How Many Nuclear Spins Are Coupled With Each Other In Condensed Matter At Room Temperature? Shangwu Ding, Cheng Lung Chen 丁尚武，陳正隆 Department of Chemistry, National Sun Yat-Sen University 國立中山大學化學系 大連， Quantum Mechanically

The System N spin-1/2 nuclei in a liquid- or solid- state sample Room Temperature

Or One System, Two Formulae “Full Quantum” Semi-Classical Which Is Better? Are They Equivalent?

“ Mainstream ” Opinions Both are correct and they are equivalent Full quantum description is more consistent but classical description easier in calculation Never proved Consistent but incorrect?

Consequences of “ Full Quantum ” Picture NMR theory has to be reformulated High temperature approximation invalid Coherences may be created among uncorrelated spins

Example Two distant spins (maybe a billion light years apart) Double quantum coherences! “Counter-intuition” OR quantum superstition?

Resolution Two distant spins (maybe a billion light years apart) can retain their correlation IFF they have never interacted with other objects. Nuclear spins in liquids or solids, however, are in very noisy environments.

Correlation Evaluation(1) Uncorrelated spins should not be considered as in the same quantum system!

Correlation Evaluation(2) Two spins are uncorrelated if their interaction does not contribute to observable evolution

Correlation Evaluation(3) Two spins are uncorrelated if their dipolar interaction is immersed in the intrinsic linewidth. Intrinsic linewidth

Correlation Evaluation(4) Intrinsic proton linewidith >0.01 Hz  Maximum correlation length of two protons: <1000 spins are possibly quantum mechanically correlated

Quantum Measurement (1)

Quantum Measurement (2)

Quantum Measurement (3)

Conclusions At Around Room Temperature 1. “ Full Quantum Treatment ” Not Only Unnecessary But Also Incorrect 2. Spin Clusters Are Small, Even in Solids (<100)

Acknowledgments Discussion: Guo Wei WEI (MSU) Chaohui YE(WIPM) Lian-Pin HWANG (NTU) Funding: NSC, MOE 謝謝波譜會組織委員會和大化所給予這個機會