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 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
different way 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];
Hollowood a1906 [from Born's rule].

@ __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];
Bolaños EJP(18)-a1904 [phase space measurements].

@ __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].

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