Quotient-Comprehension Chains

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic, but also in probabilistic and classical logic. This relation is presented by a long series of examples, some of them easy, and some also highly non-trivial (esp. for von Neumann algebras). We have not yet identified a unifying theory. Nevertheless, the paper contributes towards such a theory by introducing the new quotient-and-comprehension perspective on measurement instruments, and by describing the examples on which such a theory should be built.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Critical phenomena of a hybrid phase transition in cluster merging dynamics

Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the theory of HPT, it is still incomplete, particularly when the transition is induced by cluster merging dynamics. Here, we aim to develop a theoretical framework of the HPT induced by such dynamics. We find that two correlation-length exponents are necessary for characterizing the giant cluster and finite clusters, respectively. Finite-size scaling method for the HPT is also introduced. The conventional formula of the fractal dimension in terms of the critical exponents is not valid. Neither the giant nor finite clusters are fractals but they have fractal boundaries.Comment: 8 pages, 6 figures, 1 tabl

Color Reflection Invariance and Monopole Condensation in QCD

We review the quantum instability of the Savvidy-Nielsen-Olesen (SNO) vacuum of the one-loop effective action of SU(2) QCD, and point out a critical defect in the calculation of the functional determinant of the gluon loop in the SNO effective action. We prove that the gauge invariance, in particular the color reflection invariance, exclude the unstable tachyonic modes from the gluon loop integral. This guarantees the stability of the magnetic condensation in QCD.Comment: 28 pages, 3 figures, JHEP styl

J/psi c\bar{c} production in e+e- and hadronic interactions

Predictions of the nonperturbative Quark Gluon Strings model based on the 1/N-expansion in QCD and string picture of interactions for production of states containing heavy quarks are considered. Relations between fragmentation functions for different states are used to predict the fragmentation function of c-quark to J/psi-mesons. The resulting cross section for J/psi-production in e+e- annihilation is in a good agreement with recent Belle result. It is argued that associated production of c\bar{c} states with open charm should give a substantial contribution to production of these states in hadronic interactions at very high energies.Comment: 7 pages, 2 figure