|Classical Limit of Quantum Theory and Quantum-to-Classical Transition|
Classical Limit > s.a. classical-quantum relationship;
Correspondence Principle; macroscopic systems.
* Idea: A limit in which the quantum uncertainties of operators vanish; Usually identified with the \(\hbar\)/action → 0 limit, but in some situations there are other possibilities [@ Rajeev ht/02-proc]; Possible settings for the limit are the following,
- As a limit for the theory, in the sense of quantum mechanics as a deformation of classical mechanics;
- As a sector for the theory containing states with classical behavior, like coherent or squeezed states;
- As an approximation to the behavior of some states, such as the WKB approximation or limited measurement accuracy;
- As a dynamical process that makes certain states acquire a more classical behavior, typically decoherence by interaction with the environment.
* Remark: In terms of information, redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects.
@ Books, intros: Maslov & Fedoriuk 81; Lazutkin 93; Brack & Bhaduri 97; Yam SA(97)jun; Landsman 98.
@ The h → 0 limit: Man'ko & Man'ko JRLR(04)qp/04 [classical mechanics not limit of quantum mechanics]; Castagnino & Gadella FP(06) [and self-induced decoherence]; Kazandjian AJP(07)aug; Klein AJP(12)nov-a1201; Driver & Tong a1511.
Quantum-to-Classical Transition > s.a. cosmological
perturbations; entanglement death;
quantum field theory states; wave-function collapse.
* Idea: The quantum-to-classical transition depends on several parameters, including an action scale \(\hbar\), a measure D of the coupling between a system and its environment, and, for chaotic systems, the Lyapunov exponent λ (the limit is achieved in a qualitatively differently for classically chaotic systems).
* Interaction with the environment: The environment may not only induce classical properties like superselection rules, pointer states or even classical behavior of the quantum system, but also allow the transition from a statistical description of infinite quantum systems to the quantum mechanics of systems with a finite number of degrees of freedom.
@ General references: Cini & Serva FPL(90) [intrinsic probabilities to classical statistics]; Habib et al PRL(02) [and decoherence]; Date CQG(07)gq/06 [constructing the classical theory]; Hartle FP(11)-a0806; Wisniacki & Toscano PRE(09)-a0810 [scaling laws]; Requardt a1009; Kofler & Brukner a1009 [fundamental limits to quantum description]; Oliveira et al a1101 [information accessibility]; Paavola et al PRA(11)-a1103 [dependence of dynamical features on the measure for non-classicality used]; Roemer a1112-conf; Hájíček JPCS(12)-a1201; Durt & Debierre IJMPB(13)-a1206 [entanglement-free regime and classical particles]; Recchia & Teta JMP(14)-a1305 [model for the emergence of a semiclassical state from interaction with the environment]; Kak NQ-a1309 [condition on probabilities]; Schlosshauer a1404-in [and decoherence, pedagogical]; Raftery et al PRX(14) [dissipation-induced]; Kak a1410 [computability and insufficiency of unitary evolution]; Briggs & Feagin a1506 [without decoherence]; Rosaler a1511 [interpretation-neutral account]; Kastner et al ed-17; Coecke et al EPTCS(18)-a1701 [two roads]; Gozzi a1806 [without the zero-Planck-constant limit].
@ Measurement limitations: Kofler & Brukner PRL(07); Angelo a0809; Jeong et al PRL(14).
@ In pilot-wave quantum theory: Dürr & Römer JFA(10)-a1003 [classical limit for Hagedorn wave packets]; Toroš et al JPA(16)-a1603 [collapse and classicality].
@ Specific mechanisms, formalisms: Korbicz & Lewenstein FP(07) [group-theoretic formalism]; Halliwell JPCS(09)-a0903 [via commuting X and P operators]; Ellis & Rothman IJTP(10)-a0912 [Crystallizing Block Universe]; Lochan et al GRG(15)-a1404 [spontaneous dynamical classicalization]; Hollowood a1803 [macroscopic systems coupled to their environments]; Bhatt et al a1808 [GRW spontaneous localization].
@ For specific systems: Fink et al PRL(03)-a1003 [for cavity QED]; Toscano & Wisniacki PRE(06)qp [in kicked oscillator]; Everitt et al PRA(09) [single field mode]; Budiyono FP(10) [single particle]; Pokharel et al a1604 [driven double-well oscillator, dynamical complexity]; > s.a. Caldeira-Leggett Model.
Related pages: see relationship classical-quantum theory; semiclassical effects and degree of quantumness.
Semiclassical Theory and Approximation > s.a. foundations
of quantum mechanics; quantum measurement.
@ Semiclassical theory: Heller & Tomsovic PT(93)jul; Baranger et al JPA(01)qp [and coherent states]; Pol'shin qp/02-wd [as phase space contraction]; de Gosson JPA(02) [and symplectic camel]; Castagnino PhyA(04)qp/05 [classical-statistical limit]; dos Santos & de Aguiar BJP(05)qp/04 [and coherent state path integral ambiguity]; Bracken & Wood PRA(06)qp/05 [semiclassical vs semiquantum]; Struyve a1507 [based on Bohmian mechanics]; Vachaspati & Zahariade a1806 [classical-quantum correspondence and backreaction, and toy model]; Baytaş et al a1811 [as a canonical dynamical system that extends the classical phase space].
@ Semiclassical approximation: Peres PS(86) [for Wigner function]; De Alwis PLB(93)ht [2D dilaton gravity]; Werner qp/95; Huang PRD(96) [conditions for consistency]; de Gosson JPA(98) [with half-densities]; Yoneda et al NCB(01) [continuous transition]; Davis & Ghandour PLA(03) [and action-angle variables]; Kowalski et al PLA(03) [and wavelet complexity]; Ballentine PRA(04) [\(\hbar\)-dependence of averages]; Vergini JPA(04) [chaotic eigenfunctions]; Stuckey et al qp/06/FP [relational blockworld]; Sen & Sengupta FPL(06) [unconventional view]; Paul a0901 [long-time results]; Yang a1703 [loss of unitarity].
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 3 jan 2019