Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference

Multiple case-study analysis of quality management practices within UK Six Sigma and non-Six Sigma manufacturing small- and medium-sized enterprises

This paper examines multiple case-study analysis of quality management practices within UK Six Sigma and non-Six Sigma manufacturing small- and medium-sized enterprises

Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes

Fluorescence in situ hybridization (FISH) is a powerful single-cell technique for studying nuclear structure and organization. Here we report two advances in FISH-based imaging. We first describe the in situ visualization of single-copy regions of the genome using two single-molecule super-resolution methodologies. We then introduce a robust and reliable system that harnesses single-nucleotide polymorphisms (SNPs) to visually distinguish the maternal and paternal homologous chromosomes in mammalian and insect systems. Both of these new technologies are enabled by renewable, bioinformatically designed, oligonucleotide-based Oligopaint probes, which we augment with a strategy that uses secondary oligonucleotides (oligos) to produce and enhance fluorescent signals. These advances should substantially expand the capability to query parent-of-origin-specific chromosome positioning and gene expression on a cell-by-cell basis