Correlations

General Notion, and Classical Physics > s.a. molecular physics [branched polymers].
* Correlation functions: Given a stochastic process described by variables x_i, the correlation function between two variables x_i and x_j is C(x_i, x_j):= x_i x_j – x_i x_j, 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.

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