$\mathcal{PT}$ Symmetry in Statistical Mechanics and the Sign Problem

Generalized PT\mathcal{PT} symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized PT\mathcal{PT}-symmetric Hamiltonian. There is a corresponding class of PT\mathcal{PT}-symmetric classical statistical mechanics models with non-Hermitian transfer matrices. We discuss a class of Z(N) spin models with explicit PT\mathcal{PT} symmetry and also the ANNNI model, which has a hidden PT\mathcal{PT} symmetry. For both quantum and classical models, the class of models with generalized PT\mathcal{PT} symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with PT\mathcal{PT} symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with PT\mathcal{PT} symmetry breaking of the ground state, and is generically a first-order transition. In the region where PT\mathcal{PT} symmetry is unbroken, the sign problem can always be solved in principle using the equivalence to a Hermitian theory in this region. The ANNNI model provides an example of a model with PT\mathcal{PT} symmetry which can be simulated for all parameter values, including cases where PT\mathcal{PT} symmetry is broken.     

Facile synthesis of isocampholenic acids by the rearrangement of camphor derivatives

A variety of substituted isocampholenic acid derivatives were prepared by rearrangement of the camphor skeleton of a variety of tertiary alcohols derived from ketopinic acid. The reaction was highly reliable and retained the stereochemical information from the camphor scaffold. This rearrangement represents an efficient way to prepare synthetically useful isocampholenic acids. Mechanistic experiments show that a short-lived carbocation is implicated in the reaction.     

Intensities of line features in vibration-rotational bands 2–0 to 6–0 of NO XΠr and experimental evaluation of a radial function for electric dipolar moment

We measured the strengths of individual line-like features, representing unresolved Λ doublets, in vibration-rotational bands 2–0 to 6–0 of ¹⁴N¹⁶O within each substate of electronic ground state X²Π_1/2,3/2 in mid and near infrared regions. Analyses of these data to derive values of matrix elements for vibrational transitions enabled production of a radial function for electric dipolar moment, containing seven parameters, that satisfactorily reproduces the intensities of about 700 such features for vibrational states up to ν = 6.     

High-pt probes of the quark-gluon plasma: STAR/PHENIX results at RHIC

In this talk I review the use of scattered high-pt partons as probes of the quark-gluon plasma formed at RHIC. Recent results from both STAR and PHENIX are used to assess our current understanding of how these partons lose energy as they travel through the plasma and the extent that energy-loss can be used to extract properties of the plasma.     

Further Dunham energy coefficients of diatomic molecules

Expressions are given for the Dunham energy coefficients Y₃₃ and Y₄₂ in terms of the potential energy coefficients a_i, for diatomic molecules. Their use is briefly discussed.