A new large N phase transition in YM2

Inspired by the interpretation of two-dimensional Yang–Mills theory on a cylinder as a random walk on the gauge group, we point out the existence of a large N transition which is the gauge theory analogue of the cutoff transition in random walks. The transition occurs in the strong coupling region, with the 't Hooft coupling scaling as $\alpha \log N$, at a critical value of α ($\alpha =4$ on the sphere). The two phases below and above the transition are studied in detail. The effective number of degrees of freedom and the free energy are found to be proportional to $N^{2-\frac{\alpha }{2}}$ below the transition and to vanish altogether above it. The expectation value of a Wilson loop is calculated to the leading order and found to coincide in both phases with the strong coupling value.     

On quantum symmetries of compact metric spaces

An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. In this study, we show that an isometric action in this sense has the following additional property: the corresponding action on the algebra of continuous functions on $X$ by the convolution semigroup of probability measures on the quantum group contracts Lipschitz constants. In other words, it is isometric in another sense due to Li, Quaegebeur, and Sabbe, which partially answers a question posed by Goswami. We also introduce other possible notions of isometric quantum actions in terms of the Wasserstein $p$-distances between probability measures on $X$ for $p\ge 1$, which are used extensively in optimal transportation. Indeed, all of these definitions of quantum isometry belong to a hierarchy of implications, where the two described above lie at the extreme ends of the hierarchy. We conjecture that they are all equivalent.     

Diffusion thermopower of the two-dimensional electron gas in GaN single quantum wells

Diffusion thermopower ($S_d$) of the two-dimensional (2D) electron gas in GaN single quantum wells is calculated in the temperature range 1 K–12 K using the Fermi–Dirac distribution function. Scattering of carriers through acoustic phonons via deformation potential and piezoelectric couplings, and through background and remote ionized impurities is included. $S_d$ is found to decrease with temperature and the 2D electron concentration, and is primarily controlled by deformation potential acoustic scattering. The dependence of $S_d$ on the well width and the ionized impurity concentration is found to be quite weak.     

Impact of local coupling on the vulnerability of 2D spatially embedded interdependent networks

Real networks are always interdependent and spatially embedded. Considering the space constraint, dependency links between networks may be established not globally but locally. In this paper, we study how the spatial coupling will impact the robustness of interdependent scale-free networks located in a 2D square plane where dependent nodes are connected within a connecting radius $r_{connect}$. Besides the traditional assortative degree–degree coupling (GD) and random coupling (GR), some novel spatial couplings are also introduced, i.e., spatial assortative degree–degree coupling (SD), spatial random coupling (SR) and nearest neighbor coupling (NN). Simulation results indicate that assortative couplings, GD and SD, can improve the robustness under topological attacks while under localized attacks, NN coupling is the best one. In addition, for SD coupling under topological attacks, we find that the robustness for small $r_{connect}$ decreases with $r_{connect}$ from 0 to the critical value $r_{c1}$, and for larger $r_{connect}$ gradually increases with $r_{connect}$ from $r_{c1}$ to the maximum value ${(r_{connect})}_{max}$. However, opposite results will be obtained under localized attacks. These findings may be helpful to understand and analyze some real interdependent infrastructures.     

Quantum integrable models of interacting bosons and classical r-matrices with spectral parameters

Using the technique of classical $r$-matrices with spectral parameters we construct a general form of quantum Lax operators of interacting boson systems corresponding to an arbitrary simple (or reductive) Lie algebra. We prove quantum integrability of these models in the physically important case of $\mathfrak{g}=gl\left(n\right)$ and “diagonal” in the root basis classical $r$-matrices. We consider in detail two classes of non-skew-symmetric classical $r$-matrices with spectral parameters and obtain the corresponding quantum Lax operators and quantum integrable many-boson hamiltonians that generalize Bose–Hubbard dimer hamiltonians.