Classical Limit of Quantum Theory – Quantum-to-Classical Transition

In General > s.a. classical-quantum relationship; Correspondence Principle; macroscopic systems.
* Idea: A limit in which the quantum uncertainties of operators vanish; Usually identified with the /action → 0 limit, but in some situations there are other possibilities [@ Rajeev ht/02-in]; 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.
* Remark: In terms of information, redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects.
* Remark: The quantum to classical transition depends on several parameters, including an action scale , a measure D of the coupling between a system and its environment, and, for chaotic systems, the classical Lyapunov exponent .
* Remark: 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.
@ The h &rarr 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.

Specific Effects, Concepts, and Examples > s.a. fluctuations; operators; phase transition; quantum information.
* Continuous spontaneous localization: In the GRW prescription, obtained with non-linear and stochastic effects.
@ Continuous spontaneous localization: Ghirardi et al PRD(86) [comment Joos PRD(87) + reply PRD(87)], FP(88); Benatti et al NCB(87) [and measurement]; Bell in(89); Ghirardi et al FP(90), PRA(90); Pearle PRA(93), in(97)qp/98.
@ Measurement and decoherence: Mensky PU(98)qp, qp/98-in, 00; Furuta PRA(01) [model]; Bhattacharya et al PRA(03)qp/02; Zurek RMP(03); Ford et al PRA(01)qp/03; Schlosshauer RMP(04)qp/03 [and interpretations]; Ghose et al PRA(05)qp/04; > s.a. decoherence, types of measurement.
@ And correspondence principle: Habib et al PRL(98) [non-linear dynamics].
@ Measures: Fedichkin et al SPIE(03)cm.
@ Non-classical states: Vogel PRL(00) [sho]; Foldi PhD(03)qp/04 [and decoherence]; > s.a. photons, thermal radiation.
@ Non-classical effects: Resch et al PRA(01) [in single- detection].
@ Examples: Brun et al PLA(97) [trajectories]; Brun et al PRL(03)qp/02, PRA(03)qp/02, PRA(03)qp/02 [random walk]; Man'ko et al PLA(05); Benet et al PRA(07)qp/06 [chemical reactions]; Jasiak et al NJP(09) [electrons in thin metal films]; Teta a0905 [straight tracks in a cloud chamber]; news seed(09)jul [Caltech experiment].
> Related topics: see locality; matter [stability]; quantum fields; quantum chaos; quantum states; relativistic quantum theory.
> States and systems: see Baker's Map; coherent states; ergodic systems; quantum systems; scattering; spin models; SQUIDs.

References > s.a. foundations of quantum mechanics; quantum measurement.
@ Books, intros: Maslov & Fedoriuk 81; Lazutkin 93; Brack & Bhaduri 97; Yam SA(97)jun; Landsman 98.
@ 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]; Greenbaum et al PRE(07)-a0705 [trajectories vs phase space distributions].
@ 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) [-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].
@ Quantum-to-classical transition: Cini & Serva FPL(90) [intrinsic probabilities to classical statistics]; Habib et al PRL(02) [and decoherence]; Toscano & Wisniacki PRE(06)qp [in kicked oscillator]; Date CQG(07)gq/06 [constructing the classical theory]; Korbicz & Lewenstein FP(07) [group-theoretic formalism]; Kofler & Brukner PRL(07) [from limited measurement accuracy]; Hartle a0806; Angelo a0809 [from low-resolution measurements]; Wisniacki & Toscano a0810 [scaling laws]; Halliwell a0903-in [via commuting X and P operators]; Everitt et al PRA(09) [for a single field mode]; > s.a. cosmological perturbations; quantum field theory states.
@ Degree of (non-)classicality: Anastopoulos PRD(99)qp/98; Hall PRA(00) [Fisher information]; Costa Dias JMP(02)qp/99; Malbouisson & Baseia qp/02 [field theory]; Avelar et al qp/03; Zurek qp/03 [information and environment]; Korbicz et al PRL(05)qp/04 [harmonic oscillator]; > s.a. distances.

main page – abbreviations – journals – comments – other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 29 oct 2009