Gr\"uneisen parameters for Lieb-Liniger and Yang-Gaudin models

Using the Bethe ansatz solution, we analytically study expansionary, magnetic and interacting Gr\"uneisen parameters (GPs) for one-dimensional (1D) Lieb-Liniger and Yang-Gaudin models. These different GPs elegantly quantify the dependences of characteristic energy scales of these quantum gases on the volume, the magnetic field and the interaction strength, revealing the caloric effects resulted from the variations of these potentials. The obtained GPs further confirm an identity which is incurred by the symmetry of the thermal potential. We also present universal scaling behavior of these GPs in the vicinities of the quantum critical points driven by different potentials. The divergence of the GPs not only provides an experimental identification of non-Fermi liquid nature at quantum criticality but also elegantly determine low temperature phases of the quantum gases. Moreover, the pairing and depairing features in the 1D attractive Fermi gases can be captured by the magnetic and interacting GPs, facilitating experimental observation of quantum phase transitions. Our results open to further study the interaction- and magnetic-field-driven quantum refrigeration and quantum heat engine in quantum gases of ultracold atoms.Comment: 6 figures, 13 page

1-(2-Fluoro­benz­yl)quinolinium bis­(2-sulfanylidene-1,3-dithiole-4,5-dithiol­ato-κ2 S,S′)nickelate(III)

The crystal structure of the title compound, (C16H13FN)[Ni(C3S5)2], consists of NiIII complex anions and 1-(2-fluoro­benz­yl)quinolinium (fbq) cations. In the complex anion, the NiIII cation is chelated by two 2-sulfanylidene-1,3-dithiole-4,5-dithiol­ate (dmit) dianions in a distorted square-planar geometry; the two dmit mean planes are twisted with respect to each other at a dihedral angle of 8.44 (3)°. In the fbq cation, the dihedral angle between the benzene ring and the quinoline ring system is 80.57 (14)°. The centroid–centroid distance of 3.860 (5) Å between benzene rings indicates π–π stacking between adjacent fbq cations. The distance of 3.4958 (18) Å between the S atom and the centroid of the pyridine ring suggests the existence of a lone-pair–aromatic inter­action between the anion and the cation. A short S⋯S contact [3.387 (2) Å] is also observed in the crystal structure