Metric adjusted skew information: Convexity and restricted forms of superadditivity

We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to general metric adjusted skew informations. We finally show that a recently introduced extension to parameter values $1<p\le 2$ of the WYD-information is a special case of (unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou

Bound States and Critical Behavior of the Yukawa Potential

We investigate the bound states of the Yukawa potential $V(r)=-\lambda \exp(-\alpha r)/ r$, using different algorithms: solving the Schr\"odinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $\alpha=\alpha_C$, above which no bound state exists. We study the relation between $\alpha_C$ and $\lambda$ for various angular momentum quantum number $l$, and find in atomic units, $\alpha_{C}(l)= \lambda [A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, with $A_1=1.020(18)$, $B_1=0.443(14)$, $A_2=0.170(17)$, and $B_2=2.490(180)$.Comment: 15 pages, 12 figures, 5 tables. Version to appear in Sciences in China

Spherical geometry and integrable systems

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.Comment: 15 pages, 5 figure

Inequalities for quantum skew information

We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations. Key words and phrases: Quantum covariance, metric adjusted skew information, Robertson-type uncertainty principle, operator monotone function, Wigner-Yanase-Dyson skew information

Monte Carlo Hamiltonian of lattice gauge theory

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.Comment: "Non-Perturbative Quantum Field Theory: Lattice and Beyond", Guangzhou, China 200

Superconductivity and Phase Diagram in (Li0.8_{0.8}Fe0.2_{0.2})OHFeSe1−x_{1-x}Sx_x

A series of (Li$_{0.8}$Fe$_{0.2}$)OHFeSe$_{1-x}$S$_x$ (0 $\leq$ x $\leq$ 1) samples were successfully synthesized via hydrothermal reaction method and the phase diagram is established. Magnetic susceptibility suggests that an antiferromagnetism arising from (Li$_{0.8}$Fe$_{0.2}$)OH layers coexists with superconductivity, and the antiferromagnetic transition temperature nearly remains constant for various S doping levels. In addition, the lattice parameters of the both a and c axes decrease and the superconducting transition temperature T$_c$ is gradually suppressed with the substitution of S for Se, and eventually superconductivity vanishes at $x$ = 0.90. The decrease of T$_c$ could be attributed to the effect of chemical pressure induced by the smaller ionic size of S relative to that of Se, being consistent with the effect of hydrostatic pressure on (Li$_{0.8}$Fe$_{0.2}$)OHFeSe. But the detailed investigation on the relationships between $T_{\rm c}$ and the crystallographic facts suggests a very different dependence of $T_{\rm c}$ on anion height from the Fe2 layer or $Ch$-Fe2-$Ch$ angle from those in FeAs-based superconductors.Comment: 6 pages, 6 figure

Orbital and interlayer Skyrmions crystals in bilayer graphene

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $$ All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of statesComment: 18 pages with 13 figure