Many-Particle Quantum Systems| 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.
main page
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