General Notion, and Classical Physics > s.a. molecular
physics [branched polymers].
* Correlation functions:
Given a stochastic process described by variables xi,
the correlation function between two variables xi and xj is C(xi, xj):=
xi xj
–
xi
xj
,
which vanishes if the variables are statistically uncorrelated; In field
theory, the field-field 2-point correlation function is often identified
with the
Green function for the theory; > s.a. N-point
functions.
* Correlation length:
The length scale at which the overall properties of components of a many-body
system begin to differ markedly from those of
the whole; Or, the distance over which fluctuations of microscopic
degrees
of freedom are significantly correlated to each other (usually a few "interatomic
spacings").
@ General references: Rajagopal & Rendell qp/05 [density
matrix formulation]; Torquato cm/06 [realizable,
random media]; Grudka et al a0802 [genuine multipartite classical correlations].
@ Decay of correlations: Lavenda JMP(82);
Xu
et
al CSF(04)
[maps and chaos].
@ Related topics: Lenard CMP(73)
[statistical state determined by correlations]; Nigmatullin TMP(74)
[time correlation functions, calculation]; > s.a. galaxy
distribution; number theory [continued
fractions].
Quantum Correlations > s.a. bell
inequalities; Coherence; experiments
in quantum mechanics; fluctuation;
Hanbury Brown–Twiss Effect.
* And non-locality: Measurements
performed on spatially separated entangled quantum systems show correlations
that are non-local, in the sense
that a Bell
inequality is violated, but cannot be used for super-luminal signalling;
It is also known that one can write down sets of "super-quantum''
correlations that are more non-local than is allowed by quantum mechanics,
yet are still non-signalling.
* Ontological status:
Results by various people have shown that correlations cannot be thought of
as elements of reality.
* Cirel'son (Tsirel'son)
bound:
The absolute value of the combination of quantum correlations appearing in
the
Clauser-Horne-Shimony-Holt (CHSH) inequality is bounded by 2
.
* Clauser-Horne-Shimony-Holt
inequality: A combination of quantum correlations can give values between
the classical bound, 2, and Cirel'son's
bound, 2
.
@ General references: Garg & Mermin PRL(82), FP(84)
[statistical implications]; Lévy-Leblond AJP(86)
[generalized Heisenberg inequality for correlations]; Cabello PRA(99)
[nature]; Laloë AJP(01)
[and paradoxes]; Plotnitsky FP(03)
[Mermin's quantum mechanics as "correlations without correlata"];
Gisin qp/05-in;
Svozil PRA(05)
[stronger than quantum]; Pitowsky PRA(08)-a0802 [geometry].
@ Quantum vs classical: Hepp CMP(74)
[classical limit]; Peres AJP(78)
[and Bell inequalities]; Henderson & Vedral qp/01;
Mermin qp/02;
Beltrametti
& Bugajski IJTP(04);
Cabello PRA(05)qp/04 [and
bounds]; Audenaert & Plenio NJP(06)qp;
Bellomo et al a0806 [non-classically-reproducible].
@ Measures
of quantumness: Usha Devi & Rajagopal a0707;
Pankowski & Synak-Radtke JPA(08);
SaiToh et al PRA(08), a0802-in.
@ Cirel'son bound: Filipp & Svozil PRL(04)qp [generalized];
Bovino et al PRL(04)
[experiment]; Buhrman & Massar PRA(05)
[and causality]; Choudhary et al qp/06 [origin,
for spins], PLA(07) [and causality]; Heydari JPA(06)
[and Grothendieck's constant].
@ Other bounds:
Cabello PRL(04)qp/03 [test];
Navascues et al PRL(07)qp/06.
@ And non-locality: Garuccio & Selleri FP(80)
[Einstein locality]; Griffiths AJP(87);
Greenberger et al in(89), AJP(90);
Wódkiewicz PRA(95)qp;
Mermin FP(99)qp/98;
Jordan PRA(99)
[and EPR, locality, reality]; Tommasini ht/01;
Zbinden et al
PRA(01)
[and moving frames]; Barrett
et al PRA(05)qp/04 [range
of possibilities]; Brassard et al PRL(06)
[stronger correlations and communication]; Gkioulekas a0707-IJTP
[breakdown over large distances]; > s.a. locality.
@ Approaches, measures: Oppenheim et al PRL(02)
[thermodynamic approach]; Kimura et al PRA(07)-a0705 [detecting
correlations].
@ And reality, information: Srikanth qp/01, qp/01 [info
transfer?]; Groisman et al PRA(05)qp/04 [types
of correlations, operational].
@ Reality, ontological status: Mermin AJP(98)qp;
Cabello PRA(99)qp/98;
Seevinck FP(06)qp/05;
Walther et al PRL(06)qp/05.
@ And separability / entanglement: Home et al PLA(91)
[using non-physical probabilities]; Majewski LMP(04); > s.a.
entanglement.
@ Types of correlations or systems: Eckert et al AP(02)
[indistinguishable particles]; Ozawa AP(06)qp/05 [perfect
correlations]; Ivanov & Wallentowitz EPL(06)qp [atoms
in bosonic gas]; Hastings & Koma CMP(06)
[fermions in lattice]; Caban & Rembielinski PRA(06)qp [EPR
correlations for massive Dirac particles]; Massar & Spindel PRD(06)
[accelerated oscillators]; Brunner et al PRL(08)-a0802 [test
of Hilbert space dimension]; > s.a. cosmological
perturbations.
@ In quantum field theory: Valentini PLA(91)
[QED]; Wald GRG(92)
[beyond the horizon]; Redhead FP(95)
[vacuum fluctuations]; Calzetta & Hu
PRD(00)hp/99 [stochastic
dynamics]; Shchukin & Vogel PRL(06)
[of radiation, proposed measurement]; Vogel PRL(08)a0706 [multimode
radiation fields]; > s.a. N-point
functions, quantum field theory in curved spacetime, vacuum.
@ In other systems: Neville PRD(99)gq/98 [quantum
gravity];
> s.a. composite systems, spin
models.
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
3 jul 2008