| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We considered the macroscopic observables in quantum spin systems. As quantum systems are given by non-commutative algebras, the physical observables do not commute with each others. However, macroscopic observables can be approximated by commuting observables.One of the key ingredient of the proof ot this theorem is the quantum Shannon McMillan theorem. We gave a simple new proof of this theorem. Furthermore,we extended this theorem to general AF C^*-systems. We also carried out the classification of gapped Hamiltonians(which are a kind of macroscopic observables.)
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