Characteristics of Quantum-Classical Correspondence for Two Interacting Spins

The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics well beyond the short-time regime of narrow states. We find that quantum-classical differences initially grow exponentially with a characteristic exponent consistently larger than the largest Lyapunov exponent. We provide numerical evidence that the time of the break between the quantum and classical predictions scales as log(${\cal J}/ \hbar$), where ${\cal J}$ is a characteristic system action. However, this log break-time rule applies only while the quantum-classical deviations are smaller than order hbar. We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.Comment: New introduction, accepted in Phys Rev A (May 2001 issue), 12 latex figures, 3 ps figure

The rs11755527 polymorphism in the BACH2 gene and type 1 diabetes mellitus: case control study in a Brazilian population

Objective: Type 1 diabetes mellitus (T1DM) is an autoimmune disorder caused by a complex interaction between environmental and genetic risk factors. BTB domain and CNC homolog 2 (BACH2) gene encodes a transcription factor that acts on the differentiation and formation of B and T lymphocytes. BACH2 is also involved in the suppression of apoptosis and inflammation in pancreatic beta-cells, indicating a role for it in the development of T1DM. Therefore, the aim of this study was to evaluate the association of the BACH2 rs11755527 single nucleotide polymorphism (SNP) with T1DM. Subjects and methods: This case-control study comprised 475 patients with T1DM and 598 nondiabetic individuals. The BACH2 rs11755527 (C/G) SNP was genotyped using real-time PCR with TaqMan MGB probes. Results: Genotype distributions of rs11755527 SNP were in accordance with frequencies predicted by the Hardy–Weinberg equilibrium in case and control groups and were similar between groups (P = 0.729). The minor allele frequency was 43.6% in cases and 42.5% in controls (P = 0.604). Moreover, the G allele frequency did not differ between groups when considering different inheritance models and adjusting for age, gender, body mass index, and HLA DR/DQ genotypes of high-risk for T1DM. Although, well-known high-risk T1DM HLA DR/DQ genotypes were associated with T1DM in our population [OR= 7.42 (95% CI 3.34 – 17.0)], this association was not influenced by the rs11755527 SNP. Conclusion: The BACH2 rs11755527 SNP seems not to be associated with T1DM in a Brazilian population