Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

Pupillary behavior in relation to wavelength and age

Pupil light reflex can be used as a non-invasive ocular predictor of cephalic autonomic nervous system integrity. Spectral sensitivity of the pupil's response to light has, for some time, been an interesting issue. It has generally, however, only been investigated with the use of white light and studies with monochromatic wavelengths are scarce. This study investigates the effects of wavelength and age within three parameters of the pupil light reflex (amplitude of response, latency, and velocity of constriction) in a large sample of younger and older adults (N = 97), in mesopic conditions. Subjects were exposed to a single light stimulus at four different wavelengths: white (5600° K), blue (450 nm), green (510 nm), and red (600 nm). Data was analyzed appropriately, and, when applicable, using the General Linear Model (GLM), Randomized Complete Block Design (RCBD), Student's t-test and/or ANCOVA. Across all subjects, pupillary response to light had the greatest amplitude and shortest latency in white and green light conditions. In regards to age, older subjects (46-78 years) showed an increased latency in white light and decreased velocity of constriction in green light compared to younger subjects (18-45 years old). This study provides data patterns on parameters of wavelength-dependent pupil reflexes to light in adults and it contributes to the large body of pupillometric research. It is hoped that this study will add to the overall evaluation of cephalic autonomic nervous system integrity.