Diketonylpyridinium cations as a support of new ionic liquid crystals and ion-conductive materials: analysis of counter-ion effects

Ionic liquid crystals (ILCs) allow the combination of the high ionic conductivity of ionic liquids (ILs) with the supramolecular organization of liquid crystals (LCs). ILCs salts were obtained by the assembly of long-chained diketonylpyridinium cations of the type [HOO^(R(n)pyH)] + and BF_(4)^(-) , ReO_(4)^(-), NO_(3)^(-), CF_(3)SO_(3)^(-), CuCl_(4)^(2-) counter-ions. We have studied the thermal behavior of five series of compounds by differential scanning calorimetry (DSC) and hot stage polarized light optical microscopy (POM). All materials show thermotropic mesomorphism as well as crystalline polymorphism. X-ray diffraction of the [HOO^(R(12)pyH)][ReO_(4)] crystal reveals a layered structure with alternating polar and apolar sublayers. The mesophases also exhibit a lamellar arrangement detected by variable temperature powder X-ray diffraction. The CuCl_(4)^(2-) salts exhibit the best LC properties followed by the ReO_(4)^(-) ones due to low melting temperature and wide range of existence. The conductivity was probed for the mesophases in one species each from the ReO_(4)^(-) , and CuCl_(4)^(2-) families, and for the solid phase in one of the non-mesomorphic Cl^(-) salts. The highest ionic conductivity was found for the smectic mesophase of the ReO_(4)^(-) containing salt, whereas the solid phases of all salts were dominated by electronic contributions. The ionic conductivity may be favored by the mesophase lamellar structure.

CB-norm estimates for maps between noncommutative Lp-spaces and quantum channel theory.

In the first part of this work, we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative Lp-spaces. Then, we use these estimates to study the classical capacity with restricted assisted entanglement of the quantum erasure channel and the quantum depolarizing channel. In particular, we exactly compute the capacity of the first one and we show that certain nonmultiplicative results hold for the second one.

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).