Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of multi-component TLL phases in 1D systems of N-component Fermi gases with population imbalance.Comment: 12 pages, 3 figure

Incorporating residual temperature and specific humidity in predicting weather-dependent warm-season electricity consumption

Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Climate warming and increasing variability challenges the electricity supply in warm seasons. A good quantitative representation of the relationship between warm-season electricity consumption and weather condition provides necessary information for long-term electricity planning and short-term electricity management. In this study, an extended version of cooling degree days (ECDD) is proposed for better characterisation of this relationship. The ECDD includes temperature, residual temperature and specific humidity effects. The residual temperature is introduced for the first time to reflect the building thermal inertia effect on electricity consumption. The study is based on the electricity consumption data of four multiple-street city blocks and three office buildings. It is found that the residual temperature effect is about 20% of the current-day temperature effect at the block scale, and increases with a large variation at the building scale. Investigation of this residual temperature effect provides insight to the influence of building designs and structures on electricity consumption. The specific humidity effect appears to be more important at the building scale than at the block scale. A building with high energy performance does not necessarily have low specific humidity dependence. The new ECDD better reflects the weather dependence of electricity consumption than the conventional CDD method

Singularity structure of the pi N scattering amplitude in a meson-exchange model up to energies W < 2.0 GeV

Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in these cases the pole positions and residues obtained by analytic continuation can substantially differ from the results predicted by the speed-plot and regularization methods.Comment: 21 pages, 4 figures, 4 table

Regularity of Kobayashi metric

We review some recent results on existence and regularity of Monge-Amp\`ere exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit at least one such exhaustion of sufficiently high regularity. A main consequence of our results is the fact that the Kobayashi pseudo-metric k on an appropriare open subset of each of the above domains is actually a smooth Finsler metric. The class of domains to which our result apply is very large. It includes for instance all smoothly bounded strongly pseudoconvex complete circular domains and all their sufficiently small deformations.Comment: 14 pages, 8 figures - The previously announced main result had a gap. In this new version the corrected statement is given. To appear on the volume "Geometric Complex Analysis - Proceedings of KSCV 12 Symposium

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

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem

A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence. For $k$ pairs of valence nucleons on $n$ different single-particle levels, it is found that solutions of the Bethe ansatz equations can be obtained from one (k+1)x(k+1) and one (n-1)x(k+1) matrices, which are associated with the extended Heine-Stieltjes and Van Vleck polynomials, respectively. Since the coefficients in these polynomials are free from divergence with variations in contrast to the original Bethe ansatz equations, the approach thus provides with a new efficient and systematic way to solve the problem, which, by extension, can also be used to solve a large class of Gaudin-type quantum many-body problems and to establish a new efficient angular momentum projection method for multi-particle systems.Comment: ReVTeX, 4 pages, no figur

Vertical Structure of Stationary Accretion Disks with a Large-Scale Magnetic Field

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because the hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. Here, we calculate the vertical profiles of the {\it stationary} accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Also, here we require that the radial accretion speed be zero at the disk's surface and we assume that the ratio of the turbulent viscosity to the turbulent magnetic diffusivity is of order unity. Thus at the disk's surface there are three boundary conditions. As a result, for a fixed dimensionless viscosity $\alpha$-value, we find that there is a definite relation between the ratio ${\cal R}$ of the accretion power going into magnetic disk winds to the viscous power dissipation and the midplane plasma-$\beta$, which is the ratio of the plasma to magnetic pressure in the disk. For a specific disk model with ${\cal R}$ of order unity we find that the critical value required for a stationary solution is $\beta_c \approx 2.4r/(\alpha h)$, where $h$ the disk's half thickness. For weaker magnetic fields, $\beta > \beta_c$, we argue that the poloidal field will advect outward while for $\beta< \beta_c$ it will advect inward. Alternatively, if the disk wind is negligible (${\cal R} \ll 1$), there are stationary solutions with $\beta \gg \beta_c$.Comment: 5 pages, 3 figure