Relationship
Between Quantum and Classical Mechanics| Relationship
Between Quantum and Classical Mechanics |
In General > s.a. 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)RL
[interplay]; Landsman qp/05-in;
Arndt & Zeilinger pw(05)mar.
@ General references: Woo AJP(86);
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;
Bracken qp/02 [classical
mechanics as deformation of quantum mechanics]; 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 qp/06-in
[classicality]; Khrennikov qp/06 [mathematical];
Nikolic a0707-in;
Spekkens PRL(08)-a0711 [negativity
and contextuality].
@ 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].
@ In Bohm / pilot wave: Shifren et al PLA(00)
[effective potential]; Allori et al
qp/01;
Allori & Zanghì 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.
@ Systems at the boundary: Aerts & Durt FP(94)
[intermediate systems]; Alicki PRA(02)qp/01 [and
fullerenes]; Baseia et al PLA(98)
[obtaining non-classical states]; Frasca qp/06-in
[and thermodynamic limit]; Doubochinski & Tennenbaum a0711-in
[amplitude quantization, or Macroscopic Quantum Effect, as bridge]; Margolus
a0805.
@ Macroscopic systems: Leggett PTPS(80),
Prosperi IJTP(94)
[and measurement]; Finkelstein qp/98 [in
many-worlds and pilot-wave]; Carati & Galgani
FP(01);
Helland qp/05;
Lanz et al JPA(07)qp [and
foundations]; Khrennikov a0705 [quantumlike
description]; Gomatam a0708;
Schützhold a0712-in
[back-reaction]; news nat(07)nov
[quantum behavior]; Zeh a0804 [Feynman, and gravitational fields]; > s.a. experiments, logic.
@ Dequantization: Isidro JPA(02)ht/01;
Abrikosov et al AP(05)qp/04 [geometric].
@ 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 [origin
of quantum mechanics].
Systems: Coupled Classical and Quantum
* Issue: Is a system with coupled classical and quantum degrees of
freedom consistent?
@ General references: Blanchard & Jadczyk PLA(93)
[model]; Anderson qp/95-in
[backreaction of quantum variables on quasiclassical ones]; Salcedo PRA(96);
Halliwell PRD(98)qp/97 [from
decoherent histories]; Prezhdo & Kisil
PRA(97)qp/96;
Antoniou et al MPLA(99)
[Hamiltonian]; Caro & Salcedo PRA(99)
[impediments]; Dias
JPA(01)qp/99 ["half
quantization"]; Diósi qp/99-in;
Peres & Terno
PRA(01)qp/00;
Kowalski et al PLA(02);
Sahoo JPA(04)qp/03 [observable
algebras]; Terno FP(06)qp/04 [inconsistency],
reply
Sudarshan qp/04;
Kisil EPL(05)qp [2
copies of Heisenberg group]; Hall & Reginatto PRA(05)qp
[classical and quantum ensembles]; Grigorescu qp/06 [quantum
particle + classical environment, variational principle]; Zhang & Wu PRL(06)
[Lorentz-like geometric force]; Zhan et al a0803 [approaches];
Hall a0804 [consistent
formulation].
@ Examples: Semenov et al JPB(06)qp/05 [oscillator
+ thermal bath]; Metaxas PRD(07)ht/06 [two
scalar fields, path integral approach]; Aguilar & Berglund a0805 [two-level
system + classical noise].
@ Ground state and coherent state: McDermott & Redmount qp/04 [2
oscillators].
@ Intervention, measurement: Diósi & Halliwell PRL(98)qp/97;
Peres PRA(00), PRA(00); > s.a. types of measurements [continuous].
States: Quantum vs Classical Effects > s.a. complex
structure; Explanation; fluctuation; phase
transition; quantumm 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 qp/06/PRA;
Everitt a0712 [SQUID ring].
@ 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 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.
@ Quantum vs classical states: Loris & Sasaki PLA(04)
[eigenvalues vs normal modes]; Everitt et al NJP(05)
[and entanglement]; Yoder AJP(06)
[probability densities]; Hen & Kalev qp/07 [quantum
states approaching classical distributions]; Groisman et al qp/07 [ito
entanglement]; Alicki & Van Ryn JPA(08),
Brida et al a0804 [test of quantumness]; Kiesel et al a0804 [based
on Glauber-Sudarshan P-function]; > s.a. distances.
@ Wave packet spreading: Ketzmerick et al PRL(97); Killip et al m.SP/01 [bounds on rate].
@ Wave packet revival: Robinett PRP(04).
@ 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; quantum chaos; quantum statistical mechanics.
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
11 jul 2008