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.

@ __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].

@ __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].

@ __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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