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.
@ Books: 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; Fabrocini et al 02; Coleman 16 [intro, r PT(17)]; Shuryak 18 [in a nutshell]; Kuramoto 20 [strong correlations].
@ General references: Dirac PRS(29); Hunziker & Sigal JMP(00); Kuzemsky a1207-conf [quantum protectorate and emergence]; Rougerie a1607-Hab; Aharonov et al PNAS(18)-a1709 [top-down structure].
@ 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]; Eckle 19.
@ 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; Chakraborty et al PRB(19)-a1810 [starting from arbitrary initial conditions]; Heyl EPL(19)-a1811 [phase transitions, survey].
@ 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]; Banks & Lucas PRE(19)-a1810 [on a lattice, emergent entropy production]; > s.a. Area Law.

Types of Systems > s.a. condensed matter and solid-state physics; 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.
@ Fermions: Jiang a1711 [quantum simulation of strongly correlated fermions].
@ 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]; Giuliani a1711-ln [order, disorder and phase transitions, transport coefficients]; Sanchez-Palencia Phys(20) [constructing field theories using quantum simulators]; Ghale & Johnson a2010 [energy]; > 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; Mean-Field Theory; networks; nuclear physics.

Approaches, Techniques > s.a. Bethe Ansatz.
* 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; A simple technique to obtain approximate but reliable ground state energies is envelope theory.
* Information scrambling: The delocalization of information under many-body dynamics; Out-of-time-order correlators have been proposed to probe it.
@ General references: Kugler et al a2101 [multipoint correlation functions and relationship betwen Feynman diagrams and Hamiltonian based approaches].
@ 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: Eisert & Plenio ed-NJP(10); Augusiak et al LNP(12)-a1003; Nahum et al PRX(18) [spreading, hydrodynamic description]; Hummel et al a1812 [reversible spreading near criticality]; Couch et al a1908 [chaotic systems, speed of information spreading].
@ Information scrambling: Sekino & Susskind JHEP(08)-a0808, Susskind a1101 [fast scramblers]; Swingle PRA(16)-a1602 [and out-of-time-order correlation functions]; Schnaack et al a1808 [lattice models, time evolution of tripartite information]; Zhuang et al a1902 [chaos and complexity]; Zanardi & Anand a2012.
@ Numerical simulations: Ostilli & Presilla JPA(04)cm [Monte Carlo dynamics]; Gardas et al PRB(18)-a1805 [hybrid classical-quantum algorithm]; Zhu et al a1905 [GDTWA, new numerical approach]; Hangleiter et al a1906 [Monte Carlo approach, easing the sign problem]; Weimer et al a1907.
@ Related topics: Prosen JPA(98) [invariants of motion], PRL(98) [integrability to ergodicity]; Fedorova & Zeitlin SPIE(05)qp, SPIE(05)qp [pattern 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-in [norm approximation and Bogoliubov theory]; Semay & Cimino a1908 [tests of envelope theory]; García & Vernon a1911 [emergence of patterns]; Semay et al a2004 [envelope theory, different particles]; Rrapaj & Roggero a2005 [RBM neural networks]; LeBlond et al a2012 [universality in the onset of chaos].
> Reated topics: see distances; green functions; matter; quantum chaos; quantum field theory in curved spacetime; quantum groups [hidden symmetries of quantum impurities]; stochastic processes; topology in physics; wigner functions.

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