Relationship
Between Quantum and Classical Mechanics| Relationship
Between Quantum and Classical Mechanics |
In General > s.a. origin
of quantum mechanics; quantum
statistical mechanics [relationship with
classical]; types
of states [semiclassical].
* Non-classical aspects:
Negativity (the necessity of negative values in certain quasiprobability representations
of quantum states such as the Wigner representation) and contextuality (the
impossibility of a hidden-variable model of quantum theory wherein the representation
of measurements does not depend on the context of the measurement (Bell-Kochen-Specker
theorem).
* Issues: The study of
the relationship between classical and quantum regimes of a theory, how the
correspondence principle really works; The main
questions are, Which states of the quantum theory have a classical interpretation?
What predictions does the quantum theory make for the classical
observables on them, and their fluctuations?
* Remark: In an abstract
mathematical sense, quantum mechanics adds a metric on phase space to the symplectic
structure used in classical mechanics.
* States: Quantum states differ from classical ones in their localization,
interference properties and entanglement.
@ Reviews and books: Park 90; Gutzwiller AJP(98)apr-RL
[interplay]; Landsman qp/05-in;
Arndt & Zeilinger pw(05)mar.
@ General references: Woo AJP(86)oct;
Landsberg FP(88);
't Hooft JSP(88);
Hemion IJTP(90);
Sibelius FP(89);
Greenberg et al PRL(95)
[invariant tori and matrix mechanics]; Wilkie & Brumer PRA(97),
PRA(97)
[Liouville dynamics]; Muga et al PLA(98)
[observables]; Halliwell PRL(99)qp, qp/99-in
[decoherent histories]; Floyd IJMPA(00)qp/99
[trajectory representation]; Bergeron JMP(01)qp;
Ghose FP(02)qp/01, & Samal
FP(02)qp/01;
Page qp/02;
Bartlett & Rowe JPA(03)qp/02;
Mittelstaedt IJTP(05)qp/02 [and
quantum logic]; Neumaier qp/03 [axiomatic];
Loris & Sasaki
PLA(04)qp/03 [simple
theorems]; Krüger qp/04 [quantum
mechanics does not imply classical mechanics]; Pankovic et al qp/04 [as
phase transition]; Curtis & Ellis EJP(06)
[perturbations and probabilities]; Dreyer JPCS(07)qp/06
[classicality]; Khrennikov qp/06 [mathematical];
Nikolic AIP(07)-a0707;
Spekkens PRL(08)-a0711 [negativity
and contextuality]; de Gosson a0808 [common
features].
@ Classical mechanics from quantum mechanics: Bracken qp/02 [as
deformation of quantum mechanics]; Isidro et al a0808,
IJMPA(09)-a0808 [Ricci
flow]; Carcassi a0902 [as
many-particle limit]; Hájícek FP(09)
[maximum-entropy packets].
@ Quantum mechanics from classical mechanics: Heslot
PRD(85);
Ghose qp/00;
Blasone et al PRA(05)qp/04,
AP(05)
[path-integral approach for 't Hooft's derivation]; Bracken qp/06-in
[semiquantum mechanics]; Khrennikov TMP(07)
[quantum mechanics as approximation to classical statistical mechanics]; Bender
et al JPA(08)
[quantum-like behavior of systems with complex energy]; Wetterich a0809 [four-state
system].
@ In Bohm / pilot-wave interpretation: Shifren et al PLA(00)
[effective potential]; Allori et al
qp/01;
Allori & Zanghì FP(09)qp/01-in;
Poirier JCP(04)-a0802;
Bowman FP(05);
Trahan & Poirier JCP(06)-a0802, JCP(06)-a0802;
Poirier & Parlant JPC(07)-a0803;
Matzkin & Nurock SHPMP(08)
[mismatch]; Poirier a0803.
@ Quantum theory not from quantization: Isidro qp/01;
Galapon JMP(04)qp/02.
> Related topics:
see classical mechanics [non-quantum systems];
quantum mechanics formalism [ambiguities] and foundations.
States: Quantum vs Classical Effects > s.a. complex
structure; Explanation; fluctuation; phase
transition; quantum effects; types
of states.
* Criterion: One way
to check when a system will start to deviate from its classical behavior is
to look for when the quantum Wigner function deviates from the corresponding
classical phase-space
probability
density.
* Issue: Is environmental
decoherence required to prevent classically chaotic systems (e.g., tumbling
satellites such as Hyperion) from exhibiting non-classical
behavior within a short time span?
@ Chaotic systems: Eckhardt
PRP(88);
Ballentine PRA(01), PRA(02);
Kaplan NJP(02);
Gong & Brumer PRA(03);
Schomerus & Jacquod JPA(05);
Wiebe & Ballentine PRA(05)
[classical Hyperion tumbling and decoherence], comment Schlosshauer FP(08)qp/06,
reply Ballentine FP(08);
Everitt NJP(09)-a0712 [SQUID
ring]; Paul a0901;
Goletz et al a0904 [semiclassical,
long-time quantum transport].
@ Quantum vs classical evolution: Emerson & Ballentine PRA(01)
[interacting spins]; Benet et al JPA(03)
[fluctuations around classical average]; Habib qp/04 [Gaussian
approximation]; Bojowald & Skirzewski RVMP(06)mp/05 [effective
equations of motion and corrections to symplectic structure]; Gosselin et al
EPJB(07)ht/06 [Berry
phase corrections]; Katz et al PRL(07)
[for driven non-linear Duffing resonator]; Gat JPA(07)
[non-linear oscillator]; > s.a. hamilton-jacobi
theory.
@ Quantum vs classical states: Loris & Sasaki PLA(04)
[eigenvalues vs normal modes]; Everitt et al NJP(05)
[and entanglement]; Yoder AJP(06)may
[probability densities]; Hen & Kalev qp/07 [quantum
states approaching classical distributions]; Groisman et al qp/07 [in
terms of entanglement]; Alicki & Van Ryn JPA(08),
Brida et al OE-a0804 [test
of quantumness]; Kiesel et al PRA(08)-a0804 [based
on Glauber-Sudarshan P-function]; Alicki et al JPA(08)
[quantumness witnesses]; > s.a. distances.
@ Wave packet spreading: Ketzmerick et al PRL(97); Killip et al m.SP/01 [bounds on rate].
@ Wave packet revival: Nauenberg et al SA(94)jun;
Robinett PRP(04);
Wang & Heller JPA(09)
[1D]; > s.a. Quantum
Carpet, quantum
systems.
@ Related topics: Senitzky PRL(81)
[statistics]; Jacquod & Amiet JPA(97)
[ergodic
behavior];
Shvedov
AP(02)mp/01 [symmetries],
mp/01 [group
actions]; Roncadelli & Schulman PRL(07)
[density of paths around a semiclassical trajectory]; > s.a. Loschmidt
Echo.
Related Topics > see decoherence; classical limit [including correspondence principle, localization]; Correspondence Principle; Ehrenfest Time; macroscopic systems; quantum chaos; quantum statistical mechanics.
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nov 2009