Classical
Limit of Quantum Theory – Quantum-to-Classical Transition| Classical
Limit of Quantum Theory – Quantum-to-Classical Transition |
In General > s.a. relationship
between
quantum and classical mechanics.
* 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 qp/04/JRLR
[classical mechanics not limit of quantum mechanics]; Castagnino & Gadella FP(06)
[and self-induced decoherence]; Kazandjian AJP(07).
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), qp/98-in.
@ 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 qp/04-PhD
[and decoherence]; > s.a. photons, thermal
radiation.
@ Non-classical effects: Resch et al PRA(01)
[in single-
detection].
@ Macroscopic systems/states: Van Zandt AJP(77)
[and interference]; Bose
et
al PRA(99);
Sewell 02; Björk & Mana qp/03 [criterion];
Biswas qp/03;
Pitowsky PRA(04);
Kofler & Brukner PRL(07)qp/06 [emergence
of macroscopic realism], a0706 [conditions
for quantum violation of macroscopic realism]; > s.a. classical
vs quantum mechanics.
@ 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);
Portolan et al PRA(06)
[emergence of macroscopic realism for photons]; Benet et al PRA(07)qp/06
[chemical
reactions].
> Related topics: see foundations
of quantum mechanics; locality; quantum
fields; quantum
chaos; quantum
measurement and states; matter [stability].
> States and systems:
see Baker's
Map; coherent states; ergodic
systems; quantum systems; scattering; spin
models.
References
@ 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].
@ Quantum-to-classical transition:
Cini & Serva FPL(90)
[intrinsic probabilities to classical statistics]; Habib et al PRL(02)
[and decoherence]; Toscano & Wisniacki qp/06 [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; > s.a. 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.
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11 jul 2008