Many-Particle Quantum Systems  

In General > s.a. quantum statistical mechanics; semiclassical quantum mechanics.
* Principle of local distinguishability: An arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems.
* History: Founded by papers by Dirac and Heisenberg on identical particles.
* 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]; Koltun & Eisenberg 88; Korepin et al 93; Mahler & Weberruß 98 [networks]; Zagoskin 98; Hunziker & Sigal JMP(00); Fabrocini et al 02; Kuzemsky a1207-conf [quantum protectorate and emergence]; Coleman 16 [intro, r PT(17)]; Rougerie a1607-Hab.
@ 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]; Cordero et al JPA(13)-a1305 [3-level atoms interacting with a 1-mode electromagnetic field, semiclassical vs quantum description].
@ Non-equilibrium theory: Gasenzer et al EPJC(10)-a1003 [far from equilibrium]; Stefanucci & van Leeuwen 13 [r CP(13)]; Eisert et al nPhys(15)-a1408.
@ Effects, phenomenology: Sewell 86 [collective phenomena]; news pw(13)nov [transition from few-body to many-body system and Fermi sea in ultracold fermionic atoms]; Continentino 17 [scaling and phase transitions]; > s.a. Area Law.

Types of Systems > s.a. condensed matter; open systems; Tensor Networks.
@ Boson gas: Lieb mp/00-proc [energy/particle], et al in(02)mp, mp/04-conf; Vakarchuk qp/05 [self-consistent]; > s.a. gas.
@ N particles: 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, PRA(09) [confined, wave function]; Braun & Garg JMP(07) [coherent state propagator]; Laing et al JMP(09)-a0808 [group-theoretical and graphical techniques]; Lipparini 08; Pezzotti & Pulvirenti AHP(09)-a0810 [semiclassical, mean-field limit]; Nolting 09; Hämmerling et al JPA(10) [collective versus single-particle motion]; Horwitz JPA(13)-a1210 [relativistic particles, spin, angular momentum and spin-statistics]; Di Stefano et al JSM(13)-a1210 [perturbative probabilistic approach]; Hummel et al JPA(14) [mean density of states]; Beugeling et al JSM(15)-a1410 [participation ratio and entanglement entropy of eigenstates]; Walter PhD(14)-a1410 [general relations between multiparticle quantum states]; Tura et al proc(16)-a1501 [entanglement and non-locality]; Sunko JNSM(16)-a1609 ["shapes" for strongly correlated fermions]; > s.a. crystals [electron states]; open systems; supersymmetry.
@ In a gravitational field: Anastopoulos PRD(96); Toroš et al a1701 [coupling of internal and external degrees of freedom, decoherence effect].
> Other systems: see Emergent Systems; entangled systems; Fermions; macroscopic quantum systems; networks; nuclear physics.

Approaches, Techniques
* Approaches: The first approximation is the mean-field theory, which is 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.
@ 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-proc, a1012-proc [derivation of the Hartree equation and Gross-Pitaevskii equation]; Ben Arous et al a1111 [fluctuations and central limit theorem]; Requist a1401 [reduced many-body dynamics, induced gauge structures]; Benedikter et al a1502-ln [rev]; Engl et al PTRS(16)-a1511 [semiclassical approach to many-body quantum propagation]; Foti et al PRA(16)-a1609 [many spin-1/2 particles as environment for a quantum mechanical oscillator].
@ Quantum information approach: Eisert & Plenio ed-NJP(10); Augusiak et al LNP(12)-a1003.
@ Related topics: Prosen JPA(98) [invariants of motion], PRL(98) [integrability to ergodicity]; Ostilli & Presilla JPA(04)cm [Montecarlo dynamics]; Fedorova & Zeitlin SPIE(05)qp, SPIE(05)qp [patterns formation]; Gori-Giorgi et al PRL(09) [density-functional theory for strongly-interacting electrons]; Carmeli et al PRA(15)-a1411 [local distinguishability]; Nam & Napiórkowski a1611 [norm approximation and Bogoliubov theory]; > s.a. matter; quantum chaos; stochastic processes; wigner functions.
> Reated topics: see green functions; topology in physics.


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