
@ Mean-field approximation: Balian & Vénéroni AP(92) [correlations and fluctuations]; Scarfone RPMP(05) [and complex non-linearity].
@ Effective evolution equations: Schlein a0807-ln; Rodnianski & Schlein CMP(09) [rate of convergence to Hartree-equation mean-field dynamics]; Schlein a0910-in [derivation of the Hartree equation and Gross-Pitaevskii equation].
@ Related topics: Prosen JPA(98) [invariants of motion], PRL(98) [integrability to ergodicity]; Ostilli & Presilla JPA(04)cm [Montecarlo dynamics]; Fedorova & Zeitlin qp/05-in, qp/05-in [patterns formation]; Gori-Giorgi et al PRL(09) [density-functional theory for strongly-interacting electrons]; > s.a. matter; network; nuclear physics; wigner functions.

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